e1e-mail<EMAIL_ADDRESS>
11institutetext: Department of Physics, University of Surrey, Guildford, GU2
7XH, Surrey, UK 22institutetext: Manipal Academy of Higher Education, Manipal,
Karnataka 576104, India 33institutetext: Nuclear Data Section, International
Atomic Energy Agency, A-1400 Vienna, Austria 44institutetext: Instituto de
Fisica Corpuscular (IFIC), CSIC-Universidad de Valencia, 46071 Valencia, Spain
55institutetext: Institute of Nuclear Research (ATOMKI), Debrecen, Hungary
66institutetext: Laboratoire Subatech, University of Nantes, CNRS/IN2P3,
Institut Mines Telecom Atlantique, 44307 Nantes, France 77institutetext:
Physics Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
88institutetext: Institute of Innovative Research, Tokyo Institute of
Technology, Tokyo 152-8550, Japan 99institutetext: Physics Faculty, University
of Warsaw, PL-02-093, Warsaw, Poland 1010institutetext: Variable Energy
Cyclotron Centre, Kolkata 700064, India 1111institutetext: Physics Division,
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
1212institutetext: Nuclear Science and Technology Department, Building 817,
Brookhaven National Laboratory, Upton, NY 19973-5000, USA

#  Improving Fission-product Decay Data for Reactor Applications: Part I -
Decay Heat

A.L. Nichols1,2  P. Dimitrioue1,4  A. Algora3,5  M. Fallot6  L. Giot6
F.G. Kondev7  T. Yoshida8  M. Karny9  G. Mukherjee10  B.C. Rasco11  K.P.
Rykaczewski11  A.A. Sonzogni12  J.L. Tain3

(Received: date / Revised version: date)

###### Abstract

Effort has been expended to assess the relative merits of undertaking further
decay-data measurements of the main fission-product contributors to the decay
heat of neutron-irradiated fissile fuel and related actinides by means of
Total Absorption Gamma-ray Spectroscopy (TAGS/TAS) and Discrete Gamma-ray
Spectroscopy (DGS). This review has been carried out following similar work
performed under the auspices of OECD/WPEC-Subgroup 25 (2005-2007) and the
International Atomic Energy Agency (2010, 2014), and various highly relevant
TAGS measurements completed as a consequence of such assessments. We present
our recommendations for new decay-data evaluations, along with possible
requirements for total absorption and discrete high-resolution gamma-ray
spectroscopy studies that cover approximately 120 fission products and various
isomeric states.

††journal: Eur. Phys. J. C

##  1 Introduction

Decay heat is generally defined as the energy released from the direct and
indirect fission reaction products, neglecting the contribution of
antineutrinos that do not deposit any energy in the reactor core. The main
contributors to reactor decay heat are the fission products that accumulate
during reactor operation, followed by the actinides generated via neutron
capture along with their heavy-element decay products and various activation
products Tobias1980 ; Nichols2002 . Such decay heat is extremely significant
at short and intermediate cooling times after a planned or accidental shutdown
of a nuclear reactor, and is most immediately dependent on the resulting
inventory of fission products, actinides and their decay products as a
function of the time after shutdown. Accurate estimates of the resulting decay
heat are required in safety assessments of all types of reactor and fuel-
handling plant, the storage of spent fuel, the transport of fuel-storage
flasks, and the intermediate-term management of any resulting radioactive
waste. Most of the above phenomena are also associated with the related
emission of antineutrinos that provide an important means of monitoring
reactor operations in a benign manner, as well as defining the constraining
fundamental physics quantities that determine their oscillation properties.

Both the actinide and fission-product inventories of neutron-irradiated fuel
are calculated for known operational conditions and all subsequent cooling
periods. These inventory data are used in conjunction with radionuclidic half-
lives, and all relevant heavy-particle, light-particle and electromagnetic
radiation characteristics to determine the total energy release rates for
heavy particles, light particles and electromagnetic radiations. Heavy
particles are primarily identified with alpha particles, light particles are
defined as $\beta$-, $\beta$+, and internal-conversion and Auger electrons,
and electromagnetic radiation consists of $\gamma$, X-rays, annihilation
radiation and internal bremsstrahlung. Along with neutron-induced cross
sections and fission yields, the radioactive decay data constitute key input
to the summation calculations used to determine the release of decay heat
during reactor operation and as a function of time after the termination of
fuel irradiation within the reactor core Tobias1980 ; Nichols2002 ; Tobias1989
. These calculations require the inclusion of mean $\alpha$, $\beta$ and
$\gamma$ energies derived normally from the decay schemes of a significant
number of radionuclides dominated by fission products at early and
intermediate cooling times, and the results need to be compared with
experimental decay-heat benchmarks. However, the determination of $\beta$-
emission probabilities has long been problematic in decay-scheme studies.
Although $\gamma$-ray emission probabilities and internal conversion
coefficients can be used to derive $\beta$- feeding to daughter nuclear
levels, experiments based on Ge detectors suffer from low efficiency for the
detection and quantification of high-energy $\gamma$ rays above $\sim$ 1.5 MeV
that undermines such an approach. The determination of direct $\beta$- decay
to the ground state of the daughter nucleus can also pose serious problems.
Hardy $et~{}al.$ proposed that $\sim$ 20$\%$ of the true $\gamma$-ray
intensity above 1.7 MeV for a fictional radionuclide (Pandemonium) may remain
undetected Hardy1977 , impacting significantly on the use of $\gamma$-ray
singles data to calculate $\beta$- transitions by means of gamma population-
depopulation balances of the proposed nuclear levels. This problem also exists
in experiments based on coincident data even in the case of relatively high-
efficiency Ge detector arrays Hu2000 ; Algora2003 . Furthermore, defining the
nature of each individual $\beta$- transition can result in differing energy
distributions to create distinct total $\beta$- energy spectra. Such unknown
beta shape factors may impact on the average $\beta$- energy of many of the
radionuclides under consideration. Total Absorption Gamma-ray Spectroscopy
(TAGS) measurements can overcome these difficulties in order to provide the
necessary mean beta and gamma decay energies for more comprehensive and
satisfactory decay-heat calculations Greenwood1996 ; Greenwood1997 ;
Algora2010 .

While fission-product and actinide decay are the most significant contributors
to decay heat, caution is required with respect to the first $\sim$ 200 s
after reactor shutdown as other effects play immediate initial roles, such as
a brief plant-driven period of continued thermal impact along with declining
fission multiplication driven by delayed-neutron precursors Hill2011 . Beyond
200 s after reactor shutdown, $\beta$\- and $\gamma$-decay processes of the
fission products play a dominant role leading up to approximately 106 s (12
days). While both 239U and 239Np make noteworthy contributions up to one hour
and $<$ 106 s cooling times, respectively, other actinides such as 238Pu,
241Am and 242,244Cm take their place in this respect at much longer times.
Following on from assessment studies discussed and undertaken in 2005-2007,
2009/2010 and late 2014 Yoshida2007 ; Nichols2009 ; Gupta2010 ; Dimitriou2015
and various highly relevant TAGS measurements completed as a consequence of
such assessments, further efforts have now been made to re-assess the
requirements for additional measurements that effectively embrace singles
$\gamma$-ray spectroscopy, $\gamma$-$\gamma$ coincidence and TAGS. One
extended aim would be for TAGS to quantify the degree of Pandemonium in
particular fission products through the existence of previously unknown and
ill-defined nuclear levels populated in the $\beta$- decay process. Such
studies would also underline the requirements for more extensive singles
$\gamma$-ray spectroscopy and $\gamma$-$\gamma$ coincidence techniques with
appropriate types of detector by which to recognise and quantify the higher-
energy gamma emissions in order to improve decay-heat assessments, as well as
dosimetry and shielding calculations.

Several exploratory studies have been carried out recently in order to improve
specific $\beta$- decay data as an aid in undertaking more accurate and
precise antineutrino spectral calculations Sonzogni2015 ; Sonzogni2016 ;
Sonzogni2017 ; Sonzogni2018 ; Hayes2018 ; Estienne2019 . Recommendations have
been made to perform TAGS measurements that differ in priority to current
decay-heat requirements due to the fact that such antineutrino calculations
are more relevant and sensitive to the nature of the shorter-lived fission
products. While work is underway to extend this effort towards the
determination of the antineutrino spectral requirements for $\gamma$-ray
spectroscopy, $\gamma$-$\gamma$ coincidence and TAGS measurements, these
particular assessments are beyond the scope of the current publication and
will be the subject of a future article.

##  2 Total Absorption Gamma-Ray Spectroscopy (TAGS/TAS)

Nuclear structure and decay data are important facets and spectral aspects of
nuclear physics. These properties and associated parameters aid extensively in
the characterisation of the nucleus, and provide definitive descriptive
features of all nuclei for direct adoption in a wide range of nuclear
applications that include the safe control and normal operation of power
reactor systems and the detection of any clandestine procedures, as well as
extending our basic understanding of the more exotic features of nuclear
physics. The emission probabilities of beta-decay are important in this
respect from the point of view of quantifying the mean beta (most frequently
the main contributor to the light-particle component of the decay process) and
mean gamma decay heat (most frequently the main contributor to the
electromagnetic component), along with the antineutrino spectral signatures
that can potentially assist greatly in the detection of illegal procedures
undertaken to produce weapons-grade materials.

A major problem in both decay-heat and antineutrino studies is determining
both the $\beta$- and $\gamma$ feeding with good accuracy and confidence,
which has in the recent past relied most frequently on direct experimental
studies by means of various forms and arrays of Ge detector. While these
detector systems are entirely suitable for multiple coincidence studies to
define and resolve nuclear levels and decay schemes, they have long been known
to possess limited $\gamma$-ray detection efficiency that falls dramatically
with increase in $\gamma$ energy particularly above 1.5 MeV, as noted in
Section 1. Under these circumstances, an entirely different method of spectral
study and analysis has been considered and developed, based on the attempted
total absorption of all $\gamma$-ray emissions to determine full $\beta$-
feeding to all individual nuclear levels Duke1970 ; Johansen1973 ; Rubio2005 ;
Rubio2017 ; Algora2018 . Although complete 100$\%$ efficiency is not fully
feasible, scintillator $\gamma$ detector systems with geometries as close to
4$\pi$ as possible possess the capabilities to determine $\beta$- feeding up
to an excitation energy of the daughter nucleus that could match the parent
Q-value. While under development in the early 1970s, TAGS/TAS involved the
adoption of two large cylindrical NaI detectors, before moving in the 1990s to
one large NaI-well counter to host the radioactive source of interest along
with Si detectors Greenwood1992 ; Rubio2005 ; Rubio2017 . Other larger NaI(Tl)
crystals have subsequently been used with a high degree of success in
conjunction with various other smaller NaI, Ge-planar and thin Si $\Delta$E
positron detectors to determine specific forms of coincidence, for example,
GSI TAS (GSI) Karny1997  and Lucrecia TAS (ISOLDE) Rubio2005 . These studies
have been extended to significant arrays of Ge detectors in a compact
geometry, such as Clustercube and Gammasphere to study a number of more
complex beta spectra, providing opportunities to compare the results obtained
by means of different techniques Hu2000 ; Algora2003 .

Recent measurements related to power reactor operations and antineutrino
physics have been performed at the IGISOL facility in Jyvÿskylä, Finland.
These studies have involved the use of the ion-guide technique in which many
of the refractory fission products of interest have been successfully
generated, and high isotopic purity has been achieved by means of the JYFL
Penning trap operated as a high-resolution mass separator Algora2018 .
Accurate and valid analyses of the spectral data have also been an important
feature of this work, based on a sound starting knowledge of the level scheme
up to a reasonable excitation energy. As outlined in Refs. Rubio2017 ;
Algora2021 ; Rasco2015b , these spectral analyses take into account non-
linearity of the light output in the NaI(Tl) scintillator and pile-up in the
electronic signals.

Exploiting the experience gained, various spectrometers have been commissioned
to better absorb and quantify all gamma emissions. These studies have extended
our understanding of the nucleus with respect to $\beta$ decay and the weak
interaction, and so aided in the development of related modelling calculations
over the full chart of the nuclides. Improvements have also been made in the
handling of the radioactive species to obtain clean beams for spectral studies
by means of various forms of ancillary detector located close to the main
counting area of the multi-array of segmented 4$\pi$ NaI(Tl) scintillators. A
key aspect of this work is ”segmentation” whereby additional information on
the multiplicity of the gamma cascades can be used to test assumptions made
during the analyses. Rocinante is an example of such a detector system, which
is composed of twelve optically-isolated BaF2 crystals assembled in a
cylindrical geometry and operated in conjunction with an approximately 30$\%$
efficient Si detector or plastic detectors, together with the ion-guide source
of the IGISOL mass separator and JYFLTRAP Penning trap at the University of
Jyvÿskylä Algora2014 ; Valencia2014 ; Valencia2017 . A similar segmented
arrangement of sixteen modular NaI(Tl) scintillators in a combined cuboid form
has been developed as the DTAS (Decay Total Absorption Spectrometer) for
DESPEC (DEcay SPECtroscopy) at FAIR (Facility of Antiproton and Ion Research,
near Darmstadt, Germany) Tain2015 ; Guadilla2016 ; Guadilla2017a . These
detector systems have been used to study various beta-decaying radionuclides
of relevance to decay-heat assessments and the prediction of antineutrino
spectra that arise from reactor operations, along with more basic nuclear
structure research in facilities such as RIKEN and GSI(FAIR).

A segmented detector array has been designed, developed, and assembled as the
Modular Total Absorption Spectrometer (MTAS) at the Holifield Radioactive Ion
Facility of the Oak Ridge National Laboratory. MTAS consists of nineteen
NaI(Tl) hexagonal modules arranged as a honeycomb-like structure. Radioactive
sources are delivered by means of a moving-tape system to the central module
which also contains two Si-strip detectors for $\beta$- coincidence studies.
Initial measurements of seventy fission products from 238U fast fission have
focused on TAGS studies of 86,89Br, 89,90Kr, 88,89,90,90m,92Rb, 96Y, 98Nb,
137I, 137,139Xe, 142Cs, 142Ba and 142La Fijalkowska2014b ; Wolinska2014 ;
Karny2016 ; Rasco2016 ; Rasco2017a ; Shuai2022 ; Rasco2022 . Measurements have
also been performed at Argonne National Laboratory with isotopically pure
beams, see for example Laminack2022 . The SuN spectrometer is another example
of a segmented TAS detector that was originally designed for reaction studies
Simon2013 , and has also been used for decay studies in fragmentation
facilities Spyrou2014 ; Spyrou2016 ; Gombas2021 ; Dombos2021 . A new segmented
central module for MTAS has been provided by the University of Warsaw
Karny2019 , and the array assembled at the Facility for Rare Isotope Beams
(FRIB), Michigan State University, East Lansing, USA. This improved detector
system has been located at the FRIB Decay Station initiator (FDSi), and is
operational Rykaczewski2022 .

##  3 Analytical procedures and assessments

Extensive inventory and decay-heat calculations have been performed with the
UKAEA FISPACT-II code by Fleming and Sublet Fleming2015 ; Fleming2015a ;
Fleming2015b . All relevant nuclear data addressed in these studies have
involved the main fission-product contributors from thermal and fast fission
identified with all the fissile radionuclides to be found in various types of
irradiated fuel (Table 1).

Table 1: Irradiated fuel inventories and decay-heat calculations Fleming2015 ; Fleming2015a ; Fleming2015b .  thermal-neutron pulse |  235U, 238Pu, 239Pu, 240Pu,
---|---
(0.0253 eV) |  241Pu, 242Pu, 241Am, 242mAm,
|  243Am, 243Cm, 245Cm
fast-neutron pulse |  232Th, 233U, 238U, 237Np
(400 or 500 keV) |
cooling times (s) | 10, 100, 1000, 5011 and 10000

Selection criteria for the current assessment of Pandemonium include the
following: identification and detailed inspection of the nuclear structure of
fission products with $\geq 2\%$ contribution to the total decay heat, along
with both their light-particle and electromagnetic components; comparison of
the Q-values recommended in AME2020 AME2020  with the highest known energies
of daughter nuclear levels that possess either unknown or commensurate spin-
parity with the ground state of the parent fission-product; and assessment of
possible Pandemonium within the decay schemes as currently defined. Under such
circumstances, such judgements are inevitably subjective in nature and are
best described as indicative, with emphasis placed on the possible existence
of previously undetected high-energy $\gamma$-ray emissions. The primary aim
has been to identify radionuclides that may possess the potential for
Pandemonium so as to formulate recommendations concerning the need for further
quantification of individual fission-product decay schemes by means of Total
Absorption Gamma-ray Spectroscopy (TAGS/TAS) and/or Discrete Gamma-ray
Spectroscopy (DGS). Furthermore, improved quantification of the related
nuclear structure and antineutrino emissions will also be inevitable
consequences of such dedicated studies. These assessments may either support
TAGS measurements for the first time, or reveal the need for further
additional TAGS along with improved $\gamma$-ray spectroscopy and
$\gamma$-$\gamma$ coincidence studies that will be more fundamentally
necessary if TAGS reveals the existence of significant Pandemonium. Such
judgements have been made on the basis of what we know about the nuclear
structure of each of almost 120 fission products chosen for consideration from
the FISPACT-II decay-heat calculations for the thermal fission of 235U,
238,239,240,241,242Pu, 241Am, 243,245Cm, and fast fission of 232Th, 233,238U
and 237Np.

