# Investigation of 11B and 40Ca levels at $8$$-$$9$ MeV by Nuclear Resonance
Fluorescence

D. Gribble  Department of Physics & Astronomy, University of North Carolina at
Chapel Hill, NC 27599-3255, USA  Triangle Universities Nuclear Laboratory
(TUNL), Duke University, Durham, North Carolina 27708, USA  C. Iliadis
Department of Physics & Astronomy, University of North Carolina at Chapel
Hill, NC 27599-3255, USA  Triangle Universities Nuclear Laboratory (TUNL),
Duke University, Durham, North Carolina 27708, USA  R.V.F. Janssens
Department of Physics & Astronomy, University of North Carolina at Chapel
Hill, NC 27599-3255, USA  Triangle Universities Nuclear Laboratory (TUNL),
Duke University, Durham, North Carolina 27708, USA  U. Friman-Gayer  Triangle
Universities Nuclear Laboratory (TUNL), Duke University, Durham, North
Carolina 27708, USA  Department of Physics, Duke University, Durham, North
Carolina 27708-0308, USA  Krishichayan  Triangle Universities Nuclear
Laboratory (TUNL), Duke University, Durham, North Carolina 27708, USA
Department of Physics, Duke University, Durham, North Carolina 27708-0308, USA
S. Finch  Triangle Universities Nuclear Laboratory (TUNL), Duke University,
Durham, North Carolina 27708, USA  Department of Physics, Duke University,
Durham, North Carolina 27708-0308, USA

###### Abstract

We report on the measurement of 11B and 40Ca levels between excitation
energies of $8$ and $9$ MeV using nuclear resonance fluorescence (NRF). The
experiment was carried out with nearly-monoenergetic and linearly polarized
photon beams provided by the High-Intensity $\gamma$-ray Source (HI$\gamma$S)
facility at the Triangle Universities Nuclear Laboratory (TUNL). States in 11B
are important for calibrations of NRF measurements, while the properties of
40Ca levels impact potassium nucleosynthesis in globular clusters. For 40Ca,
we report on improved excitation energies and an unambiguous $2^{-}$
assignment for the state at $8425$ keV. For 11B, we obtained improved values
for $\gamma$-ray multipolarity mixing ratios and branching ratios of the
$8920$-keV level.

##  I Introduction

Nuclear resonance fluorescence (NRF) experiments using linearly polarized
$\gamma$-ray beams allow for the measurement of level energies and widths,
spins, parities, multipolarity mixing ratios, and branching ratios, and,
therefore, represent an important tool for probing nuclear structure Kneissl
_et al._ (1996); Pietralla  _et al._ (2003); Zilges  _et al._ (2022). These
properties are equally important for nuclear astrophysics, since they enter
either directly in the determination of thermonuclear reaction rates, or
indirectly via energy and efficiency calibrations. For example, the impact of
such measurements on the rate of the 22Ne $+$ $\alpha$ s-process neutron
source reactions has been demonstrated by Longland et al. Longland  _et al._
(2009). In the latter work, only dipole excitations were observed, mostly by
measuring deexcitations to the 26Mg ground state.

The goal of the present work was primarily to investigate what else can be
learned for nuclear astrophysics from NRF experiments. We report here on a
measurement of 11B and 40Ca levels at energies between $8$ and $9$ MeV. Levels
in the former nucleus are interesting because they often provide energy and
efficiency calibrations for NRF experiments Rusev  _et al._ (2009). States in
the latter represent low-energy resonances in the 39K(p,$\gamma$)40Ca reaction
Longland  _et al._ (2018), which is of relevance for nucleosynthesis in
globular clusters Iliadis  _et al._ (2016); Dermigny and Iliadis (2017). While
the present results will likely not significantly impact the 39K $+$ $p$
reaction rate, improved information on the nuclear structure of 11B and 40Ca
was obtained.

In Sec. II, we describe our experimental procedure. Excitation energies and
spin-parity assignments to 40Ca levels are presented in Sec. III.
Multipolarity mixing ratios of levels in 11B are discussed in Sec. IV. Section
V provides a concluding summary. In Appendix A, we comment on phase
conventions. A reanalysis of literature data pertaining to 11B levels is given
in App. B. Our energy calibration procedure is presented in App. C.

##  II Experimental procedure

The experiment was performed with the High-Intensity $\gamma$-ray Source
(HI$\gamma$S) at the Triangle Universities Nuclear Laboratory (TUNL). Nearly-
monoenergetic photon beams were produced by Compton backscattering of laser
photons from relativistic electrons in a storage ring. The photon beams were
linearly polarized, with the polarization vector pointing parallel to the
horizontal direction. The HI$\gamma$S facility is described in detail in Ref.
Weller  _et al._ (2009).

The beam-defining lead collimator had a $19.05$-mm diameter and a $15.24$-cm
length. Incident $\gamma$-ray beam energies used during the experiment were
$8.4$, $8.6$, and $8.8$ MeV. The beam energy profile had a spread of
approximately $300$ keV at full width at half maximum (FWHM). The beam
irradiated a target, which was secured inside a plexiglass vacuum tube to
reduce background counts from incident photons scattering on air. Two targets
were used. The first consisted of boron powder ($\approx 2.1$ g), and the
second of high-purity CaO powder ($\approx 6.8$ g) containing at least
$99.95\%$ CaO by mass. The target materials were placed in cylindrical
polycarbonate containers, with outer dimensions of $2.2\,\mathrm{cm}$
diameter, $2.0\,\mathrm{cm}$ length, and $0.1\,\mathrm{cm}$ wall thickness.

Scattered $\gamma$ rays were detected using an array of three HPGe detectors –
two (n-type) with $60\%$ and one (p-type) with $100\%$ relative efficiency
(see Fig. 1). The two $60\%$ HPGe detectors were placed in a plane
perpendicular to the beam, with a polar scattering angle of $\theta$ $=$
$90^{\circ}$, and azimuthal angles of $\phi$ $=$ $180^{\circ}$ and
$90^{\circ}$, as measured from the vertical direction. The $100\%$ HPGe
detector was arranged at $\theta$ $=$ $135^{\circ}$ and $\phi$ $=$
$90^{\circ}$. The $60\%$ and $100\%$ detectors were placed at a distance from
the center of the target of $10.28$ and $15.24$ cm, respectively. All
detectors were surrounded by passive shields made of copper and lead to reduce
low-energy backgrounds.

Figure 1:  Setup used for the present experiment. The incident $\gamma$-ray
beam moves inside a plexiglass vacuum tube and impinges on a sample (boron
powder or CaO). The direction of the linear polarization of the beam points
parallel to the horizontal plane. The dewars of the two 60% (D1 and D2) and
the 100% (D3) HPGe detectors are colored green and blue, respectively. The
front face of each detector is covered by a passive shield (yellow) to reduce
backgrounds. For reference, the pairs of polar and azimuthal angles,
($\theta$, $\phi$), are depicted for each detector. The gray parts indicate
the mechanical support structure of the setup.

For $\gamma$-ray energies below 3.5 MeV, detector energy and efficiency
calibrations were performed with 60Co, 152Eu, and 56Co sources. In addition,
precisely-known $\gamma$-ray energies from the decays of the $E_{x}$ $=$
$6792$ and $8920$-keV levels in 11B were used for energy calibration. Monte
Carlo particle simulations were performed with the Geant4 toolkit Agostinelli
_et al._ (2003); Allison  _et al._ (2006, 2016) to extend the efficiency curve
to higher energies. The simulated geometry included the detectors and their
shielding, the plexiglass tube, and the radioactive source or target from
which the gamma rays were emitted. All measured peak intensities were
corrected for detector efficiency, dead time, and solid-angle attenuation
effects, by using a combination of the radioactive source measurements and
Geant4 simulations.

The two-step angular correlation is given by Iliadis and Friman-Gayer (2021)

$\displaystyle
W(\theta,\phi)=A_{0}(1)A_{0}(2)+\sum\limits_{n=2,4,...}A_{n}(2)Q_{n}(k)~{}\times$
$\displaystyle\left[A_{n}(1)P_{n}(\cos\theta)+P_{\gamma}E_{n}(1)P_{n}^{|2|}(\cos\theta)\cos(2\phi)\right]$
(1)

with (1) and (2) labeling the excitation and deexcitation transition,
respectively; $\theta$ is the (polar) angle between the incident and emitted
$\gamma$ rays; $\phi$ is the (azimuthal) angle between the vertical axis and
the projection of the emitted $\gamma$-ray linear momentum onto the plane
perpendicular to the incident beam direction; $A_{n}$ and $E_{n}$ are
theoretical coefficients (see, e.g., Ref. Iliadis and Friman-Gayer (2021))
that depend on the quantum numbers and multipolarity mixing ratios involved in
the transition; and $P_{n}$ and $P_{n}^{|2|}$ are the unassociated and
associated Legendre functions, respectively. Equation (II) contains two
quantities that correct for experimental artifacts: $Q_{n}(k)$, the solid-
angle attenuation factor of detector $k$, and $P_{\gamma}$, the degree of
polarization.

The $Q$ coefficients were calculated using Geant4 by recording the initial
$\gamma$-ray emission angle for each event depositing its full energy in a
given detector. The attenuation coefficient of order $n$ is given by Camp and
Van Lehn (1969)

$Q_{n}=\frac{1}{N}\sum_{j=1}^{N}P_{n}(\cos\alpha_{j})$ (2)

with $N$ denoting the number of detected events. The initial $\gamma$-ray
emission angle, $\alpha_{j}$, of the $j$th detected event is defined relative
to a line connecting the center of the target to the center of the detector.

The beam polarization was determined by measuring the pronounced angular
correlation of the $0$ keV $\rightarrow$ $8579$ keV $(2^{+})$ $\rightarrow$
$0$ keV sequence in 40Ca. We find a linear polarization of $\geq$99%, and
assumed for the subsequent analysis a value of $100$%.

