# Production of hypernuclei from antiproton capture within a relativistic
transport model

A. Schmidta Corresponding author<EMAIL_ADDRESS>T. Gaitanosb A.
Obertellia and J.-L. Rodríguez-Sánchezc

(aTechnische Universität Darmstadt, Fachbereich Physik, Darmstadt 64289,
Germany
bPhysics Department, School of Physics, Aristotle University of Thessaloniki,
Thessaloniki 54124, Greece
cCITENI, Campus Industrial de Ferrol, Universidade da Coruña, Ferrol 15403,
Spain)

##  1 Introduction

Knowledge of the baryon-baryon interactions is an essential premise for the ab
initio description of baryonic few- and many-body systems. In the nucleonic
(N) sector, these interactions can be described by phenomenological boson-
exchange models [1, 2] or using potentials derived from chiral effective field
theory [3, 4], relying on precise existing NN-scattering data as well as
measured binding energies of light nuclei.
The introduction of a hyperon (Y) inside a nucleus additionally requires data
to constrain the interaction of Y with nucleons [5]. In case of the lightest
hyperon, the -baryon (valence quarks $u,\,s,\,d$), the N interaction has a
short attractive range, typically modelled via the exchange of pions or
heavier mesons [6]. Additional contributions arise from the allowed strange
meson exchange as well as the strong N-N coupling [7, 8, 9].
The latter effect is also essential to reproduce astrophysical observations of
neutron stars of two solar masses [10, 11] with models that account for the
equilibrium of production and decay of strange baryons in the dense core of
neutron stars [12], but additional experimental data are needed to constrain
the parameters of the respective models.

Historically, experiments focused on the investigation of the scattering cross
sections of baryons on protons, mostly in the final state of a kaon- or pion-
induced strangeness production [13, 14, 15, 16]. Recently, $p$ scattering was
investigated at J-PARC [17, 18]. Additional constraints on the $p$ and $pp$
interaction are obtained by analyzing particle correlations via the femtoscopy
technique applied to ultra-relativistic $p$-$p$ and $p$-Pb collisions measured
by the ALICE experiment at the LHC [19, 20, 21]. In contrast to protons, there
are no experimental data on $n$ scattering. Properties of the YN interactions
inside a nuclear environment can also be extracted from the spectroscopy of
bound systems of nucleons and hyperons, i.e., hypernuclei. Several
phenomenological models [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]
and ab initio quantum Monte Carlo and no-core shell models have been made
possible for such hypernuclei [35, 36, 37, 38, 39, 40]. The experimental study
of hypernuclei to constrain the N interaction has been performed by
investigating their mass [41], -decay of excited states [42, 43, 44, 45, 46,
47, 48] and mesonic weak decay [49, 50]. For that, a hypernucleus is typically
produced by a strangeness exchange (K-,-) reaction [51, 52, 53], a strangeness
pair creation such as the (+,K+) process [54, 55, 56] or an electromagnetic
($e,e^{\prime}\mathrm{K}^{+}$) reaction [57, 58].
Pioneering experiments in 1973 [59] showed that ion collisions with energies
in the order of GeV can also be used for the production of light hypernuclei.
Related experiments at Dubna in the 1980s used light projectiles at energies
of about 2 GeV/nucleon and a [12][]C target [60], followed by the HypHI
experiment at GSI [61, 62]. At such energies, the main production mechanism is
the elementary NN $\rightarrow$ KN reaction with a threshold energy at 1.6
GeV. Heavier projectiles and targets, e. g. Ag-Ag and Au-Au, are used by the
HADES [63] and STAR [64] collaborations. Ultra-relativistic $p$-Pb and Pb-Pb
collisions at the ALICE experiment at LHC also allow the reconstruction of
light hypernuclei [65] emerging from the freeze-out of a quark-gluon plasma
[66, 67].
Simulations also indicate the possible population of heavier neutron-rich
hypernuclei in the fragmentation of residues with radioactive ion beams [68].
A dedicated experiment based on charge exchange reactions with heavy-ion
projectiles has been proposed [69].
Hypernuclei can also be produced in a strangeness exchange reaction
(K${}^{-}p\rightarrow$ 0 and K${}^{-}n\rightarrow$ - ) following an antiproton
annihilation on a nucleus or via a strangeness pair production in a pion-
nucleon interaction [70]. Such hypernuclei have first been experimentally
observed via delayed fission following antiproton stopping at the CERN-PS-177
experiment at the low-energy antiproton ring (LEAR) with an estimated
production rate of about 0.3 % to 0.7 % per annihilation [71, 72] on Bi and U
targets, respectively. Additionally, the future PANDA experiment at FAIR plans
to investigate the production of double- hypernuclei using a two-step reaction
[73, 74].
In this article, the production of hypernuclei using low-energy antiprotons
following the formation of antiprotonic atoms is investigated. In antiprotonic
atoms, the annihilation in the nuclear density tail occurs at rest [75], which
is simulated in the present work by an incident collision energy of few eV.
Previous simulation studies considered antiproton-induced reactions for
momenta in the range of GeV/$c$, thus investigating a different regime of the
antiproton-nucleus interaction [76, 77], where elastic and charge-exchange
channel become competitive with the annihilation [78]. Via the simulations,
the yields of specific hypernuclei with different stable target nuclei are
estimated, the production mechanism is discussed and the target’s isospin
dependence on the yields is investigated.