A notable feature of the various sets of fission products is that they exhibit
a fair degree of commonality. What we observe is that the more dominant decay-
heat fission products for 232Th, 233,238U and 237Np fast fission and 241,242Pu
and 245Cm thermal fission are those that do not appear in such a manner in the
equivalent exercise for 235U, 238,239,240Pu, 241Am and 243Cm thermal fission
as a consequence of differences in the individual fission yields and the
subsequent impact of their decay chains. The potential for Pandemonium within
the known $\beta$- decay of a particular fission product are based on the
documented nuclear properties, Q-value of the $\beta$- decay, and the possible
existence of higher-energy nuclear levels that could be populated by $\beta$-
emissions and depopulated by as yet unknown high-energy $\gamma$ rays, both of
which would impact on their contribution to their decay-heat components. A
further issue in such assessments is the perceived correctness and accuracy of
the absolute intensity of $\beta$- decay feeding directly to the ground state
of the daughter, which could possibly impact the complete decay scheme greatly
through the normalization of the beta intensities (i.e., all $\beta$-
emissions, $\gamma$ rays, antineutrino spectra, and additional features of the
decay process).

TAGS/TAS measurements can improve our understanding of incomplete and
therefore erroneous decay schemes as formulated mainly by $\gamma$-ray
spectroscopy identified with Ge-based detectors. Comments concerning TAGS/TAS
and other $\gamma$-decay studies are given in Tables 5 and 6 of A. A total of
almost 120 fission products have been assessed as significant contributors to
the decay heat of various fissile materials used to determine and benchmark
the residual post-irradiation decay heat for the fast fission of 232Th,
233,238U and 237Np, and the thermal fission of 235U, 238,239,240,241,242Pu,
241Am and 243,245Cm. A similar statement can also be made when considering
predictive spectral calculations of the resulting antineutrinos emitted by
operational reactor systems. References assigned Nuclear Science References
(NSR) keynumbers that appear in Tables 5 and 6 are fully listed in Table 7 of
A. Highly-specific recommendations have been made as to whether additional
discrete $\gamma$-ray spectroscopy and/or TAGS/TAS measurements are merited,
as comprehensively summarized in Table LABEL:tab:5.

##  4 Relevant TAGS/TAS measurements

Various nuclear decay data derived from TAGS/TAS have been compared with the
equivalent data to be found in recommended decay data libraries, and more
specifically the Evaluated Nuclear Structure Data File (ENSDF) ENSDF , the
Evaluated Nuclear Data File/B-VII and VIII Chadwick2006 ; Chadwick2011 ;
Brown2018 , the Joint Evaluated Fission and Fusion Files 3.x Kellett2009 ;
Kellett2016 ; Plompen2020 , and the Japanese Evaluated Nuclear Data Files
JENDL-Decay Data File-2011, 2015 and JENDL-5 Katakura2011 ; Katakura2015 ;
Iwamoto2021 . ENSDF is primarily defined as an evaluation of experimental
nuclear structure and decay data which constitutes a comprehensive database
maintained on a mass-chain basis over an approximate eight- to ten-year re-
evaluation cycle. The decay-data files within ENDF/B-VIII are incremental
updates of the re-evaluated contents of ENSDF with various additions and a
series of modest modifications as defined at the time of their assembly and
issue for public access. An improved and updated re-release occurred in early
2018 as ENDF/B-VIII.0 Brown2018 . Similarly, the JEFF-3.3 decay data sub-
library is the latest version of an assembly of decay data Plompen2020  from
ENSDF, the Decay Data Evaluation Project (DDEP) ddep  and evaluations
performed for the United Kingdom UKPADD-6.7 and UKHEDD-2.5 libraries
Kellett2009 ; Perry2014 . The recently released JENDL-5 decay data sub-library
includes evaluated data from ENSDF combined with theoretical calculations
using the Skyrme-Hartree-Fock theory combined with the Quasi-particle Random-
Phase Approximation (Skyrme HF+QRPA) approach of Minato Minato2016 .

An impressive systematic study of TAGS spectra for almost 50 important fission
products was undertaken in the 1990s by Greenwood and co-workers at the Idaho
National Engineering Laboratory, USA Greenwood1996 ; Greenwood1997 ;
Greenwood1992 . A tape system was used to collect and transport selected
fission-isotope mass fractions from the spontaneous fission of a 252Cf-based
ISOL system (Isotope Separation On-Line) for spectral analysis by means of a
large single-ingot NaI(Tl) scintillation detector with an axial well that
contained a Si detector to provide the means of obtaining $\beta$-$\gamma$
coincidence data along with $\beta$- and $\gamma$ singles spectra. Their
pioneering work involved TAGS measurements ranging from rubidium (starting
with 89Rb) to yttrium (ending with 95Y) and from caesium (starting with 138Cs)
to samarium/europium (ending with 158Eu) that has been substantially
reconfirmed in more recent years, as outlined below. A major gap in their work
arose as a consequence of the inability at that time to volatilise effectively
the fission products of elemental refractory zirconium, niobium, molybdenum,
technetium, ruthenium and rhodium in order to achieve optimum/suitable source
preparation. Some of the radionuclides identified with these particular
elements are expected to be important contributors to resulting reactor
inventories, decay heat and antineutrino emissions of commercial irradiated
nuclear fuel.

During the course of earlier assessments of the nuclear data needs for decay-
heat and antineutrino spectral calculations as encouraged by the OECD-NEA and
IAEA from 2005 to 2014 Yoshida2007 ; Nichols2009 ; Dimitriou2015  and beyond,
portions of the research programmes of a number of TAGS facilities were re-
aligned towards the study of potential Pandemonium within the ill-defined
decay schemes of specific chosen fission products (see for example, Refs.
Algora2010 ; Jordan2013 ; Fijalkowska2017 ). These more recent and on-going
experimental studies are described below, along with earlier notable work that
remains highly relevant to our existing objectives within both nuclear
applications and basic nuclear physics research. First motivated by Yoshida et
al. Yoshida1999  and evaluation work undertaken as part of an OECD-NEA/IAEA
initiative Yoshida2007 , a series of dedicated experimental TAGS/TAS studies
were undertaken at the University of Jyväskylä, Finland, by the TAGS team from
the Instituto de Física Corpuscular, CSIC, Universidad de Valencia, Spain, and
co-workers. Work began to assess and confirm known decay-heat benchmarks, and
was rapidly extended to consider observed difficulties in reproducing and
defining the antineutrino spectra emitted from commercial reactor systems.
Experiments were performed at the IGISOL (Ion-Guide Isotope Separator On-Line)
facility, University of Jyväskylä, in which fission products produced by
proton bombardment of 238U recoiled out of the target and were transported by
helium gas flow to the early stages of a separator and Penning trap with a
mass-resolving power of 105 (JYFLTRAP) located adjacent to a Total Absorption
Gamma-ray Spectrometer. Adoption of the Penning trap as an isotope separator
resulted in high-purity sources that are of great benefit for this type of
study. The first measurements were performed with a TAGS spectrometer that
consisted of two cylindrical NaI(Tl) crystals, of which the larger possessed a
longitudinal hole along the axis in which a silicon detector could be placed
for coincidence studies at the defined measuring point and source location. A
large amount of $\gamma$ strength was observed for 105Mo and 104,105,106,107Tc
that had not previously been detected in earlier high-resolution $\gamma$-ray
measurements Algora2010 . Results are listed in Table 2 for a number of
related studies that focused strongly on 102,104,105Tc Algora2010 ; Jordan2013
; Algora2009 ; Algora2011 ; Algora2011b ; Algora2014b . An important
conclusion from this work was that five of the seven radionuclides studied
were found to exhibit the Pandemonium effect, with the need to confirm,
explore and improve quantification of their inadequate decay parameters in
greater detail by means of Discrete Gamma-ray Spectroscopy (DGS).

Table 2: Ground-state to ground-state $\beta$- feedings, half-lives and average $\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ energies for 86,87,88Br, 91,94,95Rb, 100,100m,101,102,102mNb, 105Mo, 102,104,105,106,107Tc, and 137I, determined from IGISOL-TAGS measurements published in the last decade Algora2010 ; Valencia2017 ; Guadilla2016 ; Jordan2013 ; Rice2017 ; Guadilla2019a ; Guadilla2019c , and compared with equivalent data determined from ENSDF database of 2022 ENSDF , ENDF/B-VIII.0 data library of 2018 (ENDF/B8) Brown2018 , JEFF-3.3 data library of 2020 Plompen2020 , and JENDL-5 data library of 2021 Iwamoto2021 . Where no values are provided for the TAGS ground-state to ground-state $\beta$- feedings, the ENSDF values available at the time were used in the analysis leading to a fair reproduction of the measured data. Nuclide |  $T_{1/2}$ (s) |  g.s. $\rightarrow$ g.s. ($\%$) |  $\overline{E}_{\beta}$ (keV) |  $\overline{E}_{\gamma}$ (keV)
---|---|---|---|---
|  | TAGS | ENSDF | TAGS | ENSDF | ENDF/B8 | JEFF-3.3 | JENDL-5 | TAGS | ENSDF | ENDF/B8 | JEFF-3.3 | JENDL-5
86Br | 55.1(4) | 20.2(50) | 15(8) | 1687(60) | 1900(300) | 1944(350) | 1943(345) | 1687(30) | 3782(116) | 3360(110) | 3300(160) | 3300 | 3782(108)
87Br | 55.65(13) | 10.1(9) | 12.0(19) | 1170(+32-19) | 1660(80) | 1660(80) | 1170(26) | 1170(8) | 3938(+40-67) | 3100(40) | 3350(40) | 3938(54) | 3938(35)
88Br | 16.34(8) | 4.7(9) |  $<$11 | 1706(+32-38) | 2240(240) | 1702(50) | 1706(35) | 1706(30) | 4609(+78-67) | 2920(50) | 3134(60) | 4609(70) | 4609(46)
91Rb | 58.2(3) |  9.2(10)a | 2(5) | 1389(44) | 1580(190) | 1370(40) | 1368(137) | 1389(13) | 2669(95) | 2270(40) | 2708(76) | 2706(271) | 2669(44)
92Rb | 4.48(3) | 87.5(25) | 95.2(7) |  | 3640(30) | 2870(700) | 3640(30) | 3498(1) |  | 170(9) | 2150(190) | 170 | 461(8)
94Rb | 2.702(5) |  $\sim$0 | 0 | 2450(+32-30) | 2020(90) | 2020(90) | 2450(30) | 2450(5) | 4063(+62-66) | 1750(50) | 1895(49) | 4063(64) | 4063(50)
95Rb | 0.3777(8) | 0.03(+10-2) |  $\leq$0.1 | 2573(+18-8) | 2320(110) | 1380(70) | 2824 | 2573(8) | 3110(+17-38) | 2050(40) | 2162(40) | 2629 | 3110(40)
96Y | 5.34(5) | 96.6(+3-21) | 95.5(5) | 3193(+2-19) | 3181(20) | 3184(17) | 3181(20) | 2656(1) | 67(+12-2) | 80(44) | 80(44) | 80 | 1206(4)
96mY | 9.6(2) |  |  | 1721(+5-9) | 1600(160) | 1600(160) | 1821 | 1600(170) | 4669(+21-12) | 4308 | 4308 | 4479 | 4308
100Nb | 1.4(2) |  40(6)b | 50(7) | 2414(154) | 2510(210) | 2540(213) | 2540(213) | 2414(7) | 959(318) | 710(40) | 708(40) | 708 | 959(36)
100mNb | 2.99(11) |  |  | 1706(13) | 1910(180) | 2000(200) | 2040 | 1706(13) | 2763(27) | 1720(50) | 2210(70) | 2056 | 2210(69)
101Nb | 7.1(3) |  |  | 1797(133) | 1800(300) | 1830(300) | 1830(300) | 1797(8) | 450(280) | 244(22) | 244(22) | 244(22) | 445(21)
102Nb | 4.3(4) |  |  | 1948(27) | 2280(170) | 2300(170) | 2400 | 1948(6) | 2764(57) | 2090(100) | 2090(100) | 2400 | 2764(97)
102mNb | 1.3(2) |  44.3(28)b |  | 2829(82) | – | 2420 | 2276(169) | 2829(82) | 1023(170) | – | 2420 | 2094 | 1023(170)
105Mo | 35.6(16) |  |  | 1049(44) | 1900(300) | 1049(44) | 1049(44) | 1049(3) | 2407(93) | 548(24) | 2407(93) | 2407(93) | 2407(24)
102Tc | 5.28(15) |  |  | 1935(11) | 1945(16) | 1945(16) | 1945(16) | 1935(1) | 106(23) | 81(4) | 81(5) | 81(5) | 106(5)
104Tc | 1098(18) |  |  | 931(10) | 1590(70) | 931(10) | 931(10) | 931(4) | 3229(24) | 1890(30) | 3229(24) | 3229(24) | 3229(31)
105Tc | 456(6) |  |  | 764(81) | 670(70) | 764(81) | 764(81) | 764(6) | 1825(174) | 86.6(23) | 1825(174) | 1825(174) | 1825(19)
106Tc | 35.6(6) |  |  | 1457(30) | 1900(70) | 1457(30) | 1457(30) | 1457(4) | 3132(70) | 2190(50) | 3132(70) | 3132(70) | 3132(51)
107Tc | 21.2(2) |  |  | 1263(212) | 1890(240) | 1263(212) | 1263(212) | 1263(7) | 1822(450) | 511(11) | 1822(450) | 1822(450) | 1822(11)
137I | 24.5(2) |  45.8(13)b | 45.2(5) | 1934(+35-56) | 22.8(7) | 1920(30) | 1861 | 1934(1) | 1220(+121-74) | 4.0(3) | 1135(20) | 1212 | 1220
140Cs | 65.7(3) |  36.0(15)b | 35.9(17) | 1903(+32-69) | 1950(70) | 1893(55) | 1890(50) | 1910(2) | 1792(+149-68) | 1765(21) | 1796(21) | 1819(18) | 1864(25)
aSeparation of the two $\beta$- emissions that populate the ground and first
excited states is difficult to achieve.
bDetermined by means of a revised Greenwood procedure Guadilla2020  (general
principals and original procedure described in Greenwood et al. Greenwood1992b
).

As shown in Refs. Algora2010 ; Jordan2013 , the inclusion of TAGS average-
energy values for 105Mo and 104,105,106,107Tc (particularly for 104,105Tc) in
decay-heat summation calculations for a thermal-fission pulse in 239Pu results
in significant improvement and better agreement with compiled experimental
decay-heat benchmark data over cooling times from 300 to 3000 s, supporting
the importance of identifying potential Pandemonium as highlighted by Yoshida
et al. Yoshida1999 . Equivalent comparisons with a thermal-fission pulse in
235U exhibit much less impact on the summation calculations, that can be
attributed to the reasonably large differences in their cumulative fission
yields (these particular cumulative fission yields in 239Pu are a factor of
2.5 higher than for 235U). Another point of note is that the $\beta$- decay of
102Tc involves a significant fraction of direct feeding to the daughter ground
state, which is deemed to be difficult to describe by means of gross $\beta$-
theory. Efforts were also made to describe the Gamow-Teller $\beta$- decay
properties of both 102,104Tc Jordan2013  employing the complex excited VAMPIR
code and the gross theory of $\beta$- decay.