For visualizing the measured angular correlations, we introduce two
quantities: the first is the analyzing power at $\theta$ $=$ $90^{\circ}$,
defined by Iliadis and Friman-Gayer (2021)

$A(\theta=90^{\circ})=\frac{W(90^{\circ},180^{\circ})-W(90^{\circ},90^{\circ})}{W(90^{\circ},180^{\circ})+W(90^{\circ},90^{\circ})}$
(3)

and the second is the ratio, $R$, involving the detector at ($\theta$, $\phi$)
$=$ (135∘, 90∘),

$R=\frac{W(135^{\circ},90^{\circ})}{W(90^{\circ},180^{\circ})+W(90^{\circ},90^{\circ})}.$
(4)

Below, we will display our data, together with theoretical predictions, in the
$R$ vs. $A$ plane.

For the extraction of multipolarity mixing ratios, previous works have
frequently applied an approximate analysis procedure (see, e.g., Ref. Rusev
_et al._ (2009)). With this “min-max” method, each calculation is performed
three times, i.e., for the mean value of the measured analyzing power and for
both of its experimental bounds. The range of mixing-ratio values is then
obtained from the intersections of the measured analyzing power (1$\sigma$
region) with the theoretically predicted curve. This procedure is not rigorous
from a statistical point of view, and can lead to unreliable results,
especially if the 1$\sigma$ uncertainties of the measured analyzing powers are
significant. In this work, we will instead analyze the data using a rigorous
method based on Bayesian statistics, and estimate mixing ratio values from
posterior probability densities Hilbe  _et al._ (2017).

##  III Results for 40Ca

###  III.1 Excitation energies

One goal of the present work was to derive precise excitation energies of 40Ca
levels that may contribute to the 39K(p,$\gamma$)40Ca thermonuclear reaction
rate. Consider, as an example, the $96$-keV resonance (center-of-mass energy),
corresponding to the $8425$-keV level (see Tab. 1), which dominates the total
reaction rates in the temperature region of $20$ $-$ $80$ MK (see Fig. 5 in
Ref. Longland  _et al._ (2018)). If the energy of this resonance is varied by,
say, $0.5$ keV (or $1.0$ keV), and all other parameters are kept at their same
values, the total rate at $40$ MK would change by $16$% (or $34$%). This
sensitivity results from the fact that the energies enter exponentially in the
expression of the narrow-resonance reaction rates Iliadis (2015), and
emphasizes the importance of a reliable energy calibration. Our calibration
procedure is described in detail in App. C. Results for 40Ca level energies
are listed in Tab. 1 and compared to previous values provided by the Evaluated
Nuclear Structure Data File (ENSDF) Chen (2017).

Present (column 3) and previous (column 4) measured $\gamma$-ray energies
agree within 1$\sigma$ only for the $8092$ keV $(2^{+})$ $\rightarrow$ $0$ keV
transition, although our uncertainty is significantly larger. For the $8425$
keV $(2^{-})$ $\rightarrow$ $3737$ keV transition, no uncertainty is provided
in Ref. Chen (2017) in its table of “adopted Levels, Gammas” (however, see
footnote “g” in Tab. 1). For the remaining three transitions, $8579$ keV
$(2^{+})$ $\rightarrow$ $0$ keV, $8748$ keV $(2^{+})$ $\rightarrow$ $0$ keV,
and $8982$ keV $(2^{+})$ $\rightarrow$ $0$ keV, our $\gamma$-ray energies have
smaller uncertainties compared to the evaluation of Ref. Chen (2017).

We derived 40Ca excitation energies by applying the recoil correction to the
measured $\gamma$-ray energies. No corrections for Doppler shifts were needed
because the detector was located at an angle of $\theta$ $=$ $90^{\circ}$. The
results are listed in column 5 of Tab. 1. Column 6 provides the literature
values, which represent the evaluated and recommended values based on a number
of previous experiments. The differences, $E_{x}^{\text{present}}$ $-$
$E_{x}^{\text{ENSDF}}$, are displayed in Fig. 2. As was the case for the
$\gamma$-ray energies, the present and previous excitation energies agree
within 1$\sigma$ only for the $8092$ keV $(2^{+})$ level (label “1”). For the
$8982$ keV $(2^{+})$ state (label “5”), the mean values differ by $1.3$ keV
and our uncertainty ($\pm 0.35$ keV) is smaller than the previously evaluated
result ($\pm 0.5$ keV).

Table 1: 40Ca excitation energies. Level111Level numbers correspond to those shown in Fig. 2. | Transition (keV) |  $E_{\gamma}^{\text{present}}$ (keV)222Values do not include the recoil correction; no correction for the Doppler shift is required (see text). |  $E_{\gamma}^{\text{ENSDF}}$ (keV)666According to Ref. Chen (2017), “…values with uncertainties are averaged values from different $\gamma$-ray studies. A large number of values without uncertainties are from 39K(p,$\gamma$), which are from level-energy differences since most $\gamma$-ray energies are not available.” |  $E_{x}^{\text{present}}$ (keV)555Present results; uncertainties include those for peak centroids and the energy calibration (common uncertainty: $\pm 0.10$ keV). |  $E_{x}^{\text{ENSDF}}$ (keV)666According to Ref. Chen (2017), “…values with uncertainties are averaged values from different $\gamma$-ray studies. A large number of values without uncertainties are from 39K(p,$\gamma$), which are from level-energy differences since most $\gamma$-ray energies are not available.”
---|---|---|---|---|---
1 |  $8092$ $(2^{+})$ $\rightarrow$ $0$ | 8090.49$\pm$0.51 | 8090.6$\pm$0.2 | 8091.37$\pm$0.51 | 8091.61$\pm$0.17
2 |  $8425$ $(2^{-})$ $\rightarrow$ $3737$ | 4687.37$\pm$0.31 | 4687.8777Ref. Chen (2017) lists $4688.2\pm 1.5$ keV from (p,p${}^{\prime}\gamma$) in the comment section of their table. | 8424.35$\pm$0.31888Calculated from the $\gamma$-ray energy in column 3, the recoil correction, and the energy of the final excited state, $E_{x}$ $=$ $3736.69\pm 0.05$ keV Chen (2017). | 8424.81$\pm$0.11
3 |  $8579$ $(2^{+})$ $\rightarrow$ $0$ | 8578.10$\pm$0.14333Weighted average of independent measurements performed at three different incident beam energies. | 8577.7$\pm$0.2 | 8579.08$\pm$0.14 | 8578.80$\pm$0.09
4 |  $8748$ $(2^{+})$ $\rightarrow$ $0$ | 8747.55$\pm$0.19444Weighted average of independent measurements performed at two different incident beam energies. | 8748.4$\pm$0.2 | 8748.59$\pm$0.19 | 8748.22$\pm$0.09
5 |  $8982$ $(2^{+})$ $\rightarrow$ $0$ | 8980.13$\pm$0.35 | 8981.4$\pm$0.5 | 8981.21$\pm$0.35 | 8982.5$\pm$0.5
Figure 2:  Excitation energies of 40Ca levels observed in the present work
(red circles) as compared to the previously evaluated results Chen (2017)
(blue squares). For better comparison, the ordinate refers to the difference
relative to the previous mean value. The state labels on the abscissa
correspond to those listed in column 1 of Tab. 1.

###  III.2 Spin-parity of the $8425$-keV state

The $8425$-keV level in 40Ca corresponds to a $p$-wave resonance in the
39K(p,$\gamma$)40Ca reaction at a center-of-mass energy of $96$ keV. The spin-
parity is listed as $J^{\pi}$ $=$ $2^{-}$ in Ref. Chen (2017), and the level
decays mainly to the $3737$-keV ($3^{-}$) state. The $8425$-keV level
dominates the thermonuclear reaction rates below a stellar temperature of
$100$ MK (see Fig. 5 in Ref. Longland  _et al._ (2009)). If this level had
$J^{\pi}$ $=$ $2^{+}$ instead, it would correspond to an $s$-wave resonance,
implying a dominant 39K(p,$\gamma$)40Ca rate contribution at even higher
temperatures. In addition, a $2^{+}$ (natural parity) assignment would imply a
contribution to the 39K(p,$\alpha$)36Ar rate. Since this spin-parity
assignment has significant implications for potassium nucleosynthesis in
globular cluster stars Iliadis  _et al._ (2016), it must be considered
carefully.

Arguments for a $2^{-}$ assignment to the $8425$-keV level are presented by
ENSDF Chen (2017). They are based on measurements of the
41Ca(3He,$\alpha$)40Ca pick-up reaction Cline  _et al._ (1974), 39K(d,n)40Ca
Fuchs  _et al._ (1969) and 39K(3He,d)40Ca Erskine (1966); Seth  _et al._
(1967) transfer reactions, inelastic scattering of polarized protons Hosono
_et al._ (1982); Horen  _et al._ (1985), and inelastic electron scattering
Steffen  _et al._ (1980). However, neither the $\ell$ $=$ $2$ transfer
observed in Ref. Cline  _et al._ (1974), nor the mixed transfer of $\ell$ $=$
$1$ $+$ $3$ observed in Ref. Fuchs  _et al._ (1969) result unambiguously in a
$2^{-}$ assignment. Erskine Erskine (1966) reports a preliminary assignment of
“($2^{-}$),” but locates the level at $8465\pm 12$ keV, about $40$ keV higher
than the values listed in Tab. 1. He states that, because of many contaminant
peaks in this region of the spectrum, “identification of the (…) $8.465$-MeV
levels as states in 40Ca is a little uncertain.” Seth et al. Seth  _et al._
(1967) reported a $2^{-}$ assignment, but the fact that their angular
distribution data were consistent with an $\ell$ $=$ $3$ fit does not
unambiguously determine the spin-parity. Furthermore, they write
“Unfortunately, the shape of the measured angular distribution is not very
well determined.” The 40Ca($\vec{p},p^{\prime})^{40}$Ca study by Hosono et al.
Hosono  _et al._ (1982) did not determine a $2^{-}$ assignment, but rather
assumed this value, based on an earlier compilation Endt and van dèr Leun
(1973). In addition, their analyzing power fit does not describe the data
well. Horen et al. Horen  _et al._ (1985) reported much improved
40Ca($\vec{p},p^{\prime})^{40}$Ca data consistent with a $2^{-}$ assignment,
but their overall energy resolution was only $80$ keV at FWHM. Similarly, the
40Ca($e$,$e^{\prime}$)40Ca study of Ref. Steffen  _et al._ (1980) measured
data consistent with $2^{-}$, but does not provide proof for an unambiguous
assignment.