##  2 Framework

Antiprotonic atoms are first formed by the collision of an incident antiproton
with a single or multiple bound atomic electrons. After one of these
collisions, if the kinetic energy of the antiproton is similar to the electron
binding energy, it can be captured by the residual Coulomb potential into a
bound antiprotonic orbit [75]. The principal quantum number of the captured
antiproton $n_{\mathrm{\bar{p}}}$ scales with the principal quantum number of
the knocked out electron $n_{\mathrm{e}}$ and the square-root of quotient of
antiproton and electron masses as
$n_{\mathrm{\bar{p}}}\approx\sqrt{m_{\mathrm{\bar{p}}}/m_{\mathrm{e}}}\cdot
n_{\mathrm{e}}$. This implies that the antiproton is captured in an orbital
with similar size and binding energy $E_{\mathrm{B}}\sim
m_{e(\bar{p})}/n_{e(\bar{p})}^{2}$ as the knocked-out electron. Typically,
states with high angular momentum are populated due to the higher number of
available substates [79, 80]. From this highly excited state, the antiproton
deexcites via the emission of atomic Auger electrons and X-rays, favoring the
occupation of circular states ($n$, $l=n-1$) during the cascade [81]. For
principal quantum numbers of $n_{\mathrm{\bar{p}}}$ = 3 - 8, the orbitals
start to overlap with the nuclear wavefunction, leading to an annihilation
process for small overlap, i.e., in the tail of the nuclear density [79]. This
is consistent with measurement results from LEAR [82]. The mesons produced in
this annihilation at the nuclear surface can then interact with the residual
nucleus via final state interactions (FSI), which eventually lead to the
production of strange baryons. As the full process, from capture to
annihilation, occurs over a wide range of energy scales and interactions, it
cannot be treated fully microscopically. This paper focuses on the final
annihilation process and presents approximate simulations in the form of
ultra-peripheral collisions with low relative energy. All simulations
presented are performed in two steps. In the first step, the peripheral
annihilation of an antiproton with low relative momentum and the subsequent
production of an excited hypernucleus are simulated with the Gießen-Boltzmann-
Uehling-Uhlenbeck (GiBUU) transport framework [83]. The deexcitation of the
excited hypernucleus into a ground state via nucleon, and photon emission is
then performed in the second step with the ABLA++ evaporation and fission
module [84].
The transport code GiBUU and the simulated flow of particles in a reaction are
based on the relativistic Boltzmann-Uehling-Uhlenbeck equation [85], which
reads

$\left[k^{*\mu}\partial_{\mu}^{x}+\left(k_{\nu}^{*}F^{\mu\nu}+m^{*}\partial_{x}^{\mu}m^{*}\right)\partial_{\mu}^{k^{*}}\right]f\left(x,k^{*}\right)=\mathcal{I}_{\text{coll}}.$
(1)