TAGS/TAS measurements by the Valencia-led team at the University of Jyväskylä
have also included the possibility of identifying Pandemonium within the decay
schemes of beta-decaying isomers such as 100Nb, 100Nbm and 102Nb, 102Nbm
Guadilla2019a ; Guadilla2019b . A natural uranium target was irradiated at the
IGISOL facility with 25-MeV protons to induce fission prior to high-resolution
mass separation within the JYFLTRAP double-Penning trap in order to isolate
zirconium parents and niobium daughter nuclides for delivery to and study by
means of the DTAS detector array (operated as eighteen modular NaI(Tl)
scintillators in cuboid form). Several techniques were used to separate the
different contributions of the metastable and ground-state decays, and their
results were consistently compared. Both 100Nb and 102Nb exhibited evidence
for metastable states of similar half-lives to those of their ground states,
whereby 100Zr (0+) and 102Zr (0+) populated the low-spin niobium levels of
100Nbg and 102Nbm, respectively. Absolute $\gamma$-ray emission probabilities
were determined on the basis of their depopulation of 100Mo and 102Mo nuclear
levels that had been populated by the $\beta$- decays of 100,100mNb and
102,102mNb, respectively, and these values were in good agreement with known
equivalent data when the branching-ratio matrix employed in the analysis was
modified. Significant $\beta$- intensity was found at high excitation energies
for which there were no previously known data, and the resulting average
$\beta$ and $\gamma$ energies obtained in this work impacted significantly on
calculations of both decay heat and antineutrino spectra (listed in Table 2).
Thus, the $\gamma$ component of decay heat for 235U and 239Pu exhibited an
increase of $\sim 3\%$ at 10 s cooling time and a decrease of between 1$\%$
and 3$\%$ at shorter cooling times; reactor antineutrino spectral calculations
revealed evidence of the significant impact of these measurements in the
energy region of 5 to 7 MeV by up to 2$\%$ for 235U and 6$\%$ for 239Pu over
what has previously been known as an area of excessive shape distortion
Guadilla2019b .

The Valencia-Nantes-Surrey-Jyväskylä team has explored $\beta$- intensities to
daughter states above the neutron separation energy, which has involved
extensive determination of the $\gamma$-ray emissions from the $\beta$- decay
of 87,88Br and 94Rb by means of TAGS Valencia2014 ; Valencia2017 ; Tain2015b ;
Agramunt2016 ; Tain2017 . Rocinante is a twelve-fold segmented BaF2 detector
system that has been operated in conjunction with the IGISOL mass separator
and JYFLTRAP Penning trap to achieve a total $\gamma$ detection efficiency of
greater than 80$\%$ for $\gamma$ cascades, while also possessing the advantage
of reduced neutron sensitivity when compared with equivalent NaI(Tl)
scintillator systems. Detailed contamination analyses of descendant $\beta$-
and $\beta$-n decay have been conducted, along with the derivation of overall
uncertainty estimates. As shown in Table 2, all three radionuclides exhibit a
significant Pandemonium effect, and none more so than 94Rb with an overall
average $\gamma$ energy that is a factor of 2.14 larger than the calculated
value from the ENDF/B-VIII.0 database. However, the thermal fission yield of
94Rb is relatively small in 235U/239Pu nuclear fuel, which mitigates against
such a radionuclide playing a significant role in the generation of
substantial decay heat. A further comparison shows that the integrated
intensity of $\gamma$ decay above the neutron separation energy ($S_{n}$) in
the case of 87Br is larger than $P_{n}$, and is eight times more intense than
known previously from high-resolution $\gamma$ spectroscopy Valencia2017 .
TAGS data from all three of these fission products impact in various modest
degrees on decay-heat summation calculations at short cooling times,
particularly the photon component of 94Rb and 88Br to a lesser degree, while
the calculated antineutrino spectrum exhibits a reduction of intensity by a
maximum of 6$\%$ at 7.2 MeV for the thermal fission of 235U and 239Pu
Valencia2017 ; Tain2015b . As an important follow-up to the above, the new
DTAS detector assembly of eighteen modular NaI(Tl) crystals has been used to
study 93,95Rb, 103Mo, 103Tc and 137,138I, with the provision to install large
ancillary detectors for improved energy resolution and enhanced detection
efficiency Guadilla2016 ; Tain2017 ; Guadilla2017b . As mentioned earlier,
TAGS has been successfully used to study $\gamma$-ray emissions above $S_{n}$
in $\beta$-delayed neutron emitters, and in doing so has provided accurate
information to improve (n,$\gamma$) cross-section assessments far from
$\beta$- stability. One surprising observation from this work has been the
high ratio of the integrated $\gamma$ intensity for emissions from the states
above the neutron separation energy ($S_{n}$) to the total intensity for many
of the radionuclides studied. Such behaviour points firmly towards the need to
improve our understanding of photon-strength functions and neutron
transmission coefficients Tain2017 ; Tain2017b . These studies are complicated
by contamination from $\beta$-n decay branches, and therefore efforts were
made to evaluate the systematic uncertainties with greater accuracy and
confidence. As described above, the decay measurements of 87,88Br and 94Rb
were part of an integral experimental effort to study these beta delayed-
neutron emitters by means of a number of complementary experimental
techniques.

Some of the experimental work was directed towards measurements of the
$\beta$-delayed-neutron emission probabilities for particular fission products
of importance to decay-heat and antineutrino studies. As developed initially
in Spain, the BELEN-20 4$\pi$-neutron counter consists of twenty 3He
proportional counters arranged as two rings of eight and twelve tubes within a
large polyethylene neutron moderator around a central hole that contained
either a 0.5-mm thick Si detector or 3-mm thick plastic scintillator to count
$\beta$- emissions from sources of high-purity fission products implanted into
a movable tape after passage through the IGISOL mass separator and JYFLTRAP at
the University of Jyväskylä. Another noteworthy feature of this detector
system is the incorporation of self-triggered digital data acquisition with
reduced deadtime Agramunt2016 . Early studies were directed towards the
delayed-neutron decay of 88Br, 94,95Rb and 137I Agramunt2016 , and have been
further extended to $P_{n}$ measurements of 135Sb, 138,139,140I and 137,138Te
decay following the development of the BELEN-48 array of forty-eight 3He
proportional counters located in three rings of six, twelve and thirty tubes
around the central hole Agramunt2017 . Measured Pn data from these experiments
are compared in Table 3 with recommended values evaluated during the course of
an IAEA-coordinated research project Liang . All compiled and evaluated Pn
data contained within Ref. Liang  are available in the form of an IAEA
Reference Database of beta-delayed-neutron data (http://www-nds.iaea.org/beta-
delayed-neutron/database.html).

Table 3: Experimentally determined branching fractions of $\beta$-n decay modes Agramunt2016 ; Agramunt2017 , compared with recommended values from the evaluation of Liang et al. Liang . Nuclide | $P_{n}$ | Ref. Liang
---|---|---
135Sb | 0.245(10) | 0.200(29)
137Te | 0.0260(30) | 0.0291(16)
138Te | 0.0480(23) | 0.0482(23)
137I | 0.0776(14) | 0.0763(14)
138I | 0.0498(18) | 0.0530(21)
139I | 0.0927(33) | 0.0974(33)
140I | 0.0760(28) | 0.0788(43)

TAGS/TAS measurements performed by the Valencia-Jyväskylä-Nantes team have
expanded over the years in order to improve benchmark calculations of the
resulting antineutrino spectra by undertaking individual experimental
measurements of 86Br and 91Rb Rice2017 ; Algora2017 , 92Rb Zakari2014 ;
Fallot2017 ; Zakari2015 , 100,100m,102,102mNb and 140Cs Guadilla2017a  (see
Table 2), 100Tc Guadilla2017  and 142Cs Fallot2017 . The $\beta$- decay of
91Rb is highly relevant in decay-heat studies because the decay of this
radionuclide has been adopted as a calibration point in the average $\gamma$
energy measurements performed by Rudstam et al. Rudstam1990B , assuming that
91Rb does not suffer from the Pandemonium effect. The work of Rice et al.
Rice2017  shows that this is not the case, and that the average energies
quoted by Rudstam et al. should be re-normalised by an adjustment factor of
1.14.

Rocinante with twelve segmented BaF2 crystals and DTAS with eighteen modular
NaI(Tl) scintillators in cuboid form have also been employed as $\gamma$
detector assemblies to improve our knowledge of the decay of particular
fission-product nuclides in terms of the quantification of their total
energies, average $\beta$ and $\gamma$ energies, and contributions to summed
antineutrino spectra of operational interest. Both 95Rb and 137I are
$\beta$--delayed neutron emitters, and were prepared on the IGISOL facility
coupled to the JYFLTRAP for isobaric separation prior to $\gamma$-ray spectral
analysis by means of DTAS and HPGe, along with a plastic scintillator for the
detection of $\beta$- emissions for gated spectra Guadilla2019c . A
significant amount of $\beta$- intensity was observed to populate states above
the neutron separation energy, which underwent subsequent $\gamma$-ray de-
excitation with comparable emission probabilities to those of the delayed
neutrons. While the TAGS data in Table 2 for 95Rb show the average $\gamma$
energy to be significantly underestimated and the average $\beta$ energy to be
more modestly underestimated in ENDF/B calculations, the low cumulative
fission yield of this particular fission product in 235U and 239Pu thermal
fission will result in relatively low impact, and therefore has not been
considered in Tables 5 and 6. Average energy data in ENDF/B calculations for
137I are in reasonable agreement with the average $\beta$ and $\gamma$
energies determined by TAGS (Table 2) such that the database already contains
and reflects the $\beta$- population of the higher-energy nuclear levels of
137Xe and delayed-neutron decay to 136Xe. Both the extracted ground-state
feeding and average $\gamma$ energy validate the previous MTAS 137I values,
representing another example of two distinct sets of TAGS/TAS measurements
obtaining consistently similar results. The $\beta$- decay of 140Cs to 140Ba
has been studied by means of the DTAS spectrometer at IGISOL IV as part of a
measurement campaign undertaken in 2014. Since the half-lives of 140Cs and
daughter 140Ba are 63.7 s and 12.75 days, respectively, the only contamination
in the measurements was summing pile-up. Results from a preliminary analysis
have been presented by Guadilla et al. Guadilla2017a . The feeding
distribution is in good agreement with previous results obtained by Greenwood
et al. employing a different experimental set-up and analysis technique
Greenwood1997 . These high-resolution data exhibit evidence of the Pandemonium
effect. The $\beta$- decay of 100Tc was also studied Guadilla2017  with the
aim of assessing if the decay process suffers from Pandemonium, and as a
consequence would impact on related double-beta decay studies. Furthermore,
100Tc $\beta$- decay is of relevance for reactor applications as the product
of a second-order process, which is based on fission followed by neutron-
capture activation of the fission product before $\beta$- decay occurs. This
phenomenon has been explored as a possible explanation for the distortion of
the antineutrino spectrum from reactors in the 4-6 MeV energy range Huber2016
. Continued TAGS/TAS measurements and more extensive data analyses are also
being jointly planned or are underway that include the mass region around
100Sn by RIKEN-Valencia Algora2018b ; Algora2016a  and the mass region around
208Pb at GSI(FAIR)-Valencia Tain2020 .

TAGS/TAS experimental studies commenced in early 2012 at the On-Line Test
Facility (OLTF) of the Tandem accelerator of the Holifield Radioactive Ion
Beam Facility (HRIBF) at the Oak Ridge National Laboratory (ORNL). The Modular
Total Absorption Spectrometer (MTAS) has been designed, constructed and
assembled, and work undertaken to measure and characterise the decay products
from 40-MeV energy 50 nA proton-beam irradiations of a 238UCx target. An array
of nineteen hexagonal-shaped NaI(Tl) detectors weighing 1000 kg are aligned in
a honey-combed geometry covering 99$\%$ of the solid angle around the activity
to be measured. Each NaI(Tl) crystal is 53 cm in length and just over 20 cm
maximum diameter. Surrounded by bespoke shielding, including over 5000 kg of
lead and borated high-density polyethylene neutron shielding, the $\gamma$
background has been reduced by a factor of 1000. Nuclei of interest are
deposited on to a tape transport system monitored by HPGe detectors for
isotope identification. The tape transports these nuclei to auxiliary $\beta$-
detector triggers, two 1-mm thick segmented Si crystals (each divided into
seven 8.5-mm wide strips) surrounding the transport tape over 95% of the solid
angle, and resulting in greater than 90% $\beta$--trigger efficiency for most
fission nuclides. The activity triggers the silicon detectors for
$\beta$-$\gamma$ coincidence studies between these detectors and the MTAS
NaI(Tl) array. Simulated response functions and spectral modelling combined
with a series of preliminary experimental studies have assisted greatly in the
development of the spectrometer towards nuclear applications and more basic
nuclear physics research Rasco2015b ; Fijalkowska2014b ; Wolinska2014 ;
Karny2016 ; Rasco2016 ; Fijalkowska2017 ; Fijalkowska2014a .

Seventy-seven fission products were studied at various times over the course
of 2012 to 2016 by means of MTAS. Relevant spectral analyses have been
reported for 86Br, 89,90Kr, 89,90,90m,92Rb, 137I, 139Xe, and 142Cs
Fijalkowska2014b ; Rasco2016 ; Fijalkowska2017 ; Fijalkowska2014a ;
Fijalkowska2018 , and to a greater extent and emphasis for 89Br, 96Y, 137I,
137Xe, 142Ba and 142La Wolinska2014 ; Karny2016 ; Rasco2017a ; Rasco2015a ;
Rasco2017b ; Wolinska2017 . Table 4 lists the various ground-state to ground-
state and other selected $\beta$- emission probabilities, as well as the
average $\beta$ and $\gamma$ energies for 86Br, 88,89,90Kr, 88,89,90,90m,92Rb,
96Y, 98Nb, 137I, 137,139Xe and 142Cs as derived from MTAS measurements
Rasco2016 ; Rasco2017a ; Shuai2022 ; Rasco2022 ; Fijalkowska2017 ;
Fijalkowska2018 , compared with equivalent data in the ENDF/B-VIII Brown2018 ,
JEFF-3.3 Plompen2020 , and JENDL-5 Iwamoto2021  libraries.