Considering all the evidence together, it is likely that the $8425$-keV state
has a spin-parity of $2^{-}$. This conclusion is consistent with the shell-
model interpretation of this state being the $J$ $=$ $2$, $T$ $=$ $1$ level of
the $(d_{3/2}^{-1}f_{7/2})$ configuration, since the observed excitation
energy agrees with those of the $2^{-}$ isobaric analog states in 40K and
40Sc. However, it is worthwhile to determine the spin-parity unambiguously
from a single measurement.

Relevant parts of our pulse-height spectra, measured at an incident
$\gamma$-ray energy of $8400$ keV, are presented in Fig. 3. The spectra of the
vertical (D1), horizontal (D2), and out-of-plane (D3) HPGe detectors are
depicted in red, blue, and green, respectively. The peaks in the spectra
correspond to the transition from the $E_{x}$ $=$ $8425$ keV level in 40Ca to
the state at $E_{x}$ $=$ $3737$ keV, and the subsequent decay to the ground
state. The unambiguous identification of the two peaks with the excitation of
the $E_{x}$ $=$ $8425$-keV level in 40Ca is based on the following arguments.
First, the measured $\gamma$-ray energies agree with those of the expected
primary ($8425$ keV $\rightarrow$ $3737$ keV) and secondary ($3737$ keV
$\rightarrow$ $0$ keV) transitions. Second, we observed the two peaks only at
an incident energy of $8400$ keV; i.e., at the higher bombarding energies of
$8600$ keV or $8800$ keV these peaks are absent. (Recall that our incident
beam resolution was about $300$ keV; see Sec. II.) Third, the only other 40Ca
states that could have been populated at $8400$ keV bombarding energy, and
potentially fed either the $E_{x}$ $=$ $8425$-keV level or the $3737$-keV
state, are located at $E_{x}$ $=$ $8484$ keV (1-, 2-, 3-), $8540$ keV (1, 2+),
and $8579$ keV (2+) Chen (2017):

(i) Only a ground state transition has been reported for $E_{x}$ $=$ $8579$
keV, and we observed this decay at $8400$ keV bombarding energy. If this level
would feed the $E_{x}$ $=$ $8425$ keV or $3737$ keV states at $8400$ keV
bombarding energy via so far unobserved branches, we should have observed the
decays of the latter two states also at $8600$ keV bombarding energy, where
the $8579$-keV level is more strongly populated. However, as already mentioned
above, no such decays have been observed at this higher bombarding energy;

(ii) Similarly, the $E_{x}$ $=$ $8540$ keV level has known branches to the
ground state and to the state at $3353$ keV. We observed none of these
transitions. Again, if the $8540$-keV level would feed the $E_{x}$ $=$
$8425$-keV or $3737$-keV states at $8400$ keV bombarding energy via so far
unobserved branches, we should have observed the decays of the latter two
states also at $8600$ keV bombarding energy, but we did not;

(iii) The $E_{x}$ $=$ $8484$ keV level has reported branches to the $3737$\-
and $5903$-keV states. However, we did not observe the corresponding primary
decays feeding these levels (see Fig. 3). A significant, and so far
unobserved, transition from the $8484$-keV state to the $8425$-keV level would
imply a transition energy of only $59$ keV. We find this highly unlikely,
considering that the decay of the $8484$-keV state can proceed, in principle,
via $E1$, $M1$, or $E2$ multipolarities to about $40$ lower-lying levels with
much larger transition energies. Furthermore, the energy of the $8484$-keV
level is about half-way between the $8400$ and $8600$ keV bombarding energies.
If this level did indeed feed the $8425$-keV state at $8400$ keV bombarding
energy, such feeding would also have occurred at $8600$ keV bombarding energy.
Again, we observed the $8425$ keV $\rightarrow$ $3737$ keV and $3737$ keV
$\rightarrow$ $0$ keV transitions only at $8400$ keV bombarding energy.

We did not detect any of the other known decays of the $E_{x}$ $=$ $8425$ keV
level ($8425$ keV $\rightarrow$ $5903$ keV and $8425$ keV $\rightarrow$ $6025$
keV), since they have much smaller reported branching ratios ($24$% and $19$%,
respectively Chen (2017)). Their primary-transition energies are smaller,
resulting in a higher detection efficiency, but also a higher background,
compared to the energy region of the observed transitions.

Figure 3:  Pulse height spectra measured at an incident $\gamma$-ray energy of
$8400$ keV. The spectra of the vertical (D1), horizontal (D2), and out-of-
plane (D3) HPGe detectors are depicted in red, blue, and green, respectively.
See also Fig. 1. The peaks are labeled according to the initial and final
state energies (given in units of keV) of the transition. The spectrum in
green was scaled down by a factor of $\approx$2 to account for the ratio of
detection efficiencies; detectors D1 and D2 had similar efficiencies. (Left
panel) Energy region of the secondary decay from the $E_{x}$ $=$ $3737$ keV
level in 40Ca to the ground state, $3737$ keV $\rightarrow$ $0$ keV. (Right
panel) Energy region of the primary transition from the $E_{x}$ $=$ $8425$ keV
level to the $E_{x}$ $=$ $3737$ keV state, $8425$ keV $\rightarrow$ $3737$
keV.

Based on our measured intensities, Fig. 4 presents the ratio, $R$, versus the
analyzing power, $A$, for the $8425$ keV $\rightarrow$ $3737$ keV primary
transition (top) and the $3737$ keV $\rightarrow$ $0$ keV secondary one with
the primary transition unobserved (bottom). The measured data are given in
black, with the dashed line depicting the associated 68% error ellipse. Colors
signify theoretical predictions based on different choices of $J^{\pi}$ values
for the $8425$-keV level. Only predictions for dipole and quadrupole
transitions (i.e., $J^{\pi}$ $=$ $1^{\pm}$, $2^{\pm}$ ) are shown, as higher
multipoles are unlikely. The colored circles, squares, and triangles depict
theoretical predictions for mixing ratios of $\delta$ $=$ $-10$, $0$, and
$+10$, respectively. For $J^{\pi}$ $=$ $1^{\pm}$, we only present the results
for pure transitions ($\delta$ $=$ $0$), as mixed decays would imply
multipoles higher than quadrupole radiation.

Figure 4:  Ratio vs. analyzing power for the deexcitation of the $8425$-keV
level in 40Ca. (Top) Primary transition, $8425$ keV $\rightarrow$ $3737$ keV.
(Bottom) Secondary transition, $3737$ keV $\rightarrow$ $0$ keV, with the
primary transition unobserved. The measured values are shown in black, where
both the error bars and the dashed black line (error ellipse) correspond to
68% coverage probability. Different colors refer to theoretical values based
on given choices of $J^{\pi}$ for this level. The purple and green lines
correspond to the theoretical results for a range of multipolarity mixing
ratios of the measured transitions. Colored circles, squares, and triangles
indicate theoretical values for mixing ratios of $\delta$ $=$ $-10$, $0$, and
$+10$, respectively. For $J^{\pi}$ $=$ $1^{-}$ and $1^{+}$, only the values
corresponding to $\delta$ $=$ $0$ are indicated (see text). Notice that, in
the top panel, the purple and green squares (signifying $\delta$ $=$ $0$) are
covered by the yellow and red ones, respectively.

The measurement of the primary transition (top panel), for which we found
values of $A$ $=$ $-0.05\pm 0.18$ and $R$ $=$ $0.43^{+0.11}_{-0.08}$, does not
allow for an unambiguous $J^{\pi}$ assignment because the predictions for all
spin-parity choices, $1^{+}$, $1^{-}$, $2^{+}$, or $2^{-}$, intersect with the
experimental error ellipse. However, the measurement of the secondary
transition (bottom panel), for which we obtained $A$ $=$ $+0.27\pm 0.27$ and
$R$ $=$ $0.43^{+0.15}_{-0.10}$, excludes both the $J^{\pi}$ $=$ $2^{+}$ and
$1^{-}$ values. We can also exclude $1^{+}$, as it would imply an $M2$
transition to the $3737$-keV level. Since the $8424$-keV state can, in
principle, decay to many lower lying 40Ca levels via $E1$, $M1$, or $E2$
transitions, an $M2$ transition for the strongest $\gamma$-ray branch is
highly unlikely. This leaves $J^{\pi}$ $=$ $2^{-}$ as the only possibility
consistent with our data, in agreement with the result evaluated in Ref. Chen
(2017). Although the $3737$-keV level is fed by the side-branch $8425$ keV
$\rightarrow$ $6025$ keV $\rightarrow$ $3737$ keV, its branching ratio is
small ($10$%) and its effect is contained in the error bars of the measured
peak intensities.