Table 4:  Ground-state to ground-state $\beta$- feedings, half-lives and average $\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ energies for 86Br, 88,89,90Kr, 88,89,90,90m,92Rb, 98Nb, 139Xe and 142Cs, as derived from MTAS measurements Rasco2016 ; Rasco2017a ; Shuai2022 ; Rasco2022 ; Fijalkowska2017 ; Fijalkowska2018 , and compared with equivalent data determined from ENSDF database of 2022 ENSDF , ENDF/B-VIII.0 data library of 2018 (ENDF/B8) Brown2018 , JEFF-3.3 data library of 2020 Plompen2020 , and JENDL-5 data library of 2021 Iwamoto2021 . Nuclide |  $T_{1/2}$ (s) |  g.s. $\rightarrow$ g.s. ($\%$) |  $\overline{E}_{\beta}$ (keV) |  $\overline{E}_{\gamma}$ (keV)
---|---|---|---|---
|  | MTAS | ENSDF | MTAS | ENSDF | ENDF/B8 | JEFF-3.3 | JENDL-5 | MTAS | ENSDF | ENDF/B8 | JEFF-3.3 | JENDL-5
86Br | 55.1(4) |  $\approx$ 20 | 15(8) | 1687(30) | 1900(300) | 1944(350) | 1943(345) | 1687(30) | 3782(116) | 3360(110) | 3300(160) | 3300 | 3782(108)
88Kr | 10170(68) | 12.9(25) | 14(4) |  | 370(50) | 370(50) | 370(50) | 370(50) |  | 1950(40) | 1954(40) | 1950(40) | 1950(40)
89Kr | 189(2) | 11(1) | 23(4) | 1250(40) | 1470(100) | 1470(100) | 1470(100) | 1250(6) | 2240(80) | 1844(23) | 1930(20) | 1836 | 2240(24)
90Kr | 32.32(9) | 7(1) | 29(4) | 1130(20) | 1360(100) | 1360(100) | 1325 | 1130(5) | 1690(20) | 1320(40) | 1320(40) | 1277 | 1690(40)
88Rb | 1066.4(11) | 78.2(20) | 76.51(11) |  | 2050(5) | 2050(5) | 2057(20) | 2050(5) |  | 677(3) | 677(3) | 667(20) | 677(3)
89Rb | 918(6) |  NDa | 18.8(13) | 930(30) | 970(50) | 970(50) | 928 | 935(3) | 2260(70) | 2240(50) | 2240(50) | 2231 | 2230(50)
90Rb | 158(5) |  15(1)b |  26(2)b | 1920(50) | 2050(130) | 1900(110) | 2036 | 1920(6) | 2300(100) | 1980(40) | 2270(80) | 2014 | 2230(40)
90mRb | 258(4) |  5(1)b |  15(4)b | 1100(100) | 1400(110) | 1115(33) | 1400(110) | 1150 | 4000(200) | 3240(60) | 3870(120) | 3240 | 3240(60)
92Rb | 4.48(3) | 91(3) | 95.2(7) | 3570(70) | 3640(30) | 2870(700) | 3640(30) | 3498(1) | 385(8) | 170(9) | 2150(190) | 170 | 461(8)
96Y | 5.34(5) | 95.5(20) | 95.5(5) | 3200 | 3181(20) | 3184(20) | 3181(20) | 2656(1) | 100 | 80(4) | 80 | 80 | 1206(4)
98Nb | 2.86(6) | 61(3) | 57(6) |  | 1776(144) | 1776(144) | 1778(144) | 1630(4) | 275(29) | 321(14) | 321(16) | 321 | 855(13)
137I | 24.5(2) | 49(1) | 45.2(5) |  | 1897(15) | 1920(30) | 1861 | 1934(1) | 1250 | 1070(18) | 1135(20) | 1212 | 1220.00(15)
137Xe | 229.1(8) | 67(2) | 67(3) | 510 | 1700(70) | 1698(71) | 1703(71) | 1703(1) | 190 | 189(14) | 189(14) | 189 | 189(14)
139Xe | 39.68(14) | 2(1) | 15(10) | 1580(30) | 1760(230) | 1790(210) | 1700 | 1518(7) | 1340(30) | 965(14) | 1020(20) | 1007 | 1342(20)
142Cs | 1.684(14) | 43(3) | 56(5) | 2480(90) | 2920(180) | 2460(100) | 2920(180) | 2480(4) | 1720(50) | 676(25) | 1704(50) | 676 | 1720(25)
|  |  $<$ 0.5c |  7.2(12)c |  |  |  |  |  |  |  |  |  |
aND - studied but not declared in Ref. Fijalkowska2017 .
b$\beta^{-}$ emission probability from 90g,mRb states to the first-excited 2+
state of 90Sr at an energy of 831.68 keV.
c$\beta^{-}$ emission probability from 142Cs ground state to the first-excited
2+ state of 142Ba at an energy of 359.60 keV.

  * •

Studies of 86Br include the suggested introduction of 65 pseudo-levels
starting at an excitation energy of 5 MeV, along with the observation of 487
additional branches that require incorporation into the proposed decay scheme
Fijalkowska2014b . Ground-state to ground-state $\beta$- feeding was
determined to be just over 20$\%$, compared with a previously assigned value
of 15(8)$\%$. These results are also in good agreement with the studies of
Rice $et~{}al.$ Rice2017 .

  * •

89Kr studies indicate the need for substantial changes in the accepted decay
scheme that would appear to be incomplete and erroneous. A shift of $\beta$-
feeding from lower-energy states of 1530-2400 keV to higher levels was
observed, and ground-state to ground-state $\beta$- feeding was determined to
be 11(1)$\%$ compared with a previously accepted value of 23(4)$\%$
Fijalkowska2017 .

  * •

90Kr also exhibits the need for substantial changes to be made to the accepted
decay scheme. Ground-state to ground-state $\beta$- feeding was determined to
be 7(1)$\%$ compared with a previously assigned value of 29(4)$\%$
Fijalkowska2017 .

  * •

Reductions were observed in the $\beta$- feeding by both 90Rb and 90Rbm to the
first excited 2+ state of 90Sr to be found at 831.68 keV (15(1)$\%$ for 90Rb,
and 5(1)$\%$ for 90Rbm, compared with previously adopted values of 26(2)$\%$
and 15(4)$\%$, respectively) Fijalkowska2017 .

  * •

TAGS measurements of 92Rb by means of MTAS are consistent and in good
agreement with the studies of Zakari-Issoufou et al. Zakari2015 . Ground-state
to ground-state $\beta$- feeding was determined to be 91(3)$\%$ by Rasco et
al. Rasco2016 , compared with a similarly determined value of 87.5(25)$\%$
Zakari2015 .

  * •

Beta-decay studies of 98Nb by Rasco et al. have quantified ground-state to
ground-state feeding, along with beta feeding to the second ${}^{+}0$ state in
98Mo that de-excites via an E0 transition by exploiting the modularity of the
MTAS detector and coincidences with the beta detector Rasco2022 . An average
gamma energy of 275(29) keV has also been deduced. $\beta$- feedings to eight
excited levels above the 2608 keV level in 98Mo are reported, along with an
overall impact on antineutrino calculations.

  * •

Direct MTAS studies of 137I $\beta$- decay (T1/2 of 24.5(2) s) show a dominant
ground-state to ground-state $\beta$- transition of 49(1)$\%$ Rasco2017a ,
compared with a recommended value of 45.2(5)$\%$ in ENSDF, while the average
$\overline{E}_{\gamma}$ increases by 19$\%$ from 1050 to 1250 keV. Measured
$\beta$- feeding at the neutron separation energy is also greater by a factor
of two, and increases by a further factor of five or more above this
separation energy when compared with the ENSDF database . Altogether, there
are sufficient differences in MTAS measurements and the currently recommended
decay scheme data for 137I to merit further well-defined $\gamma$ singles and
$\gamma$-$\gamma$ coincidence studies. An additional noteworthy observation is
that a Pn branch of 0.079 $(\pm~{}0.004(sys))(\pm~{}0.002(fit))$ has been
derived which is in good agreement with a value of 0.0776 $\pm$ 0.0014
obtained by Agramunt $et~{}al.$ based on the use of BELEN Agramunt2016 .

  * •

139Xe exhibits the need for substantial changes in the accepted decay scheme.
$\beta$- emission probabilities to nuclear levels above 2500 keV increased by
over 15$\%$, along with the introduction of various new $\beta$- feedings to
proposed levels above 3600 keV. Ground-state to ground-state $\beta$- feeding
was determined to be 2(1)$\%$ compared with a previously accepted value of
15(10)$\%$.

  * •

Although the $\beta$- decay of 142Cs is insufficient to register as
significant in decay-heat calculations, the decay chain from this radionuclide
generates both 142Ba and 142La that have much greater impact. Under these
circumstances, TAGS and DGS decay-scheme studies of the parent fission product
are of some importance and relevance. 142Cs exhibits a need for substantial
changes in the accepted decay scheme, whereby $\beta$- emissions were observed
to populate a number of new higher-energy nuclear levels. Ground-state to
ground-state $\beta$- feeding was determined to be 43(3)$\%$ compared with a
previously adopted value of 56(5)$\%$, and ground-state $\beta$- feeding to
the first excited 2+, 359.60-keV nuclear level of 142Ba was reduced to $<$
0.5$\%$ compared with a previously agreed value of 7.2(12)$\%$. While a major
contributor to the high-energy component of $\overline{\nu}_{e}$ spectra, at
energies below 1800 keV, $\overline{\nu}_{e}$ of 142Cs increases to 23(3)$\%$,
thereby reducing $\overline{\nu}_{e}$ interaction with matter.

  * •

As studied by Wolińska-Cichocka $et~{}al.$ by means of the MTAS Wolinska2014 ,
the decay scheme of 142La (T1/2 of 5466(30) s) was found to be in good
agreement with another TAGS study Greenwood1997 , but to differ somewhat from
the recommended decay data within ENSDF. $\beta$- feeding to the first excited
state of daughter 142Ce (2+, 641.282 keV) was determined to be a factor of two
higher than the value of 1.4(4)$\%$ in ENSDF. Discrepancies were also observed
in the $\beta$\- population of levels over the energy region of 2-5 MeV, along
with consideration of possible $\beta$- feeding at even higher levels close to
the energy limit. Further TAGS/TAS analyses of existing 142La spectra would
seem to be merited as an important aid in resolving these disparities.

Definitive points of note from the above MTAS campaign are the requirements
for in-depth $\gamma$ singles and both $\beta$-$\gamma$ and $\gamma$-$\gamma$
coincidence measurements of 86Br, 89,90Kr, 90,90m,92Rb, 139Xe and 142Cs
$\beta$- decay, along with further TAGS and DGS studies of 98Nb, in order to
strive for the determination of an appropriate and comprehensive set of decay
schemes.

MTAS studies of other radionuclides have included observations that are in
good agreement with existing HPGe measurements of their $\gamma$-ray decay,
and hence align with the recommended decay schemes to be found in the ENSDF
database:

  * •

Decay data identified with the $\beta$-delayed neutron decay of 89Br have been
obtained from MTAS spectral analyses involving the operation of the central
NaI(Tl) crystal in coincidence with the ancillary Si detector, along with an
energy gate of 6.6 MeV to the Q($\beta$-)-value on the inner, middle and outer
rings of the main NaI(Tl) detectors. Two $\gamma$ peaks were evident at
approximately 750 and 1600 keV that correspond to $\gamma$ depopulation from
the first two excited states of 88Kr with energies of 775.32 and 1577.43 keV.
The response function of the MTAS detector system to mono-energetic neutrons
of differing kinetic energies was also shown to agree well with various other
forms of dedicated experimental study Karny2016 .

  * •

Ground-state to ground-state feedings of the $\beta$- decay of 88Kr and 88Rb
have been determined by Shuai et al. Shuai2022 . Data precision was improved
in the case of 88Kr, and the sensitivity to the shape of the first forbidden
decay in the determination of the ground-state to ground-state $\beta$-
emission of 88Rb was also considered. Small differences in the feeding
distributions were observed in both 88Rb and 88Kr decay with respect to
earlier high-resolution studies.

  * •

TAGS data for 89Rb are in good agreement with existing $\gamma$ singles
spectroscopy; little to no evidence of the Pandemonium effect.

  * •

96Y (T1/2 of 5.34(5) s) was determined by MTAS to possess a high ground-state
to ground-state $\beta$- emission probability of 95.5(20)$\%$, in agreement
with the recommended value of 95.5(5)$\%$ in ENSDF. Difficulties in detection
arose as a consequence of the E0 transition from the 0+, 1581.34-keV first
excited state to the 0+ ground state of 96Zr, which is effectively via
conversion electrons that are too energetic to achieve an efficient response
in the 1-mm thick silicon detectors Rasco2016 ; Rasco2017b . The impact of the
E0 transition in this beta decay has also been fully considered in the recent
work of Guadilla et al. Guadilla2022 .

  * •

137Xe (T1/2 of 229.1(8) s) was determined by MTAS to decay almost exclusively
via $\beta$- emission to both the first excited state (5/2+, 455.491(3) keV)
and ground state (7/2+, 0.0 keV) of 137Cs with emission probabilities of
31(1)$\%$ and 67(2)$\%$, respectively, to give a total probability of
98(2)$\%$. All of these particular decay data are in agreement with the
equivalent recommended values of 31(3)$\%$, 67(3)$\%$ and 98(4)$\%$ in ENSDF.
Another decay parameter to be highlighted is the $\beta$- feeding ratio for
the population of the 2850.04(9)- and 2849.11(13)-keV nuclear levels of
daughter 137Cs with values of 8.0(9) measured by MTAS and 7.2(13) in ENSDF.
This constitutes reasonably good agreement in a relatively complex decay
scheme of predominantly low-intensity transitions, other than two higher-
energy $\beta$- emissions and their associated $\gamma$ ray Rasco2017a ;
Rasco2015a .

  * •

142Ba (T1/2 of 636(12) s) decay scheme as determined by MTAS was found to be
in good agreement with another TAGS study Greenwood1997  and existing HPGe
$\gamma$-ray measurements. As would be expected under such circumstances, the
MTAS data for the $\beta$- decay of 142Ba are also in good agreement with the
equivalent data in the ENSDF database Wolinska2014 ; Wolinska2017 .

Over sixty fission products studied by means of MTAS remain to be fully
analysed and evaluated, and this work continues Rykaczewski2018 . Further MTAS
measurements and data analyses are also being planned that will involve the
Californium Rare Isotope Breeder Upgrade (CARIBU) of the Argonne Tandem Linac
Accelerator System (ATLAS facility) at the Argonne National Laboratory (ANL),
USA. Along with existing lead and neutron shielding, a concrete wall
separating the 252Cf spontaneous fission source of CARIBU from MTAS has
reduced the background activity substantially over an energy range of 30 keV
to 8 MeV, from 2.4 kHz at ORNL to 1.9 kHz at ANL. The existing facilities at
ANL include a gas cell and high resolution mass separator able to handle the
isotopes of refractory elements that include 98,99,100,101,102Nb,
103,104,105Mo and 103,104,105,106,107Tc. New activities are envisaged along
with some repeat measurements at lower background conditions with an MTAS of
greater efficiency and modularity. As noted in Section 2, MTAS in an improved
form has also been installed as a research tool at the Facility of Rare Ion
Beams (FRIB), Michigan State University, East Lansing, USA Karny2019 ;
Rykaczewski2022 . An extensive range of silicon PIN detectors, double-sided
silicon-strip detector (DSSD), silicon surface barrier detector and a summing
NaI(Tl) SuN detector have been used to monitor and determine the half-lives of
a number of separated relevant fission fragments from the spallation reaction
of a 120 MeV/u 124Sn beam on a 9Be target Dombos2019 . TAGS/TAS studies have
been performed by means of the SuN array of eight segments of NaI(Tl), with
each segment containing three photomultiplier tubes. Both TAGS and the sum-of-
segments spectra were used to identify the radionuclides of interest and
determine their half-lives. Seven such nuclides were studied in this manner,
of which 102Nbm with a half-life of 1.33(27) s and 104Nbm with a half-life of
0.97(10) s are of particular note. While not considered in this wide-ranging
assessment because of their questionable existence in the earlier stages of
our work, there is increased merit in re-considering their present status with
respect to their roles in the calculation of decay heat and antineutrino
spectra.

Properties of neutron-rich nuclei in the fission-product and light rare-earth
regions have been explored experimentally at Argonne National Laboratory
Kondev2019 ; Hartley2018 ; Hartley2020 ; Orford2020 ; Orford2020-1 . Discrete
$\beta$-$\gamma$-$\gamma$ spectroscopy measurements were conducted by means of
a newly-commissioned decay station at the Gammasphere facility, along with
related studies employing a Canadian Penning trap and X-array spectrometer
(five Ge clover detectors). Initial studies were motivated by nuclear
structure research whereby the emphasis was placed on 160,162Eu, followed by
DGS measurements of 98Y, 102,104Zr, 98Nb, 102Nbg,m, 104Nbg,m, 102,104Mo,
144,146Ba, 144La, 146Lag,m and 146Ce. Neutron-rich 98Nb, 102Nbg,m, 104Nbg,m,
102,104Mo, 144Ba, 144La and 146Lag,m are of particular interest with respect
to decay-heat and antineutrino calculations, and these measurements will be
further analyzed and assessed in order to improve our knowledge of their decay
schemes.

##  5 Impact of TAGS measurements on decay-heat calculations

Nuclear fuel decay-heat calculations require individual quantitative inventory
data for all the actinides, their heavy-element decay products, and nearly a
thousand fission products produced within the fuel as a function of the
cooling time after shutdown. After the changing inventories of all the
fission-product nuclides and actinides have been calculated on the basis of
their formation cross sections and subsequent decay, these data for a
particular radionuclide can be multiplied by the relevant decay constant and
the various average energies released per decay. These energies are summed
over all the radionuclides and all possible decays to yield the resulting
total decay heat at designated cooling times. The total average energy per
decay $\overline{E}_{T}$ released by a fission product or actinide consists of
contributions from the average energy released as the kinetic energy of light-
particle transitions $\overline{E}_{LP}$ (most frequently as $\beta{{}^{-}}$
emissions), heavy particles $\overline{E}_{HP}$, and as electromagnetic
radiation $\overline{E}_{EM}$:

$\displaystyle\overline{E}_{T}=$
$\displaystyle\overline{E}_{LP}+\overline{E}_{EM}+\overline{E}_{HP},$

where

$\displaystyle\overline{E}_{LP}$ $\displaystyle=$
$\displaystyle\overline{E}_{\beta^{-}}+\overline{E}_{\beta^{+}}+\overline{E}_{ce}+\overline{E}_{Auger},$
$\displaystyle\overline{E}_{EM}$ $\displaystyle=$
$\displaystyle\overline{E}_{\gamma}+\overline{E}_{X-ray}+\overline{E}_{annih}+\overline{E}_{bremss},$
$\displaystyle\overline{E}_{HP}$ $\displaystyle=$
$\displaystyle\overline{E}_{\alpha}+\overline{E}_{n,p}+\overline{E}_{SF}~{}...,$

in which:
$\overline{E}_{\beta^{\pm}}$ is the average kinetic energy of $\beta^{\pm}$
particles,
$\overline{E}_{ce}$ is the average kinetic energy of the internal-conversion
electrons,
$\overline{E}_{Auger}$ is the average kinetic energy of the Auger electrons,
$\overline{E}_{\gamma}$ is the average $\gamma$-ray energy,
$\overline{E}_{X-ray}$ is the average X-ray energy,
$\overline{E}_{annih}$ is the positron annihilation energy associated with
$\beta^{+}$ decay,
$\overline{E}_{bremss}$ is the internal bremsstrahlung energy,
$\overline{E}_{\alpha}$ is the average kinetic energy of the $\alpha$
particles,
$\overline{E}_{n,p}$ is the average kinetic energy of neutron/proton
emissions,
and $\overline{E}_{SF}$ is the total recoverable energy associated with
spontaneous fission.
These average energies are normalized per decay of the fission-product
nuclides and parent actinides (including spontaneous fission), and are
determined or adopted directly from decay-data libraries containing best
recommended data for the radioactive properties of the emitted light
particles, heavy particles and electromagnetic radiation.

The first appropriate decay-data libraries were developed at the end of the
1970s as a consequence of separate efforts in Europe, Japan and the USA. These
libraries were largely based on experimental discrete spectral data available
at the time. However, they all failed to reproduce the integral-type sample-
irradiation measurements of decay heat performed by Dickens et al. Dickens1980
and Akiyama and An Akiyama1982  that had become available as potential
benchmarks to validate the above three libraries. Comparisons of the measured
light-particle (LP) and electromagnetic (EM) decay heat with calculated values
indicated that the LP (${\beta^{-}}$) component was overestimated, while the
EM (${\gamma}$) component was significantly underestimated.

Members of the Japanese Nuclear Data Committee (JNDC) implemented the gross
theory of $\beta^{-}$ decay Takahashi1969 ; Koyama1970 ; Takahashi1971  in
calculations of the average $\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$
energies per decay. After applying the gross theory to fission-product nuclei
for which no experimental information was available, this approach was applied
further to all fission products with high $Q_{\beta}$ values, leading to
significant improvements in the ${\beta}$ and ${\gamma}$ components of the
decay heat in reproducing the sample-irradiation experiments Yoshida1981 . An
NEANDC specialists meeting on fission yields and decay data held in 1983
reached the following conclusions regarding the status of the decay-heat
calculations Chrien1983 : (1) discrepancies between the calculated components
of decay heat and their experimental measurements were defined as a
manifestation of the Pandemonium effect in beta decay arising from incomplete
high $Q_{\beta}$-value decay schemes used in the benchmark calculations, (2)
adoption of gross $\beta^{-}$ theory was only free from the problem in an
average or aggregate sense, and (3) targeted experiments such as TAGS were
required to assist in solving the problem. Extensive TAGS measurements of an
impressive range of fission products of interest were performed by Greenwood
et al. Greenwood1997  in the mid-1990s. The introduction of these resulting
data into decay-heat summation calculations revealed the usefulness of this
approach compared with the averaging inadequacies of the gross $\beta^{-}$
theory Hagura2006 . More focused studies designed to address the decay heat of
239Pu were completed and made available for analysis by means of further
decay-heat calculations approximately thirteen years later Algora2010 .

Theoretical values obtained from gross $\beta^{-}$ theory were adopted for the
mean decay energies of nuclides with $Q_{\beta}\geq$ 5 MeV in the JNDC
fission-product decay data library Tasaka1983 , which eventually became part
of JENDL. A similar approach that involved fitting parameters in a model based
on gross $\beta^{-}$ theory to replace $\beta^{-}$ and $\gamma$ experimental
energies was tentatively applied to the ENDF/B-IV decay-data sub-library with
some success, and has been used up to and including ENDF/B-VI England1992 .
Both JENDL and the ENDF/B decay-data libraries up to version VI are
effectively ”contaminated” by theoretical values, creating difficulties in
disentangling and clearly demonstrating the importance of TAGS data. On the
other hand, average $\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ decay
energies in the JEFF-3 decay-data files from the first release of JEFF-3.1 are
based solely on experimentally-determined decay schemes. When no reliable or
complete experimental decay data are available, the empirical $Q_{\beta}/3$
rule has been used as an estimate of the partition of the total released
energy ($Q_{\beta})$ into $\overline{E}_{LP}$, $\overline{E}_{EM}$ and the
unrecoverable neutrino energy. The first TAGS data included in the JEFF-3.1.1
decay-data library Kellett2009  were taken from Greenwood et al. Greenwood1997
. A comparison of the decay-heat calculations obtained with different versions
of the series of JEFF-3 libraries in their chronological order offers insights
into the growing impact of TAGS. Partial decay-heat calculations based on
different releases of the JEFF-3 library are compared in Fig. 1 with the
Tobias evaluated decay-heat data for thermal pulse fission of 239Pu Tobias1980
. JEFF-3.1 Kellett2009  does not include any gross $\beta^{-}$ theory or TAGS
data, and overestimates the LP ($\beta$) component and underestimates the EM
($\gamma$) component. JEFF-3.1.1 Kellett2009  includes several of the
Greenwood et al. TAGS data Greenwood1997  to give considerably improved
agreement when compared with the experimental data for both the LP and EM
components of decay heat. This is mainly attributed to the TAGS data being
Pandemonium-free and more correctly representative of the relative
contributions of $\beta^{-}$ and $\gamma$ emission energies per decay. Further
improvement is obtained with JEFF-3.3 Plompen2020 , especially for the EM
($\gamma$) component between 30 and 4000 s cooling times after the fission
burst, which now agrees with the evaluated decay-heat data. JEFF-3.3 includes
the TAGS data for Nb, Mo and Tc isotopes which were measured by Algora et al.
Algora2010  after they were identified as primary sources of the large
Pandemonium problem affecting 239Pu decay heat. Figures appearing hereafter
follow the same convention as Fig. 1 in which the vertical axis is decay heat
(MeV/fission/s) $\times$ time after fission pulse (s) in order to achieve
reasonably compact and comprehensive displays.

Figure 1: Comparison of decay heat for 239Pu thermal fission obtained using
different JEFF libraries that attempt to deal with the Pandemonium effect over
the years listed. The evaluated data of Tobias Tobias1980  were taken from the
IAEA CoNDERC database conderc .

We have studied the impact of TAGS data on the calculated decay-heat
components (LP/EM) for the different fission-based systems discussed in
Section 3 (see Table 1), focusing on the effect of the new TAGS data mentioned
in Section 4 (Tables 2, 4). Decay-heat calculations were performed on the
basis of three available evaluated nuclear-data libraries (ENDF/B, JENDL and
JEFF), with their associated decay-data and fission-yield sub-libraries. All
decay-data sub-libraries by definition include the average decay energies
$\overline{E}_{LP/EM/HP}$ followed by the individual components listed in the
earlier equations above. However, in the latest versions of these sub-
libraries, only the $\overline{E}_{LP/EM/HP}$ values are included in the data
section, while the breakdown into individual components that include
contributions from the atomic radiation processes
($\overline{E}_{ce/Auger/X-rays/...}$) are listed in the comments section.
When TAGS data are incorporated in the ENDF/B, JENDL and JEFF libraries, the
average $\overline{E}_{LP/EM}$ energies are replaced by the TAGS-derived
average $\overline{E}_{\beta,\gamma}$ decay energies, omitting any possible
contributions from the atomic radiation, internal bremsstrahlung, etc.
Contributions from the atomic radiation processes to the average energy
emitted per decay are usually small and can normally be neglected. However,
there are certain cases such as 101Nb and 105Tc, in which the sum of the
conversion electron $\overline{E}_{ce}$ and Auger electron
$\overline{E}_{Auger}$ mean energies as derived from the discrete $\gamma$-ray
spectra in ENSDF ENSDF  amounts to $\sim$ 100 keV, i.e., $\approx$ 5% and 13%
of the average TAGS-derived $\overline{E}_{\beta}$ for 101Nb and 105Tc,
respectively. Full consideration of the various atomic contributions requires
sound knowledge of the decay scheme measured by TAGS, and re-calculation of
these atomic data for inclusion in the corresponding average decay energies.

Three sets of decay-heat calculations have been performed in combination with
each one of the three fission-yield sub-libraries:

  1. 1.

decay data without measured Algora (2010) TAGS data (baseline);

  2. 2.

decay data with measured Algora (2010) TAGS data Algora2010  (+ TAGS 2010);

  3. 3.

decay data with recent measured TAGS data published or communicated before the
cut-off date of February 2022 (listed in Tables (2, 4) (+ TAGS 2021).

Results have been generated for the thermal fission of 235U, 239Pu, 241Pu, and
fast fission of 232Th, 233U, 237Np, 238U, for which experimental decay-heat
measurements on neutron pulse irradiations exist. Pulse irradiation decay-heat
data for single-actinide targets were obtained from the IAEA CoNDERC database
conderc . Further comparisons of the decay-heat calculations are discussed in
Sub-section 5.4, as obtained with the existing general purpose libraries
ENDF/B-VIII.0, JEFF-3.3 and JENDL-5 for all sixteen fissioning systems
mentioned in Section 3.

###  5.1 ENDF/B-VIII.0 library

ENDF/B-VIII.0 decay-data and fission-yield sub-libraries have been combined to
calculate the LP and EM components of decay-heat for seven fissioning systems
for which experimental pulse decay-heat data exist. Average
$\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ decay energies determined
mainly from the discrete decay schemes recommended in ENSDF ENSDF  are
included in the ENDF/B-VIII.0 decay-data sub-library. Conversion-electron,
Auger-electron and X-ray contributions have also been derived from the decay
schemes by means of dedicated codes with their input data obtained from
atomic-data libraries RADLIST . The library also includes average
$\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ energies from the TAGS
measurements of Greenwood et al. Greenwood1997  for the following fission
products: 90,90m,91,93Rb, 93,95Sr, 95Y, 140,141Cs, 143,144,145Ba,
142,143,144,145La, 147Ce, 146,147Pr and 149Nd. Beta feedings taken from
Tengblad et al. Tengblad1987  were used to determine Eβ for 88,89Br and 138I.
When no experimental decay scheme was available, average energies were
obtained from the Finite-Range-Liquid-Drop + QRPA model of Möller et al.
Moeller2016 . From the most recent TAGS measurements listed in Tables (2, 4),
the data for 104,105,106,107Tc and 105Mo by Algora et al. (2010) Algora2010
and 142Cs by Rasco et al. (2016) Rasco2016  and Fijałkowska et al. (2017)
Fijalkowska2017  have also been incorporated into the ENDF/B-VIII.0 decay-data
sub-library.

The three-step process to assess the impact of the recent TAGS measurements
described above was implemented as follows:

  * •

Step 1, baseline calculations: average $\overline{E}_{\beta}$ and
$\overline{E}_{\gamma}$ decay energies of Algora et al. (2010) Algora2010
were replaced with average $\overline{E}_{LP}$ and $\overline{E}_{EM}$
energies derived from the discrete decay schemes in ENSDF ENSDF . Same was
done with the average decay energies of Rasco et al. (2016) Rasco2016  and
Fijałkowska et al. (2017) Fijalkowska2017  in the case of 142Cs. Therefore,
baseline calculations with the ENDF/B-VIII.0 decay-data sub-library included
only the Greenwood TAGS data Greenwood1997  listed above (referred to as
ENDF/B-VIII.0 (Greenwood)), data from Tengblad et al. Tengblad1987  and model
calculations Moeller2016 .

  * •

Step 2: adopted ENDF/B-VIII.0 decay-data file as default, which includes five
of the seven fission products measured by Algora et al. (2010) Algora2010 ,
and added TAGS average energies for 102Tc and 101Nb Algora2010  \- although
not impacted by Pandemonium, with TAGS and ENSDF-derived average energies in
agreement. TAGS average decay energies of 142Cs Rasco2016 ; Fijalkowska2017
were replaced by ENSDF-derived values (+ TAGS 2010).

  * •

Step 3: all of the remaining TAGS data listed in Tables 2, 4 (+ TAGS 2021)
were added to the decay-data sub-library that had been modified in step 2.
Hence, this sub-library included all of TAS/DTAS studies mentioned by Algora
et al. (2021) Algora2021  and MTAS measurements on 89,90Kr, 89,90,90mRb, 96Y,
137,139Xe and 142Cs from Rasco et al. (2016) Rasco2016  and Fijałkowska et al.
(2017) Fijalkowska2017 . However, known TAGS data for 96mY, 98Nb, and 140Cs,
were not included as they were published or provided through private
communication after the cut-off date (February 2022) for these wide-ranging
inventory calculations.

Experimental pulse simulations and inventory calculations were performed with
the FISPACT-II code fispact  at incident neutron energies for which decay-heat
and fission-yield data exist, and are available in the relevant ENDF/B-VIII.0
sub-libraries (i.e., at thermal (0.0235 eV) and fast (500 keV) neutron
energies). The three sets of calculations are compared with experimental
decay-heat data in Figs. 2, 3. A consistent trend is emerging for all of the
fissioning systems and energies whereby the inclusion of average
$\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ energies derived from
measured TAGS data leads to a decrease in the LP and an increase in the EM
decay heat components, respectively. These gradual modifications in this
manner to the relative contributions of the LP($\beta$) and EM($\gamma$)
components of decay heat is direct confirmation of the fact that the TAGS-
derived data are nominally free from the Pandemonium effect.

Figure 2: Decay heat as a function of cooling time as obtained using the
ENDF/B-VIII.0 fission-yield and decay-data sub-libraries Brown2018 , with the
addition of TAGS data from Algora2010  (+ TAGS 2010) and Tables (2, 4) (+ TAGS
2021). Experimental data have been taken from the CoNDERC database conderc .

Figure 3: Same as Fig. 2.

While the three sets of calculations reproduce the experimental decay-heat
components fairly well, a particularly marked improvement is observed when
including the TAGS data of Algora et al. Algora2010  (+ TAGS 2010) in the
decay-data sub-library. This much improved agreement had already been observed
in the thermal decay-heat studies of 239Pu Algora2010 , with the present
results for the decay-heat components of 238U fast and 241Pu thermal also
exhibiting better alignment with their equivalent experimental data. The
decay-heat components of the heavier actinides are sensitive to the decay heat
of five of the previously selected fission products: 105Mo, 104,105,106,107Tc
Yoshida2007 . These observations contrast sharply with the negligible impact
of these TAGS data on decay-heat calculations for 232Th, 233U and 237Np fast-
neutron fission. Consideration of 235U thermal fission is both important and
noteworthy: the LP component of decay heat is not affected by the inclusion of
the TAGS data and is in good agreement with the experimental data, while the
EM component for all three available sets of decay-heat data exhibits
discrepancies Tobias1989 ; Dickens1980 ; Schier1997  . At cooling times
ranging from 1 to 400 s, these data sets agree within the experimental
uncertainties, while above 400 s there is disagreement. Without the TAGS data
of Algora et al. Algora2010 , the calculated EM component agrees with the
Dickens data below 400 s Dickens1980 , and with the evaluated data of Tobias
above 400 s Tobias1989  \- these observed differences between the Dickens data
and Tobias evaluation remain unresolved to date.

Inclusion of all of the recent TAGS measurements (+ TAGS 2021) displayed in
Tables 2, 4 (with the exception of 96Ym and 98Nb) leads to a small
underestimation of the LP decay heat at cooling times in the range 10 - 1000 s
for 233,238U fast and 235U, 239,241Pu thermal fission. The EM components for
233,235,238U, 241Pu and 232Th fission exhibit improved agreement at shorter
cooling times below 100 s, whereas the relatively large increase in the EM
component of 239Pu approaches the upper experimental limits. These results
indicate that the inclusion of the (+ TAGS 2021) data is insufficient such
that additional TAGS measurements of the remaining high priority fission
products are merited to arrive at a robust description of the experimental
pulse decay-heat data.