We close this section by noting that populating the $8424$-keV state in our
NRF experiment is not fundamentally surprising. For the corresponding $M2$
ground-state transition, Fagg et al. Fagg  _et al._ (1971) measured a
$\gamma$-ray width of $2.6^{+10}_{-8}\times 10^{-2}$ eV in their
$(e,e^{\prime})$ experiment111This experimental ground-state width was not
adopted by ENSDF Chen (2017) and the reason can be traced back to Ref. Endt
and Van Der Leun (1978), who wrote in the footnote to their Tab. 40.17, “The
ground-state width of $2.6\pm 0.9$ eV in [Fagg et al.] from $(e,e^{\prime})$,
leading to an $M2$ strength of $350$ W.u., should be rejected as erroneous.”
Unfortunately, Ref. Endt and Van Der Leun (1978) adopted a value that is
erroneous by two orders of magnitude.. This value corresponds to $3.5$ W.u.,
which is smaller than the recommended upper limit (RUL) of $5$ W.u. for $M2$
isospin-allowed ($\Delta T$ $=$ $1$) transitions Endt (1993).

##  IV Results for 11B

The 11B ground-state spin-parity is $3/2^{-}$ and, unlike the case of 40Ca,
transitions can proceed via multipolarity mixing in both the first
(excitation) and second (deexcitation) transition. The utility of the
11B($\gamma$,$\gamma$)11B reaction as a calibration standard and, in
particular, the reliable knowledge of the mixing ratios for measurements of
the photon flux in NRF experiments has been pointed out by Rusev et al. Rusev
_et al._ (2009). The latter work was performed at the HI$\gamma$S facility
with a detection setup similar to ours, except that all the detectors were
positioned in a plane perpendicular to the beam ($\theta$ $=$ $90^{\circ}$).
In other words, only the analyzing power, $A$, was measured, but not the
ratio, $R$ (see Eqs. (3) and (4)). We were particularly interested in mixed
transitions from the well-known state at $E_{x}$ $=$ $8920.47\pm 0.11$ keV
($5/2^{-}$) Kelley  _et al._ (2012). This level decays mainly to the ground
state, but also has a small branch to the $4445$-keV ($5/2^{-}$) state. Since
the ground-state spin of 11B is $3/2$, both the excitation and deexcitation
transitions can be of mixed multipolarity, requiring two mixing ratios in Eq.
(II).

Relevant parts of our pulse-height spectra, measured at an incident
$\gamma$-ray energy of $8920$ keV, are presented in Fig. 5. The spectra of the
vertical (D1), horizontal (D2), and out-of-plane (D3) HPGe detectors are
depicted in red, blue, and green, respectively. The left panel represents the
energy region of the $8920$ keV $\rightarrow$ $4445$ keV and $4445$ keV
$\rightarrow$ $0$ keV transitions, whereas the right panel displays the energy
region of the $8920$ keV $\rightarrow$ $0$ keV transition.

Figure 5:  Pulse height spectra measured at an incident $\gamma$-ray energy of
$8920$ keV. The spectra of the vertical (D1), horizontal (D2), and out-of-
plane (D3) HPGe detectors are depicted in red, blue, and green, respectively.
See also Fig. 1. The peaks are labeled according to the initial and final
state energies (given in units of keV) of the transition. The spectrum shown
in green was scaled down by a factor of $\approx$2 to account for the ratio of
detection efficiencies; detectors D1 and D2 had similar efficiencies. (Left
panel) Energy region of the primary transition to the $E_{x}$ $=$ $4445$ keV
level in 11B, $8920$ keV $\rightarrow$ $4445$ keV, and the subsequent
secondary transition, $4445$ keV $\rightarrow$ $0$ keV. (Right panel) Energy
region of the primary transition to the 11B ground state, $8920$ keV
$\rightarrow$ $0$ keV.

Unfortunately, the results published in Ref. Rusev  _et al._ (2009) are
subject to an inconsistent phase definition in the angular correlation
expressions they adopted, as explained in more detail in App. A. The erroneous
mixing ratio values have also been adopted in ENSDF Kelley  _et al._ (2012).
Therefore, we reanalyzed the data of Ref. Rusev  _et al._ (2009) and extracted
from their published asymmetries (column 3 of their Tab. I) the allowed
mixing-ratio ranges. The results are presented in App. B. We will compare
below our results with these “corrected Rusev et al. values.”

Present and previous results for the $\gamma$-ray multipolarity mixing ratios
and branching ratios are listed in Tab. 2.

###  IV.1 Transition of the $8920$-keV level to the ground state

For the $8920$-keV ground-state transition, Comsan et al. Comsan  _et al._
(1968) reported an $E2/M1$ multipolarity mixing ratio of
$\delta^{\text{Comsan}}$ $=$ $-0.11\pm 0.04$, which was derived from their
10B(d,p$\gamma$)11B experiment. Unfortunately, they did not state their
adopted phase convention for the definition of $\delta$. Rusev et al. Rusev
_et al._ (2009) reported a value of $\delta^{\text{Rusev}}$ $=$ $0.000\pm
0.014$. However, without additional assumptions, their measurement restricted
the mixing ratio to two ranges, one near $\delta^{\text{Rusev}}$ $=$ $-1.3$
and one near $0$. They excluded the former solution “because [it] leads to
$E2$ admixtures that are unusually large compared with known values” Rusev
_et al._ (2009). As already pointed out above, their reported numerical
results are erroneous. The reanalysis of their data (see App. B and Tab. 3)
yields four, instead of two, possible solutions: $\delta^{\text{Rusev}}=$
$-6.7^{+0.9}_{-1.8}$, $-0.387^{+0.019}_{-0.018}$, $-0.001^{+0.027}_{-0.028}$,
and $+3.06^{+0.28}_{-0.19}$. While it may be reasonable to exclude the first
and last solutions because of implied unusually large $E2$ admixtures,
disregarding the second solution without further evidence is questionable.

Our experimental results are presented in Fig. 6. The purple line depicts the
theoretical solutions for a range of mixing ratios, $\delta$. Purple circles,
squares, and triangles indicate theoretical values of $\delta$ $=$ $-10$, $0$,
and $+10$, respectively. The four regions marked by pairs of green asterisks
correspond to the possible solutions based on the reanalysis of the Rusev et
al. Rusev  _et al._ (2009) data (see App. B and Tab. 3). The result from the
present experiment is presented as a black circle. It can be seen that our
data ($A$ $=$ $-0.23\pm 0.01$ and $R$ $=$ $0.63\pm 0.01$) provide a unique
solution near a value of zero (purple square), without requiring any
additional assumptions. In particular, we can exclude three of the solutions
resulting from the data of Ref. Rusev  _et al._ (2009).

The bottom panel presents an expanded view of the top one. It is apparent that
our measurement gives a significantly more precise value for the mixing ratio
compared to the solution near zero resulting from the data of Ref. Rusev  _et
al._ (2009). By applying a Bayesian analysis directly to the measured
intensities, we obtained a value of $\delta^{\text{present}}$ $=$ $-0.023\pm
0.009$ (68% coverage probability; see Tab. 2). All signs of mixing ratios
quoted in the present work are consistent with the Steffen-Krane phase
convention (see App. A for more details on phase conventions). Consequently,
our data predict a $\approx$0.05% $E2$ contribution to the total transition
strength.

Figure 6:  Ratio vs. analyzing power for the deexcitation of the $8920$-keV ($5/2^{-}$) level to the 11B ground state ($3/2^{-}$). (Top) The measured value is depicted in black. The purple line depicts the theoretical solutions for the full range of mixing ratios. Purple circles, squares, and triangles indicate theoretical values of $\delta$ $=$ $-10$, $0$, and $+10$, respectively. The regions between pairs of green asterisks correspond to the four possible solutions from our reanalysis of the data by Ref. Rusev  _et al._ (2009) (see App. B). (Bottom) Expanded view of the top panel. Both the error bars and the dashed black line (error ellipse) refer to 68% coverage probability.  Table 2: Multipolarity mixing ratios (consistent with the Steffen-Krane phase convention, unless mentioned otherwise) and branching ratios for decaying levels in 11B. Transition (keV) |  $\delta^{\text{present}}$111From present work. Uncertainties correspond to coverage probabilities of 68%. |  $\delta^{\text{lit}}$222The mixing ratio values published in Ref. Rusev  _et al._ (2009) are erroneous (see App. A). A reanalysis of their data is presented in App. B. |  $B_{\gamma}^{\text{present}}$ (%) |  $B_{\gamma}^{\text{ENSDF}}$ (%)555From ENSDF Kelley  _et al._ (2012). For the first two transitions, the values originate from Ref. Olness  _et al._ (1965) and do not sum to 100%.
---|---|---|---|---
$8920$ ($5/2^{-}$) $\rightarrow$ $0$ ($3/2^{-}$) | $-0.023\pm 0.009$ |  $-0.11\pm 0.04$333From Comsan et al. Comsan  _et al._ (1968); the phase convention is not mentioned explicitly. | $96.83\pm 0.13$ | $95.0\pm 1.0$
$8920$ ($5/2^{-}$) $\rightarrow$ $4445$ ($5/2^{-}$) | $+0.72\pm 0.40$ |  | $3.17\pm 0.13$ | $4.5\pm 0.5$
$4445$ ($5/2^{-}$) $\rightarrow$ $0$ ($3/2^{-}$) |  |  $+0.19\pm 0.03$444From Bell et al. Bell  _et al._ (1968). Their published value has the opposite sign because they adopted the Rose-Brink phase convention. The value listed here has been converted to the Steffen-Krane convention. | $100$ | $100$

###  IV.2 Transitions of the $8920$-keV level to and through the $4445$-keV
state

Our experimental results for the $8920$ keV $\rightarrow$ $4445$ keV
transition are presented as a black data point ($A$ $=$ $+0.25\pm 0.06$ and
$R$ $=$ $0.32\pm 0.03$) and $68$% error ellipse in the top panel of Fig. 7.
The purple line was calculated with the present value of the mixing ratio,
$\delta_{1}$, for the transition exciting the $8920$-keV level (Sec. IV.1) and
a range of mixing ratios, $\delta_{2}$ $=$ $-10$ to $+10$, for the primary
decay to the $4445$-keV state. The purple symbols have the same meaning as in
Fig. 6. A Bayesian fit to our data yields a value for the mixing ratio of
$\delta_{2}^{present}=$ $+0.72\pm 0.40$. In comparison, the reanalysis of the
Rusev et. al. Rusev  _et al._ (2009) data, and adopting just one of their four
solutions for the ground-state transition ($\delta_{1}$ $=$ $-0001$), yields
two solutions for the transition to the $4445$-keV state: $\delta_{2}^{Rusev}$
$=$ $-0.08^{+0.13}_{-0.14}$ and $+1.7^{+0.7}_{-0.6}$ (Tab. 3). These are
marked in the top panel of Fig. 7 by pairs of green asterisks and red crosses,
respectively. It can be seen that our error ellipse (dashed black line) covers
a significantly more constrained range of mixing ratios, when compared to the
results of Ref. Rusev  _et al._ (2009).