A re-assessment of the known decay-scheme data for further fission products
should be undertaken to justify new TAGS measurements, along with an
investigation of the experimental pulse-irradiation decay-heat data to
determine the need for additional such studies. Apart from discrepancies in
the experimental EM decay-heat data of 235U thermal fission that remain to be
resolved, there are also issues with the experimental decay-heat data of 238U
and 237Np. The EM decay-heat data of Akiyama and An Akiyama1982  for 238U
disagree with the data from Lowell measured by Schier and Couchell Schier1997
, while the LP components are in agreement. Two sets of 237Np measurements
were performed at the YAYOI reactor by Ohkawachi and Shono Ohkawachi2001  in
the form of 100 and 500 s irradiation bursts. These two separate sets of
finite irradiation data were converted by the authors into instantaneous pulse
data for adoption as benchmarks. The correction factor utilized in this
conversion process was of the order of 2 at most, such that the experimental
data possessed large uncertainties, especially at shorter cooling times (60 to
200 s) when a large scatter in the data was observed (Fig. 3). Longer cooling
times between 2500 and 20000 s were also affected by significant uncertainties
that arose from contamination by $\gamma$ rays emitted from 238Np produced by
neutron capture on 237Np. Finally, there exists only one reliable set of data
for 232Th, 233U measured at the fast-neutron reactor YAYOI by Akiyama and An
Akiyama1982 , while for 241Pu there is only one measurement at thermal-fission
energy by Dickens et al. Dickens1980 . The significant improvement in the
decay-data sub-libraries that has been achieved in the past two to three
decades means that we are now able to explore the impact of uncertainties of
the input data on decay-heat calculations. A necessary pre-requisite is to
possess accurate and precise decay-heat data, which implies a need for new
measurements of the LP and EM components of the various fissioning systems
discussed above.

###  5.2 JEFF library

JEFF-3.1.1 decay-data and neutron-induced fission-yield sub-libraries were
used to calculate the LP and EM components of decay heat for the seven
fissioning systems irradiated under thermal or fast neutrons for which
experimental pulse decay-heat data exist. Depletion calculations for the pulse
experiments have been performed with the SERPENT2 code leppanen2015 , while
the JEFF-3.1.1 decay-data sub-library was chosen for reference calculations
because all recent TAGS measurements presented in Tables 2, 4 have not been
included in this particular database. Fission-yield data were also taken from
the relevant JEFF-3.1.1 sub-library for thermal (0.0235 eV) and fast (400 keV)
neutron energies.

The JEFF-3.1.1 decay-data sub-library was released in November 2007
Kellett2009  after decay-heat studies of various decay-data libraries
(including JEFF-3.1) by the OECD/NEA Working Party on International Evaluation
Co-operation subgroup 25 (WPEC-25) Yoshida2007 . Members of WPEC-25 concluded
that TAGS measurements to determine the average decay energies would improve
the quality of the calculated $\beta$ and $\gamma$ decay-heat components. As a
result, the mean energies of twenty-nine fission-product nuclides measured by
Greenwood et al. Greenwood1997  were initially included in JEFF-3.1.1.
Furthermore, high-quality evaluations of fifty nuclides were taken from the
United Kingdom libraries UKPADD-6.7 and UKHEDD-2.5 (Perry2014 , and Ref.
Kellett2009  for selection details), while the rest of the decay data were
adopted from ENSDF ENSDF  and the Decay Data Evaluation Project (DDEP) ddep .

Three sets of decay-heat calculations denoted earlier in the Section as (1),
(2) and (3) were performed with the same JEFF-3.1.1 fission-yield sub-library
each time. The first set of calculations was based on the JEFF-3.1.1 decay
data described above, and formed the baseline set of data. A second set of
calculations (2) was associated with the replacement of the
$\overline{E}_{LP}$ and $\overline{E}_{EM}$ energies of seven fission products
102,104,105,106,107Tc,101Nb and 105Mo by the TAGS average
$\overline{E}_{\beta}$ and $\overline{E}_{\gamma}$ energies measured by Algora
et al. (2010) Algora2010  (referred to as + TAGS 2010 in Figs. 4, 5). The last
set of calculations (3) included the addition of the remaining TAGS data
listed in Table 3 of Algora et al. (2021) Algora2021 , and those for 89,90Kr,
89,90,90mRb, 96Y, 137,139Xe and 142Cs from Rasco et al. (2016) Rasco2016  and
Fijałkowska et al. (2017) Fijalkowska2017  to the JEFF-3.1.1 decay data
library (referred to as + TAGS 2021 in Figs. 4, 5). Corresponding average
energies are displayed in Tables 2, 4. As mentioned in Sect. 5.1, the TAGS
mean energies of 96mY, 98Nb and 140Cs were not considered as they were
available after the cutoff date.

Figure 4: Decay heat as a function of cooling time as obtained using
JEFF-3.1.1 fission-yield and decay-data sub-libraries Kellett2009 , with the
addition of TAGS data from Algora2010  (+ TAGS 2010) and Tables (2, 4) (+ TAGS
2021). Experimental data have been taken from the CoNDERC database conderc .

Figure 5: Same as Fig. 4.

As shown in the Figures, results obtained for the LP and EM components of the
decay heat for the seven fissioning systems exhibit the same features reported
in the previous subsection devoted to the ENDF/B-VIII.0 decay-data and
fission-yield sub-libraries. Inclusion of the average $\overline{E}_{\beta}$
and $\overline{E}_{\gamma}$ decay energies from the TAGS measurements (+ TAGS
2010) leads to a decrease in the LP and an increase in the EM decay-heat
components, which is a direct consequence of the adoption of Pandemonium-free
decay data. TAGS 2010 data improve the agreement with the pulse decay-heat
measurements for 239,241Pu thermal and 238U fast fission, but has only a small
impact on 232Th and 233U fast fission. While decay-heat calculations of 235U
thermal fission are associated with an LP component that is not affected by
the inclusion of the TAGS 2010 data, conclusions are more difficult to draw
when considering the EM component because of discrepancies between the three
sets of experimental pulse decay-heat data.

Insertion of all the recent TAGS measurements into the JEFF-3.1.1 decay-data
sub-library (+ TAGS 2021) leads to a underestimation of the LP decay-heat
component in the 10 to 1000 s cooling time for the following fissioning
systems: 233,238U fast fission and 239,241Pu thermal fission. The LP component
in 235U thermal fission exhibits a small improvement in the decay-heat
calculations from 10 to 1000 s cooling time, along with a small yet continuous
underestimation from 400 to 1000 s cooling time. EM decay-heat components for
232Th and 233,238U fast fission, and 235U and 241Pu thermal fission also
improve for cooling times below 100 s. The conclusions and recommendations
presented in Subsection 5.1 are also valid for the impact of TAGS data into
the JEFF-3.1.1 sub-library discussed in this subsection.

###  5.3 JENDL library

As noted in the introduction to Section 5, JENDL fission-product decay-data
files contain a mixture of experimental and theoretical average decay
energies. JENDL/FPD-2000 includes experimental average energies from ENSDF
ENSDF  and theoretical values from gross $\beta$- theory, all of which are
combined to reproduce the experimental decay-heat data. An update from
JENDL/FPD-2000 to JENDL/FPD-2011 includes the TAGS 2010 data of Algora et al.
(2010) Algora2010 , while average $\overline{E}_{\beta}$ and
$\overline{E}_{\gamma}$ energies for the other fission-product nuclides have
been re-evaluated following a prescription used in all of the evaluations
performed before and after FPD-2000 up to FPD-2011: adopted decay data should
consistently reproduce, within the uncertainties of the experimental data and
theoretical calculations, not only the available experimental decay-heat data,
but also the aggregate $\gamma$-ray spectra of Ref. Dickens1980 ; Akiyama1988
and individual $\beta$/$\gamma$ spectra of Ref. Rudstam1990B . Average decay
energies were also carefully compared with the measured TAGS data of Greenwood
et al. Greenwood1997 .

The impact of the Algora et al. (2010) Algora2010  as well as the most recent
TAGS data listed in Tables 2, 4 was assessed without any ”contamination” from
theoretical data. Two baseline calculations were undertaken separately with
the JENDL FP decay-data file 2000(JENDL/FPD-2000) and JENDL FP decay-data file
2011 (JENDL/FPD-2011), and four sets of decay-heat calculations were also
performed: one baseline calculation with JENDL/FPD-2000; second calculation in
which Algora et al. (2010) TAGS data were added to the JENDL/FPD-2000 baseline
(referred to as + TAGS 2010); third calculation as a baseline with
JENDL/FPD-2011 (which includes Algora et al. (2010) TAGS data with minimum
modification to keep consistency with the beta-ray spectrum data); and fourth
calculation whereby the remaining TAGS data listed in Tables 2, 4 were added,
except for 96mY, 98Nb and 140Cs (referred to as + TAGS 2021). One notable
difference between the ENDF/B-VIII.0 and JEFF-3.1.1 used in the previous
subsections and the above JENDL decay-data sub-libraries is that the latter
does not include any of the Greenwood et al. TAGS data Greenwood1997 , whereas
the other two sub-libraries incorporate them either completely (ENDF/B-VIII.0)
or partially (JEFF-3.1.1). Under such circumstances, theoretical average decay
energies have been calculated for these specific fission products that lead to
good description of the experimental decay-heat data for their subsequent
introduction into the JENDL decay-data sub-libraries. The JENDL Fission-
product Yield Data File 2011 Katakura2011  was used in the baseline and
subsequent calculations. Both the fission-product decay and fission-product
yield files originate from the JNDC Nuclear Data Library of Fission Products,
as mentioned earlier in Section 5 Tasaka1983 .

All of decay-heat calculations undertaken in conjunction with the JENDL data
files were performed by means of the OYAK98 code Oyamatsu1999 , and the
results have been compared with available experimental decay-heat data in
Figs. 6, 7.

Figure 6: Decay heat as a function of cooling time as obtained using JENDL
fission-yield and decay-data sub-libraries jendl4  with the addition of TAGS
data from Algora2010  (+ TAGS 2010) and Tables (2, 4) (+ TAGS 2021).
Experimental data have been taken from the CoNDERC database conderc .

Figure 7: Same as Fig. 6.

Both of the baseline calculations for JENDL/FPD-2000 and JENDL/FPD-2011 lie
predominantly within the experimental uncertainties, except for a few cases
such as the EM component for 233U fast fission over cooling times of 500 to
3000 s and the LP component for 239Pu thermal fission at cooling times from
400 to 2000 s. These observations indicate that the gross $\beta$- theory
reproduces the average decay energies reasonably well, as applied and
described in the introductory part of this section. Deviations from the
baseline curves caused by the introduction of the average energies determined
from TAGS measurements are relatively small. However, the introduction of TAGS
data in the case of 239Pu thermal fission increases the EM component
considerably beyond the experimental uncertainties at cooling times of 20 to
300 s. Possible reasons for this overestimation are discussed in Subsection
5.4. Overall, all four sets of decay-heat calculations give a reasonable
description of the experimental decay-heat data as shown in Figs. 6, 7.
However, this exception should not detract from the importance of including
TAGS data in the decay-data sub-libraries - they are expected to represent the
best recommended data for each individual nuclide, whereas gross $\beta$-
theory is limited to only average-energy properties.

###  5.4 Comparison of libraries

We have undertaken studies of the impact of recent TAGS measurements on pulse
decay-heat calculations that were based upon comparisons of the available
experimental decay-heat data with the results of three different modelling
codes and differing input libraries of nuclear data. Assessments were made in
order to judge the performance of the latest general-purpose evaluated
libraries (ENDF/B-VIII.0 Brown2018 , JEFF-3.3 Plompen2020 , and JENDL-5
Iwamoto2021 ), in calculations of pulse decay heat for the sixteen fissioning
systems listed in Section 3. The relevant sub-libraries of these databases
differ in the content of their recommended cross sections, decay data and
fission-yield data. Our efforts have focused mainly on actinide and fission-
product decay-heat calculations that are most strongly dependent on the
adopted fission yields and decay data used as input to the inventory
calculations. We have described in Section 5.1 the inclusion of measured TAGS
data within the decay-data sub-library of ENDF/B-VIII.0; JEFF-3.3 includes
TAGS data from Greenwood et al. (1997) Greenwood1997 ; Kellett2009 , Algora et
al. (2010) Algora2010  (with the exception of 101Nb and 102Tc), and for 87Br,
88Br, 92Rb and 94Rb Valencia2017 ; Zakari2015 , as defined in Subsection 5.2;
JENDL-5 Iwamoto2021  contains all of the TAGS measurements performed as part
of the TAS/DTAS collaboration listed in the review article of Algora et al.
Algora2021 , and several nuclides from the MTAS collaboration published in
Fijałkowska et al. Fijalkowska2017  (see Tables 2, 4), as noted in Subsection
5.3. The JENDL-5 decay-data sub-library is judged to be the most complete
database for the inclusion of available TAGS data.

Comparisons of the various calculated decay-heat studies with experimental
pulse decay-heat data are shown in Figs. 8 to 11. The resulting decay heat
curves are in reasonably good agreement at cooling times above 1000 s, while
they can be rather discrepant at shorter cooling times below 1000 s. The most
marked discrepancies with respect to experimental decay-heat data are observed
in the following cases: 232Th fast fission, where the electromagnetic
component from 2 to 100 s cooling times is underestimated by both
ENDF/B-VIII.0 and JEFF-3.3; 238U fast-fission cooling times of 1 to 10 s
whereby JEFF-3.3 overestimates the decay heat; 237Np fast fission, for which
ENDF/B-VIII.0 and JENDL-5 overestimate the decay-heat data at around 100 s
cooling time; 239Pu thermal fission, where JENDL-5 overestimates the peak at
cooling times from 10 to 300 s.

Figure 8: Decay heat as a function of cooling time as obtained using
ENDF/B-V111.0, JEFF-3.3 and JENDL-5 evaluated libraries. Experimental data
have been taken from the CoNDERC database conderc .

Figure 9: Same as Fig. 8.

Figure 10: Same as Fig. 8.

Figure 11: Same as Fig. 8.

Given the importance of 239Pu thermal fission for power-reactor applications,
the results obtained with JENDL-5 were further investigated to identify the
possible source of this overestimation. Decay-heat calculations will also be
sensitive to the fission-yield libraries, and therefore the decay-heat
calculations were repeated for 239Pu in terms of the same JEFF-3.3 decay-data
sub-library combined with three different fission-yield sub-libraries:
ENDF/B-VIII.0 fission yields, JEFF-3.3 fission yields, and JENDL-5 fission
yields. The results are shown in Fig. 12.

Figure 12: Comparison of the EM component of the decay heat of 239Pu thermal
fission obtained from calculations with the JEFF-3.3 decay-data sub-library
and three fission-yield sub-libraries (ENDF/B-VIII.0, JEFF-3.3 and JENDL-5).

As shown clearly in Fig. 12, adoption of the ENDF/B-VIII.0 and JEFF-3.3
fission-yield sub-libraries give similar results that agree reasonably well at
and around both peaks of the experimental decay-heat data, while the JENDL-5
fission-yield sub-library leads to a significant overestimation of the first
peak of decay heat at cooling times between 30 and 200 s, similar to the
results obtained with the JENDL-5 decay-data sub-library in Fig. 9. This
overestimation would appear to be associated with the fission yields rather
than the decay data, and is now being studied in detail with respect to the
planned release of improved fission-yield data in the foreseeable future
IAEA0817 . A further investigation of the impact of the fission yields on
decay-heat calculations was obtained with the JEFF-3.3 decay-data sub-library,
and is shown in Fig. 13 for 238U and 237Np fast fission. These two cases were
chosen because of the major differences observed between JEFF-3.3 and the
other two libraries in Figs. 8 to 11. One can see from Fig. 13 that the effect
of the three different fission-yield sub-libraries differs for the two
irradiated actinides. Adoption of JENDL-5 fission-yield sub-library leads to a
significant improvement for 238U fast fission at cooling times around the
first peak (i.e., 1 to 10 s cooling time); all three fission-yield sub-
libraries give similar results for 237Np fast fission at cooling times greater
than 80 s, while ENDF/B-VIII.0 deviates from JEFF-3.3 and JENDL-5 at shorter
cooling times between 3 and 50 s.