Figure 7:  Ratio vs. analyzing power for the deexcitation of the $8920$-keV
($5/2^{-}$) level in 11B. Measured values are depicted in black, where the
dashed black lines indicate 68% error ellipses. The purple lines depict the
theoretical solutions for a range of mixing ratios. Purple circles, squares,
and triangles indicate theoretical values of $\delta_{2}$ $=$ $-10$, $0$, and
$+10$, respectively. (Top) Primary $8920$ keV $\rightarrow$ $4445$ keV
transition. The purple line was obtained with the present value of the mixing
ratio for the transition exciting the $8920$-keV level (see Tab. 2 and Sec.
IV.1) and a range of mixing ratios, $\delta_{2}$, for the primary decay to the
$4445$-keV state. The region between the green asterisks or red crosses
corresponds to the two possible solutions from our reanalysis of the data by
Ref. Rusev  _et al._ (2009) (for $\delta_{1}$ $=$ $-0.001$; see App. B and
Tab. 3). (Bottom) Secondary $4445$ keV $\rightarrow$ $0$ keV transition, with
the primary transition unobserved. The purple line was obtained assuming the
present value of the mixing ratio for the transition exciting the $8920$-keV
level, a mixing ratio of $|\delta_{u}|$ $=$ $0.72$ for the unobserved
intermediate transition (see Tab. 2), and a range of mixing ratios,
$\delta_{2}$, for the secondary decay of the $4445$-keV state.

As a final test of the internal consistency of our data, we present in the
lower panel of Fig. 7 our experimental results for the $4445$ keV
$\rightarrow$ $0$ keV secondary transition ($A$ $=$ $-0.08\pm 0.06$ and $R$
$=$ $0.55\pm 0.05$). In this case, the purple line was computed assuming the
present value of the mixing ratio for the transition exciting the $8920$-keV
level (see Tab. 2 and Sec. IV.1), a mixing ratio of $|\delta_{u}|$ $=$ $0.72$
for the unobserved intermediate radiation, and a range of mixing ratios,
$\delta_{2}$, for the secondary decay of the $4445$-keV state. Note that this
type of angular correlation is independent of the sign of the mixing ratio for
the unobserved intermediate transition, $\delta_{u}$ Iliadis and Friman-Gayer
(2021). It can be seen that the present data are not sufficiently precise to
deduce a meaningful mixing ratio, $\delta_{2}$, for the $4445$ keV
$\rightarrow$ $0$ keV transition. This is not surprising, because the
transition appears in our measurement as the last step in a three-photon
process. All that can be concluded from the lower panel of Fig. 7 is that the
present data are consistent with a broad range of mixing ratios, $\delta_{2}$
once we fix the mixing ratios, $\delta_{1}$ and $\delta_{u}$, for the
preceding steps using our measured values (Tab. 2).

Bell et. al. Bell  _et al._ (1968) utilized the 12C(t,$\alpha$)11B reaction to
measure the angular correlation of the $4445$ keV $\rightarrow$ $0$ keV
transition, resulting in a value of $\delta^{\text{Bell}}$ $=$ $+0.19\pm
0.03$. Rusev et. al. Rusev  _et al._ (2009) excited the $4445$-keV level by
NRF and the reanalysis of their data yields four solutions (see App. B):
$\delta^{\text{Rusev}}$ $=$ $-2.90^{+0.13}_{-0.18}$,
$-0.511^{+0.011}_{-0.017}$, $+0.172^{+0.019}_{-0.020}$, and
$+2.13^{+0.06}_{-0.06}$. The third solution agrees with the result of Ref.
Bell  _et al._ (1968). Although it is reasonable to exclude the first and
fourth solutions, based on an implied unusually large $E2$ admixture, it would
be questionable to disregard the third solution based on the evidence from the
data by Ref. Rusev  _et al._ (2009) alone. In view of the poor detector
resolution in the experiment of Bell et al. Bell  _et al._ (1968), and the
nearly isotropic angular correlation shown in their Fig. 5, a remeasurement of
the $4445$ keV $\rightarrow$ $0$ keV angular correlation in an NRF experiment
by using several detectors placed inside and outside the $\theta$ $=$
$90^{\circ}$ plane is recommended.

###  IV.3 Branching ratios for the $8920$-keV ($5/2^{-}$) level

Gamma-ray branching ratios for the $8920$-keV state were derived from our
angle-integrated yields. We find branching ratios of $B_{\gamma}$ $=$
$96.83\pm 0.13$% and $3.17\pm 0.13$% for the $8920$ keV $\rightarrow$ $0$ keV
and $8920$ keV $\rightarrow$ $4445$ keV transitions, respectively (see Tab.
2). Our values are more precise than those listed in ENSDF Kelley  _et al._
(2012). Notice that the erroneous relationship for the mixing ratios assumed
in Ref. Rusev  _et al._ (2009) also impacts their reported $\gamma$-ray
branching ratios. However, insufficient information is provided in their work
for us to derive corrected values.

##  V Summary

We report on a measurement of 11B and 40Ca levels at energies between $8$ and
$9$ MeV using nuclear resonance fluorescence (NRF) at the High-Intensity
$\gamma$-ray Source (HI$\gamma$S) facility at the Triangle Universities
Nuclear Laboratory (TUNL). Levels in 11B are interesting because they provide
calibration points for NRF experiments, while states in the 40Ca nucleus
represent low-energy resonances in the 39K(p,$\gamma$)40Ca reaction, which is
of relevance for potassium nucleosynthesis in globular clusters.

We present improved excitation energies for 40Ca as well as an unambiguous
$2^{-}$ assignment for the state at $8425$ keV. We also obtained improved
$\gamma$-ray multipolarity mixing ratios and more precise branching ratios for
the 11B state at $8920$ keV. Furthermore, previously published values of
mixing ratios in 11B by Rusev et al. Rusev  _et al._ (2009) were derived under
an erroneous assumption concerning phase conventions in angular correlation
expressions. We reanalyzed their data and derived corrected values for the
mixing ratios in 11B. We also comment on the relationship of different phase
conventions in NRF experiments.

###### Acknowledgements.

We would like to thank Gencho Rusev for detailed discussions about the mixing
ratio analysis presented in Ref. Rusev  _et al._ (2009), and Richard Longland,
Samantha Johnson, and S. Gaither Frye for providing comments. The help of Mark
Emamian with preparing Fig. 1 is highly appreciated. This work is supported by
the DOE, Office of Science, Office of Nuclear Physics, under grants DE-
FG02-97ER41041 (UNC) and DE-FG02-97ER41033 (TUNL).

##  Appendix A Note on phase conventions

When multipolarity mixing ratios are involved in transitions, it is important
to clearly state the adopted phase conventions. We analyzed our data using the
expressions presented in Ref. Iliadis and Friman-Gayer (2021), which are based
on the work of Biedenharn Biedenharn (1960). In the Biedenharn phase
convention, the intermediate state always appears on the right in the reduced
matrix elements, regardless of whether it is the initial or final state
involved in the transition. Applied to an NRF experiment on an odd-mass target
nucleus, where the excited state decays back to the ground state (i.e.,
elastic $\gamma$-ray scattering), this implies a relation of $\delta_{1}$ $=$
$\delta_{2}$ for the mixing ratios of the first (excitation) and second
(deexcitation) step, as pointed out in Sec. 3 of Ref. Iliadis and Friman-Gayer
(2021).

The original formulation of the Steffen-Krane formalism Krane  _et al._
(1973); Krane and Steffen (1970) provides the expressions for $\gamma$-ray
cascades. In their phase convention, the initial state always appears on the
right in the reduced matrix elements. Applying these expressions directly to
an NRF experiment on an odd-mass target nucleus, where the excited state
decays back to the ground state (see, e.g., Eqs. (4) $-$ (7) in Ref. Pietralla
_et al._ (2003)), implies a relation of $\delta_{1}$ $=$ $-\delta_{2}$ for the
mixing ratios, as pointed out by Refs. Martin (1987); Iliadis and Friman-Gayer
(2021). If one modifies the original expressions of the Steffen-Krane
formalism Krane  _et al._ (1973); Krane and Steffen (1970) by switching the
sign in front of the terms containing $\delta_{1}$ (see, e.g., Refs. Kneissl
_et al._ (1996); Zilges  _et al._ (2022)), then the mixing ratios are related
by $\delta_{1}$ $=$ $\delta_{2}$. The error made in Ref. Rusev  _et al._
(2009) was the assumption of $\delta_{1}$ $=$ $\delta_{2}$, while adopting at
the same time the original Krane  _et al._ (1973); Krane and Steffen (1970)
instead of the modified Steffen-Krane expressions. We present a reanalysis of
the previous data in App. B.