Figure 13: Comparison of light-particle decay heat of 238U fast fission and
electromagnetic decay heat of 237Np fast fission obtained from calculations
with the JEFF-3.3 decay-data sub-library and three fission-yield sub-libraries
(ENDF/B-VIII.0, JEFF-3.3 and JENDL-5).

A detailed study of the fission-yield sub-libraries and their impact on decay-
heat calculations is beyond the scope of this paper. Nevertheless,
international effort coordinated by the IAEA is ongoing with the aim of
updating and improving fission-yield data for the major actinides IAEA0817 .
We expect the output and conclusions of this effort will allow clear
conclusions to be drawn on the recommended fission-yield data to be used in
decay-heat calculations.

Both the nature and handling of uncertainties in the decay data and fission-
yield data also need to be considered. A full and respected treatment of these
uncertainties, including correlation effects identified with the fission-yield
data, would permit reliable and accurate assessments of the decay-data and
fission-yield sub-libraries, and draw definitive conclusions on the impact of
the TAGS data and the need and form of other additional measurements. Our
present results indicate certain trends in such calculations, but without
proper propagation of uncertainties they are not definitive. Ongoing efforts
to develop suitable approaches for propagating the uncertainties in decay-heat
calculations are expected to come to fruition in the near future, so that we
should eventually be able to perform uncertainty quantification of such
integral calculations with confidence.

##  6 Concluding remarks

Table LABEL:tab:5 constitutes a brief summary of the fission-product
radionuclides considered in defining the requirements for TAGS studies to
detect and quantify Pandemonium, as well as elaborate on the related needs for
$\gamma$ singles and $\gamma$-$\gamma$ coincidence measurements to improve the
definition of each individual decay scheme. Much greater detail, various
relevant information and fuller assessments are to be found within Tables 5
and 6:

  * •

relevant nuclear properties,

  * •

radionuclidic importance from the point of view of decay heat (based on each
fissile actinide as a function of cooling time), and

  * •

definitive recommendations as to whether to perform (or not perform) TAGS,
$\gamma$ singles and/or $\gamma$-$\gamma$ coincidence studies, each defined in
terms of priority from a highest of 1 decreasing to 2 and 3, or no assigned
priority at all.

Further extensive assessments need to accommodate consideration of the impact
of delayed neutrons on decay heat up to $\sim$ 10 seconds cooling time, along
with an awareness of other unrelated requirements such as antineutrino
spectral signatures and research studies within nuclear physics.

All of the recommendations constitute subjective judgements by individual
authors that when brought together in this manner will not necessarily be
fully consistent with each other. Taking these subjective judgements at face
value (Table LABEL:tab:5), the following experimental measurements would seem
to be most appropriate at the present time:

  * •

priority 1 TAGS/TAS and DGS $\gamma$ singles and $\gamma$-$\gamma$ (and
$\beta$-$\gamma$) coincidence measurements of the $\beta$- decay of 99Zr,
98,99Nb, 106Tc, 130m,132Sb, 138Cs and 142,143La;

  * •

priority 1 DGS measurements only of the $\beta$- decay of 100,100m,101,102Nb,
104,105,106Tc and 134I;

  * •

priority 2 TAGS/TAS and DGS measurements of the $\beta$- decay of 84As, 85Se,
84,89Br, 91Kr, 95Sr, 97Y, 105Nb, 103,104,105,107Mo, 107,108Tc, 133Sb,
136,137Te, 136,136mI, 140Xe, 139,140,141Cs, 141,143,144Ba and 144,147La;

  * •

priority 2 TAGS/TAS measurements only of the $\beta$- decay of 92,93,94Sr,
139Ba and 146Pr;

  * •

priority 2 DGS measurements only of the $\beta$- decay of 86,87,88Br, 89,90Kr,
90,90m,91,92,93Rb, 96,96mY, 100Zr, 102Mo, 102Tc, 130,131Sb, 133,133mTe,
132,135,137I and 139Xe.

However, requirements and priorities can be expected to change as such work
proceeds, so that consideration should also be given to some of the lesser
fission products of Table LABEL:tab:5 at later ill-defined stages of such
studies. One aim of this particular work has been to provide guidance in
improving our knowledge of the energy distribution between the light-particle
(LP) and electromagnetic (EM) components of decay heat. Along with the need to
assess properly the impact of delayed-neutron emissions on the fuel inventory
at early cooling times (LP decay heat vs EM decay heat at relatively short and
intermediate cooling times (up to 10 to 20 seconds)), we must ensure that
adopted fission-yield data are also fully fit for purpose in all of the
important decay-heat calculations. As was shown in the previous section, some
of the pronounced features in the calculated decay heat components (LP and EM)
are sensitive to fission-product yield data rather than the decay data.
Although the impact of the fission-yield sub-libraries (ENDF/B-VIII.0,
JEFF-3.3 and JENDL-5) on decay-heat calculations was found to vary within the
uncertainties of the experimental decay-heat data, larger discrepancies were
observed in the thermal decay heat of 239Pu and fast decay heat of 238U which
require further investigation. The impact of the energy dependence of the
fission-yield data on decay heat also merits further exploration. Envisaged
improvements in some of the more important decay data and their uncertainties
will inevitably necessitate better quality integral measurements of decay heat
to give conclusive comparisons and more precise benchmarking.

As for repeating this exercise at a future date, changes in the total decay
heat, LP and EM components will be relatively modest to small because much of
the relevant data should not subsequently alter much from year to year, or
even over ten years, when considering half-lives, Q-values and decay radiation
characteristics (i.e., key nuclear parameters in quantifying irradiated fuel
inventories to determine total decay heat). This statement contrasts with the
fission yields that are expected to improve significantly in the near future,
supported fully by a concerted international effort coordinated by the IAEA to
update the fission-yield database through consideration of all available
experimental data measured at advanced facilities with better precision and
higher resolution to be coupled with developments in modelling codes and more
extensive validation exercises IAEA0817 . Additional developments concerning
the uncertainties in the recommended decay-data and fission-yield libraries
should also include improved quantification of their correlation effects,
along with propagation within inventory and summation calculations. Therefore,
the current exercise should be repeated with improved fission-yield data
files, as well as with codes that can accommodate full analyses and
quantification of the overall uncertainties.

Assessments of the balance between performing further TAGS/TAS measurements or
direct $\gamma$ singles and/or $\beta$-$\gamma$, $\gamma$-$\gamma$ coincidence
spectral studies would appear best to depend upon the nature and degree of the
inconsistencies and Pandemonium effects revealed by the systematic application
of TAGS/TAS. Both types of measurement may be required, but there is always
the possibility that only one approach is merited at a particular time in
support or even contradiction of the other. Those undertaking calculations of
the resulting decay heat or antineutrino emissions require reasonably
comprehensive decay scheme data that are more reliably obtained directly, if
possible. Under such circumstances, TAGS/TAS has proven to be highly effective
at highlighting existing inadequacies within individual fission-product decay
schemes, and in doing so strongly supports $\gamma$ singles and coincidence
measurements by means of appropriate detector systems that may still be in the
process of evolution (and are not necessarily Ge based). There are existing
and will be future needs for TAGS/TAS studies that go hand-in-hand with
$\beta$- and $\gamma$-ray spectroscopy in order to improve various nuclear
parameters in a complementary manner for their confident adoption in the
evolution of nuclear physics research and a developing range of nuclear
applications that includes power-reactor decay heat on shutdown.

$Data~{}uncertainties$: Data and their uncertainties are presented throughout
the text and tables in the form 1234(x), where x is the uncertainty expressed
in terms of the last digit or digits quoted with respect to the measured or
evaluated number. This uncertainty is normally expressed at the 1$\sigma$
confidence level. Examples: 41.1(11) means 41.1$\pm$ 1.1, 6.783(8) means
6.783$\pm$0.008, 0.0820(17) means 0.0820$\pm$0.0017, 1.688(12)$\cdot 10^{-4}$
means (1.688$\pm$0.012)$\cdot 10^{-4}$, 26.3(+3-21) means
26.3${}_{-2.1}^{+0.3}$, and 8.681(+18-25) means 8.681${}_{-0.025}^{+0.018}$.

###### Acknowledgements.

The content and preparation of this paper involved both the work and support
of various individuals and their institutions. Our sincere thanks are extended
to all colleagues who have contributed to this IAEA technical project since
April 2005 when these studies were initially conceived and undertaken over a
two-year period until mid-2007 as an OECD/NEA Working Party on International
Evaluation Co-operation of the NEA Nuclear Science Committee. Furthermore, the
IAEA is grateful to all participant laboratories for their assistance in this
work since January 2009, and their support of individual staff to attend
subsequent working meetings and perform related analytical and experimental
activities. Futoshi Minato from the Japan Atomic Energy Agency is also
gratefully acknowledged for providing decay-heat calculations for the sixteen
fission systems studied herein, based on the recently released JENDL-5
libraries. Work described in this paper would not have been possible without
IAEA Member State contributions. Studies at ANL were supported by the US
Department of Energy, Office of Science, Office of Nuclear Physics, under
contract no. DE-AC02-06CH11357 and by the National Nuclear Security
Administration, Office of Defense Nuclear Nonproliferation R$\&$D (NA-22).
Work at ORNL was partially supported by the Office of Nuclear Physics, US
Department of Energy under Contract No. DE-AC05-00OR22725 and by the DOE
Nuclear Data Program, within the FOA 18 1903 project. Thanks are also due to
all collaborators who made these particular measurements possible - colleagues
at HRIBF-ORNL (D.W. Stracener) and ANL (G. Savard, D. Santiago-Gonzales, J.
Clark) for their continuous support and help, and in particular to PhD
students and associates who worked in the analysis of the data and made this
work possible including Toby T. King, Peng Shuai, Alexander Laminack (ORNL),
A. Fijałkowska, M. Wolińska-Cichocka, M. Stepaniuk (Warsaw University), Robert
Grzywacz, Michael Cooper (UTK) and Thomas Ruland (LSU). Work at BNL was
sponsored by the Office of Nuclear Physics, Office of Science of the US
Department of Energy under Contract No. DE-AC02-98CH10886 as well as by the US
Department of Energy, National Nuclear Security Administration, Office of
Defense Nuclear Nonproliferation Research and Development (DNN R&D). Work
undertaken by ALN was partially funded by the IAEA Nuclear Data Section under
Special Service Agreement no. TAL-NAPC20170620-001 (work package 2). Other
highly-related studies were supported by the CNRS challenge NEEDS and
associated NACRE project, CHANDA FP7/EURATOM project (contract no. 605203) and
SANDA project ref. 847552, the SAMPO program funded by the French Institute in
Finland as well as via the CNRS/IN2P3 PICS TAGS programme between SUBATECH and
IFIC, and Master projects Jyväskylä, OPALE and TAGS. The measurements included
in this work have also been supported by the Spanish Ministerio de Economía y
Competitividad under Grants No. FPA2011-24553, No. AIC-A-2011-0696, No.
FPA2014-52823-C2-1-P, No. FPA2015-65035-P, FPA2017-83946-C2-1-P, No.
FPI/BES-2014-068222, Ministerio de Ciencia e Innovacion PID2019-104714GB-C21
grant and the program Severo Ochoa (SEV-2014-0398), by the Spanish Ministerio
de Educación under the FPU12/01527 Grant, by the European Commission under the
European Return Grant, MERG-CT-2004-506849, and by the Junta para la
Ampliación de Estudios Programme (CSIC JAE-Doc contract) co-financed by FSE.
Also support from the STFC(UK) council grant ST/P005314/1 is acknowledged.
Thanks are due to all collaborators who participated in the measurements,
colleagues at IGISOL and the University of Jyväskylä for their continuous
support and help, and in particular PhD students and colleagues who made this
work possible and analysed the resulting data (D. Jordan, E. Valencia, S.
Rice, V.M. Bui, A.A. Zakari-Issoufou, V. Guadilla, L. Le Meur, J. Briz-Monago
and A. Porta).

##  Appendix A Assessment and reference tables

Table 5: Fission-product decay data: assessment of potential Pandemonium and
need for further TAGS and DGS (discrete gamma-ray spectroscopy involving
$\gamma$ singles and $\gamma$-$\gamma$ coincidence measurements) studies for
235U, 238,239,240Pu, 241Am and 243Cm thermal fission. Relevant references in
the literature are defined in NSR keynumber format (e.g., 2017Fi06 (NSR),
2016ORNL (equivalent non-NSR)). Spin, parity (Jπ) and half-life are from
NUBASE2020 NUBASE2020 . Q-value for ground state-to-ground state decay
(Q($\beta^{-}$)) and the neutron separation energy (Sn) are from AME2020
AME2020 . Q($\beta^{-}$) value for an excited isomer is reported as the sum of
the ground state-to-ground state decay and the excitation energy of the isomer
taken from NUBASE2020 NUBASE2020 . Beta-delayed neutron emission probabilities
Pn(%) are taken from the IAEA Reference Database for beta-delayed neutron
emission Liang ; Dimitriou2021 ; bdnIAEA . (a) Possible potential for
Pandemonium effect as a consequence of large energy differential $\Delta$
(keV) = (Q($\beta^{-}$) – excitation energy of highest known relevant nuclear
level); (b) FISPACT-II calculations of fission-product inventories and their
percentage decay-heat contributions as a function of the cooling time of
irradiated actinides Fleming2015 ; Fleming2015a ; Fleming2015b : fissile
actinide, (post-irradiation cooling time, %$\gamma$, %$\beta$, %(total decay
heat)), fission-product decay schemes assessed in terms of known $\beta$‒
decay and discrete nuclear levels of the daughter ENSDF ; (c) Request for
specific measurements denoted by $‘$y’ $\rightarrow$ ’yes’ ($‘$?’
$\rightarrow$ to be assessed further); (d) Priorities defined as 1
$\rightarrow$ high, 2 $\rightarrow$ intermediate, 3 $\rightarrow$ low, ‒
$\rightarrow$ unassigned.