A final note regarding phase conventions: for the processes discussed here,
i.e., elastic or inelastic $\gamma$-ray scattering, and an unobserved
intermediate transition in a two-photon deexcitation, the formalisms of
Biedenharn Biedenharn (1960) and Steffen-Krane Krane  _et al._ (1973); Krane
and Steffen (1970) (using either their original or modified expressions)
provide the same sign for the mixing ratio of the second (deexcitation)
transition. To avoid any confusion, we quote in the present work mixing ratio
values for deexcitation transitions only.

##  Appendix B Reanalysis of the Rusev et al. Rusev  _et al._ (2009) data

Here, we describe our reanalysis of the data of Ref. Rusev  _et al._ (2009)
and present the results. In the original publication, the authors used an
erroneous phase convention for the multipolarity mixing ratio, as described in
App. A.

Rusev et al. Rusev  _et al._ (2009) measured the asymmetry, $a$. Since their
definition of the azimuthal angle, $\phi$, differs from our convention (see
Eq. (3) and Ref. Iliadis and Friman-Gayer (2021)), their asymmetry is related
to our analyzing power by $a$ $=$ $-A(\theta=90^{\circ})$. Their method of
taking into account geometric effects in the quantity $a$ did not use $Q$
coefficients, but relied on separate Geant3 simulations for each cascade of
interest. While not mentioned explicitly, they assumed that their geometry-
correction factors, $C\left(\theta\right)$, are independent of the mixing
ratio. Rusev et al. Rusev  _et al._ (2009) observed ground-state and excited-
state transitions (which they call “branching transitions”), with asymmetries
of $a_{gs}\left(\delta_{1}\right)$ and
$a_{ex}\left(\delta_{1},\delta_{2}\right)$, respectively. The data were
analyzed in a two-step process. The first step used only the ground-state
transition and employed the experimental mode, $\bar{a}_{gs}$, and the
standard deviation, $\Delta a_{gs}$, to find a mode $\bar{\delta}_{1}$ and a
(potentially asymmetric) coverage interval
$\left[\bar{\delta}_{1}-\Delta_{-}\delta_{1},\bar{\delta}_{1}+\Delta_{+}\delta_{1}\right]$
for the mixing ratio,

$\displaystyle\bar{\delta}_{1}$
$\displaystyle=a_{gs}^{-1}\left(\bar{a}_{gs}\right)$ (5)
$\displaystyle\bar{\delta}_{1}\pm\Delta_{\pm}{\delta}_{1}$
$\displaystyle=a_{gs}^{-1}\left(\bar{a}_{gs}\pm\Delta a_{gs}\right).$

The inverse of $a_{gs}$ in this so-called “min-max” method, $a_{gs}^{-1}$, was
determined numerically. The result can be visualized as a projection of the
experimental coverage interval for $a_{gs}$ on the mixing-ratio axis.

As an example, the determination of $\delta$ for the sequence $0$ keV
($3/2^{-}$) $\rightarrow$ 4445 keV ($5/2^{-}$) $\rightarrow$ $0$ keV
($3/2^{-}$) in 11B is given in Fig. 8. The solid blue curve indicates the
theoretical dependence of the asymmetry on the mixing ratio using the correct
phase convention (see App. A). The dashed red one is obtained instead, if the
erroneous mixing-ratio phase convention of Ref. Rusev  _et al._ (2009) is
adopted222Rusev et al. Rusev  _et al._ (2009) show the dependence of their
asymmetry on the mixing ratio for the sequence $0$ keV ($3/2^{-}$)
$\rightarrow$ 4445 keV ($5/2^{-}$) $\rightarrow$ $0$ keV ($3/2^{-}$) in 11B as
a black curve in their Fig. 4. Their dependence disagrees with our dashed red
curve in Fig. 8, although both curves were obtained using the erroneous phase
convention (App. A). We can reproduce the black curve in Fig. 4 of Ref. Rusev
_et al._ (2009) if, in addition to an erroneous phase convention, we also
adopt an erroneous sign in front of the $P^{|2|}_{4}$ term in Eq. (II). The
$P^{|2|}_{4}$ term is proportional to $\delta^{4}$ for this sequence (see Ref.
Zilges  _et al._ (2022)), which would explain why an erroneous sign affects
mainly large values of the mixing ratio, $\delta$.. The experimental asymmetry
of Ref. Rusev  _et al._ (2009) is indicated as a gray horizontal region. The
possible solutions for the multipolarity mixing ratio, $\delta$, are depicted
by vertical bars (solid blue strip and red dashes for the correct and
erroneous phase convention, respectively). The significant difference in the
theoretical descriptions is apparent.

In a second step, Ref. Rusev  _et al._ (2009) employed the estimated value of
$\delta_{1}$ to determine the mixing ratio, $\delta_{2}$, for the transition
to an excited level, again using the “min-max method.” One shortcoming of this
approach is the implicit assumption that $a_{gs}$ or $a_{ex}$ increases or
decreases monotonously with the mixing ratio. However, the dependence of the
asymmetry on a mixing ratio results frequently in multiple local extrema (see
below). Furthermore, Ref. Rusev  _et al._ (2009) did not propagate the
uncertainties from the first step to the second one.

In our reanalysis of their data, we improved the “min-max method” by
propagating the uncertainty using the Monte Carlo method described in Ref.
Joint Committee for Guides in Metrology (2008). In a first step, a random
value of $a_{gs}^{\mathrm{rand}}$ was sampled from a normal distribution,
$\mathcal{N}\left(\bar{a}_{gs},\Delta a_{gs}\right)$. By numerical inversion,
$a_{gs}^{-1}\left(a_{gs}^{\mathrm{rand}}\right)$, a set of solutions
$\left\\{\delta_{1}^{\mathrm{rand}}\right\\}$ was found. In a second step, the
inversion
$a_{ex}^{-1}\left(\delta_{1}^{\mathrm{rand}},a_{ex}^{\mathrm{rand}}\right)$,
which used the set of randomly-sampled values $\delta_{1}^{\mathrm{rand}}$,
was used to find a set of solutions
$\left\\{\delta_{2}^{\mathrm{rand}}\right\\}$. From a total of $10^{5}$ valid
samples for each excited state (i.e., samples for which the inversion is
possible for all observed transitions), probability distributions for all
mixing ratios can be estimated. These distributions naturally take
correlations into account, and are not subject to the drawbacks of the min-max
method.

Our results are presented in Tab. 3. When the sampling yielded unimodal
probability densities for a mixing ratio, we quote the 68 % highest-density
interval. In cases where the distributions encompassed unbounded regions of
parameter space, we provide lower or upper limits. If Tab. 3 shows the word
“undetermined” for a mixing ratio of the transition to a low-lying excited
state, this means that all ranges were approximately equally probable. It
should be noted that we were able to reproduce all the multipolarity-mixing-
ratio results reported by Ref. Rusev  _et al._ (2009) when their erroneous
phase convention is used.

Figure 8:  Determination of the multipolarity mixing ratio, $\delta$, for the sequence $0$ keV ($3/2^{-}$) $\rightarrow$ 4445 keV ($5/2^{-}$) $\rightarrow$ $0$ keV ($3/2^{-}$) in 11B from the experimental asymmetry, $a$ $=$ $-A(\theta=90^{\circ})$, using the “min-max method.” The solid blue curve indicates the theoretical dependence of the asymmetry on the mixing ratio. The dashed red curve is instead obtained, if the erroneous mixing-ratio phase convention of Ref. Rusev  _et al._ (2009) is adopted. Both curves take into account the correction for the finite opening angle of the detectors (factor $0.95$ Rusev  _et al._ (2009)). The asymmetry measured by Ref. Rusev  _et al._ (2009) is shown as a solid gray horizontal region. The possible solutions for the multipolarity mixing ratio, $\delta$, are depicted by vertical bars (solid blue and dashed red for the correct and erroneous phase convention, respectively).  Table 3: Mixing ratios (consistent with the Steffen-Krane phase convention) in 11B from our reanalysis of the Rusev et al. Rusev  _et al._ (2009) data. Transition (keV)111Deexcitation transition of the cascade under consideration, with the energy of the excited states given in keV, and spin-parity values in parentheses; the excitation is always from the $3/2^{-}$ ground state of 11B. |  $E_{\gamma}$ (keV)222Gamma-ray energy adopted from Ref. Kelley  _et al._ (2012). |  $a$333Experimental asymmetry from Ref. Rusev  _et al._ (2009), which is related to our analyzing power by $a$ $=$ $-A(\theta=90^{\circ})$. |  $\delta_{1}$444Multipolarity mixing ratios from our reanalysis of the Rusev et al. data Rusev  _et al._ (2009). For ground-state transitions, the mixing ratio is the same for the excitation and deexcitation transitions of the cascade (see App. A) and, therefore, only $\delta_{1}$ is given. Multiple entries for the same transition correspond to alternative solutions. |  $\delta_{2}$444Multipolarity mixing ratios from our reanalysis of the Rusev et al. data Rusev  _et al._ (2009). For ground-state transitions, the mixing ratio is the same for the excitation and deexcitation transitions of the cascade (see App. A) and, therefore, only $\delta_{1}$ is given. Multiple entries for the same transition correspond to alternative solutions.
---|---|---|---|---
4445 ($5/2^{-}$) $\rightarrow$ 0 ($3/2^{-}$) | 4444.03(8) |  $+$0.026(19) | $-2.90^{+0.13}_{-0.18}$ |
|  |  | $-0.511^{+0.011}_{-0.017}$ |
|  |  | $+0.172\pm 0.020$ |
|  |  | $+2.13\pm 0.06$ |
5020 ($3/2^{-}$) $\rightarrow$ 0 ($3/2^{-}$) | 5018.98(40) |  $+$0.200(16) | $-0.055\pm 0.023$ |
5020 ($3/2^{-}$) $\rightarrow$ 2125 ($1/2^{-}$) | 2895.30(40) |  $-$0.37(5) | $-0.055\pm 0.023$ | $-1.39^{+0.18}_{-0.22}$
|  |  | $-0.055\pm 0.023$ | $-0.08^{+0.06}_{-0.08}$
7286 ($5/2^{+}$) $\rightarrow$ 0 ($3/2^{-}$) | 7282.92 |  $-$0.213(30) | $<-5$ |
|  |  | $-0.380^{+0.030}_{-0.028}$ |
|  |  | $+0.003\pm 0.038$ |
|  |  | $+3.1^{+0.4}_{-0.6}$ |
7286 ($5/2^{+}$) $\rightarrow$ 5020 ($3/2^{-}$) | 2264.9 |  $-$0.181(80) | $<-5$ | $<-2$
|  |  |  | $+0.40^{+0.15}_{-0.10}$
|  |  |  | $>+1$
|  |  | $-0.380^{+0.030}_{-0.028}$ | $-1.8^{+0.8}_{-1.6}$
|  |  |  | $-0.25^{+0.15}_{-0.18}$
|  |  | $+0.003\pm 0.038$ | $<-2.1$
|  |  |  | $+0.03\pm 0.08$
|  |  | $+3.1^{+0.4}_{-0.6}$ | undetermined
7286 ($5/2^{+}$) $\rightarrow$ 4445 ($5/2^{-}$) | 2840.23 |  $+$0.177(66) | $<-5$ | $-0.70^{+0.15}_{-0.23}$
|  |  |  | $>+1.7$
|  |  | $-0.380^{+0.030}_{-0.028}$ | undetermined
|  |  | $+0.003\pm 0.038$ | $-0.10\pm 0.13$
|  |  |  | $>+1.1$
|  |  | $+3.1^{+0.4}_{-0.6}$ | undetermined
8920 ($5/2^{-}$) $\rightarrow$ 0 ($3/2^{-}$) | 8916.67(16) |  $+$0.215(20) | $-6.7^{+0.9}_{-1.8}$ |
|  |  | $-0.387\pm 0.019$ |
|  |  | $-0.001\pm 0.028$ |
|  |  | $+3.06^{+0.28}_{-0.19}$ |
8920 ($5/2^{-}$) $\rightarrow$ 4445 ($5/2^{-}$) | 4474.5(3) |  $-$0.19(7) 101010Uncertainty reported in the literature has a typo and is a factor of 10 too small Rusev  . | $-6.7^{+0.9}_{-1.8}$ | $<-2.1$
|  |  |  | $-0.72^{+0.16}_{-0.24}$
|  |  |  | $>+1.7$
|  |  | $-0.387\pm 0.019$ | undetermined
|  |  | $-0.001\pm 0.028$ | $-0.08\pm 0.14$
|  |  |  | $+1.7\pm 0.7$
|  |  | $+3.06^{+0.28}_{-0.19}$ | undetermined

##  Appendix C Energy calibration procedure

Four precisely known $\gamma$-ray energies of transitions in 11B were used for
the detector energy calibrations: $E_{\gamma}$ $=$ $4474.51(13)$,
$4666.05(30)$, $6789.55(30)$, and $8916.59(11)$ keV. These values were
obtained from the recommended excitation energies listed in Ref. Kelley  _et
al._ (2012), and corrected for recoil shifts. Peak centroids and uncertainties
(in channel units) were estimated using “Method C” of Ref. Rodgers and Iliadis
(2021).

A linear energy calibration was then performed using a Bayesian regression
model. We used three independent chains with 500 000 steps each (with a burn-
in of 50 000 steps), to ensure convergence of the Markov chains. One novel
aspect of our fitting procedure is the inclusion of uncertainties in both $x$
(channel centroid) and $y$ ($\gamma$-ray calibration energy), which is
rigorously (in a statistical sense) implemented using the Bayesian model
described in Sec. 8.4 of Ref. Andreon and Weaver (2015). The same technique
was also successfully applied in Ref. de Souza  _et al._ (2019) in connection
with the fitting of astrophysical S-factors.

Figure 9 displays the energy residuals (i.e., the difference with respect to
the best fit line) versus peak centroid (in channels) for detector 2 (D2; see
Fig. 1). The four data points refer to the four 11B calibration energies
quoted above. The red lines show, in the parlance of Bayesian statistics,
“credible lines” for different steps of the Markov chains. The 16 and 84
percentiles of the energy residuals are plotted as blue lines. It can be seen
that, for a coverage probability of 68%, the uncertainty resulting from the
linear fit is $\approx 0.1$ keV near the $\gamma$-ray energy region of
interest ($8$ $-$ $9$ MeV, corresponding to channels 13 000 to 14 000).

To this (common) uncertainty, one must add that resulting from the measured
40Ca peak centroids (in channels). This is achieved by predicting a value,
$y_{p}$, of the $\gamma$-ray energy according to (see, e.g., Sec. 8.10 in Ref.
Andreon and Weaver (2015))

$p(y_{p}|x_{p},D)=\int_{\theta}p(y_{p}|x_{p},\theta)p(\theta|D)d\theta$ (6)

where $x_{p}$ is the experimentally determined peak centroid, $\theta$ denotes
the vector of model parameters (slope and intercept of the linear model), $D$
stands for the set of data, and $p(\theta|D)$ is the posterior (i.e., the
probability density for obtaining parameter values of $\theta$ given the data,
$D$). To account for the experimentally-determined uncertainty of a 40Ca peak
centroid, we sampled $x_{p}$ from a Gaussian probability density with a mean
and standard deviation given by the peak centroid and its uncertainty,
respectively. Finally, the $\gamma$-ray energies and uncertainties for
observed decays in 40Ca (see Tab. 1) are derived from the 50 percentile
(median) and the 16 and 84 percentiles (68% coverage probability) of the
probability density, $p(y_{p}|x_{p},D)$.

We did not include the single-escape or double-escape peaks corresponding to
the $8916.59(11)$ keV full-energy peak from 11B in our linear energy
calibration, although these three peaks together cover the entire energy range
of all 40Ca ground-state decays observed in this work. Previous work Kikstra
_et al._ (1990) has shown that the energy differences between escape peaks and
the full energy peak are systematically shifted from $511$ or $1022$ keV.
These shifts depend on the type of the detector and amount to about $100$ eV
for the hyperpure n-type germanium detector used in Ref. Kikstra  _et al._
(1990). Since this shift is very small, we performed a test by including the
escape peaks in our linear energy calibration. As a result, the $\gamma$-ray
energies of all transitions given in column 3 of Tab. 1 varied by less than
their stated standard deviation.

Potential amplifier gain shifts were monitored throughout the experiment using
room background peaks (with beam on the sample) and $\gamma$-ray lines from
radioactive sources (without beam), and no gain shifts were observed.

Figure 9:  Energy residuals (i.e., the difference with respect to the best fit
line) versus peak centroid (in channels) for detector 2 (D2; see Fig. 1). The
four data points refer to the four 11B calibration energies (see text). The
red lines show credible lines for different steps of the Markov chains. The
two blue lines enclose a coverage probability of 68%. The region of interest
for the 40Ca levels measured in the present work is located between channels
13 000 to 14 000. Only 300 out of 50 000 regression lines are plotted for the
purpose of illustration.

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11institutetext: 1Beijing University of Posts and Telecommunications
2Tomorrow Advancing Life
{jiajun.zhang<EMAIL_ADDRESS>{chenboyu, jizhilong,
<EMAIL_ADDRESS>Contribute equally

# 1st Place Solutions for the UVO Challenge 2022

Jiajun Zhang1† Boyu Chen2† Zhilong Ji2∗ Jinfeng Bai2 Zonghai Hu1

###### Abstract

This paper describes the approach we have taken in the challenge. We still
adopted the two-stage scheme same as the last champion, that is, detection
first and segmentation followed. We trained more powerful detector and
segmentor separately. Besides, we also perform pseudo-label training on the
test set, based on student-teacher framework and end-to-end transformer based
object detection. The method ranks first on the 2nd Unidentified Video Objects
(UVO) challenge, achieving AR@100 of 46.8, 64.7 and 32.2 in the limited data
frame track, unlimited data frame track and video track respectively.

##  1 Introduction

Common instance segmentation algorithms are trained on specific datasets to
learn a fixed number of categories for specific scenarios. UVO [20] discusses
a more realistic scenarios, Open-World instance segmentation. In this
scenario, we expect that the algorithm is capable of detecting or segmenting
novel objects and have the ability of incremental learning.

Compared with the end-to-end instance segmentation framework, two-stage
framework often achieves better performance. We have tried these two kinds of
methods for comparison in our initial experiments, and even the end-to-end
SOTA method Cascade Mask-RCNN [8] with backbone ViTDet [12] still has a
significant gap with the two-stage method. Therefore, we adopted the two-stage
scheme same as the last year’s winner. As mentioned in [7], stwo-stage
architecture enable us to train the detection network and segmentation network
separately on different datasets and use more complex models. Obviously, there
is a trade-off between accuracy and complexity.

To further improve the detection performance on test set and exhaustively
detecting the unseen object/class. We define this problem as Semi-Supervised
Object Detection (SSOD). Different from previous work, Soft-teacher [22]
proposed an end-to-end training framework for semi-supervised object
detection, student-teacher framework simultaneously improves the detector and
pseudo labels by leveraging a student model for detection training, and a
teacher model which is continuously updated by the student model through the
exponential moving average strategy for online pseudo-labeling.

We will detail the detection, segmentation model and semi-supervised object
detection method we used in the next chapter.