Fission Jπ Half-life Q($\beta^{-}$) $\Delta$a Sn Assessment of potential
Pandemoniumb DGSc TAGSc Priorityd product (keV) (keV) (keV) 35-Br-86 (1‒)
55.1(4) s 7633(3) 865(3) 9856.7(20) 235U (100 s, 3.9%$\gamma$, 2.7%$\beta$,
3.3%); ENSDF (2015Ne01) reports 18 levels in 86Kr populated by $\beta$‒ decay,
but also many unplaced $\gamma$-rays. TAGS measurements support possibility of
Pandemonium (2014Fi09, 2016Ka65, 2017AlZY, 2017Fi06, 2017Ri08, 2018Fi03).
$\beta$‒-decay feeding intensity to 86Kr ground state ((1‒) $\rightarrow$ 0+
transition) of 15(8)% adopted in ENSDF (based on a value of $\approx$15%
derived from $\beta$‒-decay end-point studies), compared with a more precise
value of 20.23(11)% from TAGS (2017Ri08). DGS studies should be incorporated
into ENSDF (2016Ur04), followed by consideration of further DGS measurements.
y – 2 35-Br-87 5/2‒ 55.68(12) s 6818(3) 1025(3) 5515.17(25) 235U (100 s,
3.9%$\gamma$, 2.2%$\beta$, 3.1%); ENSDF (2015Jo11) reports 139 levels in 87Kr
populated by $\beta$‒ decay. TAGS measurements support possibility of
Pandemonium (2014VaZZ, 2015Ta17, 2016ORNL, 2017TaZZ, 2017Va04). $\beta$‒-decay
feeding intensity to 87Kr ground state (5/2‒ $\rightarrow$ 5/2+ transition) of
12.0(19)% adopted in ENSDF (based on %I$\gamma$(1419.7$\gamma$) = 22.0(15)%),
compared with 10.1% from TAGS (2017Va04). DGS studies merited. Pn(87Br) =
2.53(10)%. y – 2 35-Br-88 (1‒) 16.34(8) s 8975(4) 1976(4) 7053.1(26) 235U (10
s, 2.7%$\gamma$, 2.0%); ENSDF (2014Mc01) reports 59 levels in 88Kr populated
by $\beta$‒ decay. TAGS measurements support possibility of Pandemonium
(2015Ta17, 2016Ag03, 2016ORNL, 2017TaZZ, 2017Va04). $\beta$‒-decay feeding
intensity to 88Kr ground state ((1‒) $\rightarrow$ 0+ transition) of
$\textless$11% adopted in ENSDF (based on %I$\gamma$(775.3$\gamma$) =
62.5(36)% and %$\beta$${}^{-}_{n}$ = 6.58(18)%), compared with 4.7% from TAGS
(2017Va04). Comprehensive DGS studies merited. Pn(88Br) = 6.72(27)%. y – 2
36-Kr-87 5/2+ 76.3(5) min 3888.27(25) 64(8) 9922.11(20) 235U (5011 s,
4.2%$\beta$, 2.7%), (10000 s, 2.0%$\gamma$, 4.9%$\beta$, 3.1%), 239Pu (10000
s, 2.4%$\beta$), 240Pu (10000 s, 2.3%$\beta$); ENSDF (2015Jo11) reports 14
levels in 87Rb populated by $\beta$‒ decay. TAGS measurements not reported,
with a low potential for Pandemonium given the small $\Delta$ energy
differential. $\beta$‒-decay feeding intensity to 87Rb ground state (5/2‒
$\rightarrow$ 5/2+ transition) of 30.5(22)% adopted in ENSDF. – – – 36-Kr-88
0+ 2.825(19) h 2917.7(26) 147(3) 6082.52(16) 235U (5011 s, 3.7%$\gamma$,
2.7%), (10000 s, 6.7%$\gamma$, 4.8%), 238Pu (10000 s, 2.6%$\gamma$), 239Pu
(10000 s, 2.9%$\gamma$, 2.1%), 240Pu (10000 s, 2.4%$\gamma$); ENSDF (2014Mc01)
reports 24 levels in 88Rb populated by $\beta$‒ decay. TAGS measurements have
provided the means of determining the ground-state to ground-state beta
transition of 12.9(25)% with improved precision (2022Sh20). Low potential for
Pandemonium given the relatively small $\Delta$ energy differential.
$\beta$‒-decay feeding intensity to 88Rb ground state (0+ $\rightarrow$ 2‒
transition) of 14(4)% adopted in ENSDF. – – – 36-Kr-89 3/2+ 3.15(4) min
5177(6) 491(6) 7175(5) 235U (100 s, 3.2%$\gamma$, 2.8%$\beta$, 3.0%); ENSDF
(2013Si03) reports 57 levels in 89Rb populated by $\beta$‒ decay. TAGS
measurements in support of existence of Pandemonium (2014Fi11/2017Fi06).
$\beta$‒-decay feeding intensity to 89Rb ground state (3/2+ $\rightarrow$ 3/2‒
transition) of 23(4)% adopted in ENSDF, but factor of two smaller value of
11(1)% determined from TAGS (2017Fi06). Comprehensive DGS studies merited. y –
2

Table 5:  – Continued from previous page

Fission Jπ Half-life Q($\beta^{-}$) $\Delta$a Sn Assessment of potential
Pandemoniumb DGSc TAGSc Priorityd product (keV) (keV) (keV) 36-Kr-90 0+
32.32(9) s 4406(7) 525(7) 5724(8) 235U (100 s, 2.4%$\gamma$, 2.8%$\beta$,
2.6%); ENSDF (2020Ba21) reports 32 levels in 90Rb populated by $\beta$‒ decay.
TAGS measurements in support of existence of Pandemonium (2017Fi06).
$\beta$‒-decay feeding intensity to 90Rb ground state (0+ $\rightarrow$ 0‒
transition) of 29(4)% adopted in ENSDF, but factor of four smaller value of
7(1)% determined from TAGS (2017Fi06). Comprehensive DGS studies merited. y –
2 36-Kr-91 5/2+ 8.57(4) s 6771(8) 2073(8) 6451(10) 235U (10 s, 3.6%$\gamma$,
3.3%$\beta$, 3.4%); ENSDF (2013Ba52) reports 61 levels in 91Rb populated by
$\beta$‒ decay. TAGS measurements not reported, although potential for
Pandemonium supported by large $\Delta$ energy differential. $\beta$‒-decay
feeding intensity to 91Rb ground state (5/2+ $\rightarrow$ 3/2(‒) transition)
of 9(4)% adopted in ENSDF. Merits studies by means of TAGS and DGS. y y 2
37-Rb-88 2‒ 17.78(3) min 5312.62(16) 459.6(2) 11112.870(6) 235U (5011 s,
6.4%$\beta$, 3.3%), (10000 s, 2.6%$\gamma$, 11.7%$\beta$, 6.3%), 238Pu (5011
s, 2.5%$\beta$), (10000 s, 4.9%$\beta$, 2.5%), 239Pu (5011 s, 2.7%$\beta$),
(10000 s, 5.4%$\beta$, 2.8%), 240Pu (5011 s, 2.2%$\beta$), (10000 s,
4.6%$\beta$, 2.3%), 241Am (10000 s, 3.2%$\beta$), 243Cm (10000 s,
3.0%$\beta$); ENSDF (2014Mc01) reports 14 levels in 88Sr populated by $\beta$‒
decay. TAGS measurements have provided the means of determining the ground-
state to ground-state beta transition of 78.2(20)% (2022Sh20). Low potential
for Pandemonium given the relatively small $\Delta$ energy differential.
$\beta$‒-decay feeding intensity to 88Sr ground state (2‒ $\rightarrow$ 0+
transition) of 76.51(11)% adopted in ENSDF. – – – 37-Rb-89 3/2‒ 15.32(10) min
4497(5) 403(5) 6358.72(9) 235U (1000 s, 8.9%$\gamma$, 4.5%$\beta$, 6.9%),
(5011 s, 2.4%$\gamma$, 2.1%), 238Pu (1000 s, 2.7%$\gamma$, 2.2%), 239Pu (1000
s, 3.2%$\gamma$, 2.5%), 240Pu (1000 s, 3.3%$\gamma$, 2.6%), 241Am (1000 s,
2.1%$\gamma$); ENSDF (2013Si03) reports 19 levels in 89Sr populated by
$\beta$‒ decay. TAGS measurements by 1996Gr20/1997Gr09 (no uncertainties
assigned to $\beta$‒-decay feeding intensities) and 2017Fi06 furnish evidence
of minor Pandemonium. $\beta$‒-decay feeding intensity to 89Sr ground state
(3/2‒ $\rightarrow$ 5/2+ transition) of 18.8(13)% from TAGS
(1996Gr20,1997Gr09) adopted in ENSDF. ‒ ‒ – 37-Rb-90 0‒ 158(5) s 6585(6)
962(6) 7813.2(15) 235U (100 s, 4.8%$\gamma$, 4.7%$\beta$, 4.7%), 238Pu (100 s,
2.4%$\gamma$, 2.0%$\beta$, 2.2%); ENSDF (2020Ba21) reports 35 levels in 90Sr
populated by $\beta$‒ decay. TAGS measurements by 1996Gr20/1997Gr09 (no
uncertainties assigned to $\beta$‒-decay feeding intensities) and 2017Fi06
furnish evidence of modest Pandemonium. $\beta$‒-decay feeding intensity to
90Sr ground state (0‒ $\rightarrow$ 0+ transition) of 33(4)% from TAGS
(1996Gr20,1997Gr09)) adopted in ENSDF. $\beta$‒-decay feeding intensity to
831.68-keV excited level (0‒ $\rightarrow$ 2+ transition) of 26(2)% adopted in
ENSDF, compared with 15(1)% (2017Fi06) and 13.12% (1997Gr09) from TAGS.
Comprehensive DGS measurements merited, with unambiguous separation between
ground-state and isomer $\beta$‒ decays. y ‒ 2 37-Rb-91 3/2‒ 58.2(3) s 5907(9)
1114(9) 5772(6) 235U (10 s, 2.0%$\gamma$), (100 s, 8.9%$\gamma$, 5.2%$\beta$,
7.2%), 238Pu (100 s, 4.9%$\gamma$, 2.5%$\beta$, 3.7%), 239Pu (100 s,
4.2%$\gamma$, 2.2%$\beta$, 3.2%), 240Pu (100 s, 4.0%$\gamma$, 2.2%$\beta$,
3.1%), 241Am (100 s, 3.2%$\gamma$, 2.4%), 243Cm (100 s, 2.8%$\gamma$, 2.1%);
ENSDF (2013Ba52) reports 37 levels in 91Sr populated by $\beta$‒ decay. TAGS
measurements by 1996Gr20/1997Gr09 (no uncertainties assigned to $\beta$‒-decay
feeding intensities), 2017AlZY and 2017Ri08 exhibit evidence of Pandemonium.
Direct $\beta$‒ decay feeding intensities of 2(5)% to the ground state (3/2‒
$\rightarrow$ 5/2+ transition) and 24(5)% to the 93.628-keV level (3/2‒
$\rightarrow$ (3/2)+ transition) of 91Sr adopted in ENSDF, compared with
9.21(5)% and 12.11(7)% from TAGS (2017Ri08), respectively. Combined $\beta$‒
decay feeding intensity of 17.4(39)% to ground state and 93.628-keV level in
91Sr also determined by TAGS (1996Gr20). Comprehensive DGS studies merited. y
‒ 2

Table 5:  – Continued from previous page

Fission Jπ Half-life Q($\beta^{-}$) $\Delta$a Sn Assessment of potential
Pandemoniumb DGSc TAGSc Priorityd product (keV) (keV) (keV) 37-Rb-92 0‒
4.48(3) s 8095(6) 732(6) 7287(6) 235U (10 s, 7.0%$\gamma$, 6.6%$\beta$, 6.7%),
238Pu (10 s, 4.0%$\gamma$, 3.9%$\beta$, 3.9%), 239Pu (10 s, 3.6%$\gamma$,
3.4%$\beta$, 3.5%), 240Pu (10 s, 3.7%$\gamma$, 3.5%$\beta$, 3.6%), 241Am (10
s, 2.6%$\gamma$, 2.6%$\beta$, 2.6%), 243Cm (10 s, 2.0%$\gamma$, 2.0%$\beta$,
2.0%); ENSDF (2012Ba51) reports 21 levels in 92Sr populated by $\beta$‒ decay.
TAGS measurements by 2014ZaZZ, 2015Za10, 2016Ra25, 2017FaZY, 2017Fi06,
2017Ra06 support existence of Pandemonium. $\beta$‒-decay feeding intensity to
92Sr ground state (0‒ $\rightarrow$ 0+ transition) of 95.2(7)% adopted in
ENSDF, compared with 87.5(25)% (2015Za10) and 91(3)% (2016Ra25) from TAGS.
Comprehensive DGS studies merited. Pn(92Rb) = 0.0109(7)%. y – 2 37-Rb-93 5/2‒
5.84(2) s 7466(9) 759(9) 5290(8) 235U (10 s, 5.7%$\gamma$, 3.4%$\beta$, 4.3%),
238Pu (10 s, 3.0%$\gamma$, 2.3%), 239Pu (10 s, 3.5%$\gamma$, 2.1%$\beta$,
2.7%), 240Pu (10 s, 4.4%$\gamma$, 2.6%$\beta$, 3.4%), 241Am (10 s,
2.3%$\gamma$); ENSDF (2011Ba40) reports 76 levels in 93Sr populated by
$\beta$‒ decay. TAGS measurements by 1996Gr20/1997Gr09 (no uncertainties
assigned to $\beta$‒-decay feeding intensities), 2016ORNL, 2017TaZS, 2017TaZZ
support existence of Pandemonium. $\beta$‒-decay feeding intensity to 93Sr
ground state (5/2‒ $\rightarrow$ 5/2+ transition) of 35(3)% adopted in ENSDF,
compared with 32.6(24)% from TAGS (1996Gr20). Comprehensive DGS measurements
merited to cover the full decay scheme, particularly depopulation (if any) of
93Sr nuclear levels below 1240 keV and higher-energy nuclear levels above 4000
keV. Pn(93Rb) = 1.60(10)%. y – 2 38-Sr-91 5/2+ 9.65(6) h 2699(5) 127(5)
7925.7(19) 235U (10000 s, 2.0%$\gamma$, 2.6%$\beta$, 2.2%); ENSDF (2013Ba52)
reports 16 levels in 91Y populated via $\beta$‒ decay. TAGS studies not
reported, with low potential for Pandemonium based on small $\Delta$ energy
differential. $\beta$‒-decay feeding intensity to 91Y ground state (5/2+
$\rightarrow$ 1/2‒ transition) of 28.6(22)% adopted in ENSDF on the basis of
values of 30.8% (1973Ha11) and 26.4% (1953Am08) determined from measurements
of $\beta$‒-decay end-point energies, although uncertainties unquantified.
Ill-defined $\beta$‒-decay branch to 91mY isomeric state at 555.58 keV (5/2+
$\rightarrow$ 9/2+ transition), which depopulates via IT decay. More complete
DGS studies merited. y – 3 38-Sr-92 0+ 2.611(17) h 1949(9) 565(9) 6537(9) 235U
(5011 s, 4.5%$\gamma$, 3.1%), (10000 s, 8.0%$\gamma$, 5.5%), 238Pu (5011 s,
2.6%$\gamma$), (10000 s, 5.0%$\gamma$, 3.6%), 239Pu (5011 s, 2.5%$\gamma$),
(10000 s, 5.0%$\gamma$, 3.6%), 240Pu (5011 s, 2.2%$\gamma$), (10000 s,
4.8%$\gamma$, 3.4%), 241Am (10000 s, 3.8%$\gamma$, 2.7%), 243Cm (10000 s,
2.8%$\gamma$, 2.0%); ENSDF (2012Ba51) reports 5 levels in 92Y populated via
$\beta$‒ decay. Strongest feed of 97(6)% to level at 1383.90-keV (0+
$\rightarrow$ 1+ transition) adopted in ENSDF. TAGS studies not reported, with
modest potential for Pandemonium based on relatively small $\Delta$ energy
differential. Ill-defined $\beta$‒-decay feeding intensity to 92Y ground state
(0+ $\rightarrow$ 2‒ transition) of $\textless$8% adopted in ENSDF. TAGS
measurements would be beneficial. – y 2

Table 5:  – Continued from previous page

Fission Jπ Half-life Q($\beta^{-}$) $\Delta$a Sn Assessment of potential
Pandemoniumb DGSc TAGSc Priorityd product (keV) (keV) (keV) 38-Sr-93 5/2+
7.43(3) min 4141(12) 246(12) 7482(14) 235U (100 s, 2.7%$\gamma$, 2.0%), (1000
s, 9.2%$\gamma$, 3.9%$\beta$, 6.8%), 238Pu (100 s, 2.2%$\gamma$), (1000 s,
4.9%$\gamma$, 2.2%$\beta$, 3.7%), 239Pu (100 s, 2.0%$\gamma$), (1000 s,
5.4%$\gamma$, 2.4%$\beta$, 4.0%), 240Pu (1000 s, 5.4%$\gamma$, 2.4%$\beta$,
4.0%), 241Am (1000 s, 4.0%$\gamma$, 2.9%), 243Cm (1000 s, 2.5%$\gamma$): ENSDF
(2011Ba40) reports 35 levels in 93Y populated via $\beta$‒ decay. TAGS
measurements (1996Gr20/1997Gr09), although no uncertainties assigned to
$\beta$‒-decay feeding intensities. Potential for Pandemonium judged to be low
given relatively small $\Delta$ energy differential. Ill-defined direct
$\beta$‒ feeding to the 93Y ground state (5/2+ $\rightarrow$ 1/2‒ transition)
of $\leq$4.5% adopted in ENSDF. Combined $\beta$‒ decay feeding to ground and
758.7-keV isomeric state (half-life of 0.82(4) s; 5/2+ $\rightarrow$ 9/2+
transition) of 5.8(14)% reported from TAGS (1996Gr20/1997Gr09). Further TAGS
studies merited. – y 2 38-Sr-94 0+ 75.3(2) s 3506(6) 537(6) 6196(12) 235U (100
s, 4.7%$\gamma$, 3.2%$\beta$, 4.0%), 238Pu (100 s, 4.4%$\gamma$, 2.6%$\beta$,
3.5%), 239Pu (100 s, 3.6%$\gamma$, 2.2%$\beta$, 2.9%), 240Pu (100 s,
3.3%$\gamma$, 2.7%), 241Am (100 s, 3.5%$\gamma$, 2.7%), 243Cm (100 s,
2.1%$\gamma$); ENSDF (2006Ab37) reports 9 levels in 94Y populated via $\beta$‒
decay. TAGS studies, although no uncertainties assigned to $\beta$‒-decay