##  2 Method

###  2.1 Detection

DETR [1] proposed a Transformer-based end-to-end object detector without using
hand-designed components like anchor design and NMS, and achieves comparable
performance with Faster-RCNN [16]. Many following works continue to improve
the DETR-like model, and finally make DETR-like model the current new SOTA for
object detection. For example, Deformable DETR [25] predicts 2D anchor points
and designs a deformable attention module that only attends to certain
sampling points around a reference point; DAB-DETR [14] further extends 2D
anchor points to 4D anchor box coordinates to represent queries and
dynamically update boxes in each decoder layer; DN-DETR [11] introduces a
denoising training method to speed up DETR training. It feeds noise-added
ground-truth labels and boxes into the decoder and trains the model to
reconstruct the original ones.

DINO [23] collects the above improvements, and introduce a contrastive way for
denoising training, a mixed query selection method for anchor initialization,
and a look forward twice scheme for box prediction. DINO achieves the best
result of 63.2AP on COCO val2017, which is the current SOTA and show us its
powerful performance. Hence, We adopt DINO as our detector with bakcbone SwinL
[15].

###  2.2 Segmentation

ViT [6] also performed well in the segmentation track, for example, SETR [24],
Segmenter [18]. Masked-attention Mask Transformer (Mask2Former) [3], is a new
architecture capable of addressing any image segmentation task, and
outperforms of SOTA specialized architectures on all considered tasks and
datasets. Its key components include masked attention, which extracts
localized features by constraining cross-attention within predicted mask
regions. It also use multi-scale high-resolution features which help the model
to segment small objects.

ViT-Adapter [2] design a powerful adapater for plain ViT. It consists of: 1) a
spatial prior module to capture spatial features from the input image; 2) a
spatial feature injector to inject spatial priors into the ViT; 3) a multi-
scale feature extractor to extract hierachical features fromt the ViT.

Therefore, We adopt Mask2Former [3] as our segmentor with backbone ViT-
Adapter-L [2].

###  2.3 Semi-Supervised Object Detection

Prevalent SSOD paradigm is to use a multi-stage self-training pipeline: 1)
train model on labeled data; 2) generate pseudo labels on unlabeled data; 3)
retrain model on both labeled and pseudo-labeled data; 4) repeat this process
if needed. Soft Teacher [22] proposed an end-to-end semi-supervised approach,
in contrast to previous complex multi-stage method. The end-to-end training
gradually improves pseudo label qualities during the curriculum, and the more
and more accurate pseudo labels in turn benefit object detection training. We
transplant the DINO model to the soft-teacher training framework, and finetune
our detection model on UVO test dataset as unlabeled data, and UVO train/val
dataset labeled.

##  3 Dataset

###  3.1 Frame Track limited

Only ImageNet [5] annotations and COCO17 [13] annotations (bounding box, mask,
category) are allowed in this track.

###  3.2 Frame Track unlimited

Detection: ImageNet is used to pretrain backbone network. We pre-train our
detector on Object365 [17] and COCO [13] datasets. Then, detector is finetuned
on UVO frameset trainval. Finally, the model will be trained with the pseudo-
label of test set under soft-teacher framework to improve the performance on
test set. Object365 is a large-scale detection dataset with over $1.7M$
annotated images for training, the experiments also proved that the pre-
training of object365 resulted in a significant performance improvement. One
of our observations is that using COCO pretrain did not lead to performance
boosting when our model is trained enough Object365.

Segmentation: We cropped all instances which have segmentation annotation from
OpenImage [10] and COCO [13] dataset. Our segmentation task thus becomes a
fore/background semantic segmentation of a single object. We pretrain our
model on OpenImage and COCO instances and finetune on UVO frameset trainval.

###  3.3 Video Track

Our experiments proved that video dense set contains a large number of
duplicate samples which may lead the model overfitting on training set,
results in the performance degradation on test set. Therefore, we use the same
data setting as Frame Track Unlimited. It should be noted that, the amount of
training, validation and test set has doubled, compared with the last
challenge.

##  4 Implementation Details

###  4.1 Detection

DINO [23] is composed of backbone, transformer encoder, transformer decoder
and prediction heads. To achieve SOTA results, we use the SwinL [15]
pretrained on ImageNet as our backbone. We use the same random crop and scale
augmentation during training following DINO [23]. For DINO-5scale, we extract
features from stages 1, 2, 3 and 4 of the backbone and an extra feature by
down-sampling the ouput of stage 4. We first pre-train DINO on COCO [13] with
36-epoch setting (also called 3x) and pre-train on Object365 [17] with
12-epoch setting (1x), then finetune it on UVO. DINO is pretrained in class-
agnostic way with bakcbone learning rate $1e-4$, other hyper-parameters are
same as DINO.

###  4.2 Segmentation

We trained our Mask2former-ViT-Adapter with MMSegmentation [4]. The patch size
of ViT is fixed to 16. The feature interaction times of adapter is set to
$N=4$. Deformable attention is adopted in two feature interaction operators,
in which the number of sampling points is fixed to 4. In last interaction,
three multi-scale feature extractors are stacked together. We employ an AdamW
[55] optimizer with an initial learning rate of $2\times 10^{-5}$, and weight
decay of 0.05. Random horizontal flipping, random cropping as well as random
color jittering are used as data augmentation. We use a crop size of
$512\times 512$, a batch size of 4 and train models for 320k and 80k
iterations for OpenImage COCO pre-train and UVO finetune respectively.

###  4.3 Semi-Supervised Object Detection

Let us introduce training pipeline first. As shown in Fig.1, for un-labeled
image, two views of the image are generated by a strong and a weak
augmentation. The weakly augmented view is forwarded through the teacher to
produce the detection prediction. Then the filter generates the pseudo-labels,
which are used to supervise the learning of the student on the strong
augmentation.

There are two ways to filter out low-quality candidate boxes: confidence
threshold and topK. We have done experiments on the two methods, and the
results show that topK is better and we set $K=15$. Follwing [19], for strong
augmentation, we apply horizontal flipping, random resizing, random size
cropping, color jittering, grayscale, gaussian blur, and cutout patches; For
weak augmentation, only random horizontal flipping is used. Even though we
trained on 32G V100, we still restricted by GPU memory. The maximum size of
image height and width is set to 1000, and set batch size of labeled data to
1. We believe that performance can be further improved if computing resources
are not restricted. Finally, We evaluate our model on teacher model.

Figure 1: Teacher-Student SSOD framework

###  4.4 Video tracker

We tried DeepSort [21] to track the detection bounding boxes, but the effect
was not satisfactory. So we use last year winner’s method, more details and
discussion in the next section.

##  5 Experiment Results

###  5.1 Frame Track Limited

UVO dataset contains many non-coco objects, our semi-supervised method is
dedicated to learning novel object. After our detector is pretrained well on
COCO, we use different part of UVO dataset as unlabeled data and test on
validation dataset. In Tab.1, SSOD can improve a 62.4 AR@100 by + 3.9 AR@100,
reaching 66.3 AR@100, by leveraging unlabeled data. Besides, we find that
using more unlabeled data does not bring extra benefits, that may be caused by
the big gap inside the UVO dataset.

Table 1: Different Part of dataset used for SSOD and eval on UVO validation dataset Unlabeled dataset | AR@100
---|---
Without Semi-finetune | 62.4
Val | 66.3
Train + Val | 66.1

###  5.2 Frame Track Unlimited

Fig.2 demonstates the improvements we have made during training. DINO-4scale
pretrained on COCO and fine-tune on UVO trainset is our baseline which
achieved AR@100 of 76.6. By using 5scale and training with more epochs (3x),
the performance could be improved by 1.3 points. Object365 pretrain could
boost the performance heavily by 4.1 points and achieved AR@100 of 82.0. With
the final semi-supervised object detection strategy finetune on pseudo-label,
we slightly improved by 0.2 point and achieved AR@100 of 82.2 on UVO
validation set. Compared with the obvious improvement in Tab.1, pseudo-label
finetune did not improved that much, because the pre-trained model is already
powerful.

UVO annotated instance masks in a class-agnostic way, based on our experiment
setup, our segmentation task aims to segment fore/background of a single
object. As shown in Fig.2, by increasing the amount of pretrained data, our
segmentation performance is significantly improved.

Figure 2: UVO validation Bounding box AR and foreground IoU

###  5.3 Video Track

We meant to use a different tracker from last year’s winner [7], but the
results were not good. We tried the DeepSort [21] scheme as our tracker to
track the detection bounding boxes. DeepSort is an online and real-time method
based on tracking by detection. It performs Kalman filtering in image space
and frame-by-frame data association using the Hungarian method with an
association metric that measures bounding box distances. The distance between
each bounding box is measure by CNN features extracted from well-trained Re-
identification model. We trained a simple classification model of Resnet50 [9]
according to the label annotation from UVO. After adjust hyperparameters for
several times, e.g. NMS thresh, confidence thresh and metric distance, the
highest AR@100 we got is $20.8$, which is far from 32.2 by Du et al.[7]
tracking solution.

Hence, the final results we submitted, is still used last year’s winner
tracking scheme. Althogh DeepSort achieves a good performance in terms of
tracking precision and accuracy, it returns a relatively high number of
identity switches. This is, because the employed association metric is not
accurate enough. UVO dataset annotate 80 coco categories, and for non-coco
categories, they uniformly annotate as 1 category. For non-coco target, the
features extracted from Reid model are close, which leads to unsatisfactory
tracking results.

###  5.4 Visualization

We visualize instance segmentation predictions of our method on UVO testset in
Fig. 3. UVO [20] provides 12.29 object annotations per video on average, so we
visualize the top 12 confident instances for each image visualization. Note
that, for better visual effect, random colors represent different instances
rather than categories, UVO is class-agnostic.

Figure 3: UVO testset visualization

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