It describes the evolution of the one-body phase space distribution function
$f\left(x,k^{*}\right)$ for hadrons within a hadronic relativistic mean field
with the kinetic four-momentum $k^{*}=k-V$, the vector potential $V$ in the
form of an in-medium self-energy which depends on the meson currents, the
field tensor $F^{\mu\nu}=\partial^{\mu}V^{\nu}-\partial^{\nu}V^{\mu}$, the
effective mass $m^{*}=m+S$ with the scalar potential $S$ and the contribution
of binary collisions and resonance decays $\mathcal{I}_{\text{coll}}$. The
hadron propagation in the mean field and scattering cross sections for binary
collisions are applicable for a typical energy range of tens of MeV to tens of
GeV. As the mesons produced in an annihilation of an antiproton and a nucleon
have a typical energy of tens to hundreds of MeV, their propagation is thus
suitably described by the framework.
So far, GiBUU has been used for simulating numerous phenomena such as the
dilepton production at SIS-18/GSI energies [86, 87], neutrino-induced
reactions [88], proton-induced reactions [89] and the formation of hypernuclei
in high-energy reactions [73, 90, 91]. Owing to the experience in hypernuclear
physics and the implementation of antiprotons as projectiles, including
realistic branching ratios for the annihilation process, GiBUU was chosen for
modeling the production of hyperons based on peripheral antiprotonic
annihilations.
To prepare an annihilation process at rest, the antiproton is defined as a
projectile with a low kinetic energy of 10 eV, while the nucleus of interest
is initialized as a target at rest. A variation of the antiproton projectile
energy up to 100 eV did not affect the simulation results. For a given proton
and neutron number, the respective density profiles are then derived in the
relativistic Thomas-Fermi model [92]. The impact parameter of the collision
depends on the nucleus of interest and is set to reproduce the radial
annihilation profile observed in antiprotonic atoms, which typically has a
median radius 2 fm outside the half-density radius of the nucleus. A
comparison of the annihilation site distribution derived from the GiBUU
simulations with distributions derived by the QED wavefunction overlap for 16O
and 132Xe as target nuclei are shown in Fig. 1. The theoretical distributions
are derived from the overlap of the nuclear density with the antiprotonic
orbitals, at which the annihilation occurs. In the case of [16][]O, a mixing
of $n_{\mathrm{\bar{p}}}=3,\,4$ (20 %, 80 %) is assumed based on absorption
width measurements in water targets [93, 94], and for [132][]Xe a mixing of
$n_{\mathrm{\bar{p}}}=7,\,8$ (20 %, 80 %) is interpolated from X-ray intensity
measurements on tin isotopes [95]. It is observed that an annihilation
probability density derived from the antiproton radial wavefunctions in the
orbitals of annihilations leads to a wider distribution than the simulated
annihilation locations in the particle-based transport code GiBUU, leading to
an underestimation of super-peripheral annihilation processes. This effect is
pronounced strongly for the lighter nuclei, where a sharp drop of the
annihilation probability is observed at high radii. However, the mean and
median radius of both distributions are similar, so that the majority of
annihilation locations are well reproduced.

Figure 1: Antiproton annihilation probability density simulated in GiBUU (blue
histograms) compared to a prediction based on the antiprotonic radial
wavefunction for absorption (solid blue lines) for the examples of [16][]O and
[132][]Xe, where $r$ represents the radial distance to the center of the
nucleus. The mean and median values of the distributions are similar, but the
particle-based GiBUU simulation underestimates the width compared to the QED-
based prediction. The corresponding nuclear density profiles are shown in
rose.

The annihilation process of the antiprotons with protons and neutrons in GiBUU
is modelled with phenomenological branching ratios for the annihilation
products, as summarized in appendix A. The mesons produced in the final state
of the annihilation can then interact in a second step with the residual
nucleons to produce a baryon via direct strangeness exchange with a primary
kaon (i.e., K${}^{-}n\rightarrow$ -, K${}^{-}n\rightarrow$ -,0 0,-,
K${}^{-}p\rightarrow$ 0 and K${}^{-}p\rightarrow$ +,-,0 -,+,0), which is
produced in about 5 % of annihilations, or via $s$-$\bar{s}$ pair production
induced by a pion (i.e., $\mathrm{N}\rightarrow$ K and $\mathrm{N}\rightarrow$
K for all possible charge combinations). The momentum-dependent cross sections
for the individual processes and their implementation in GiBUU are detailed in
[83], and are taken from [70] for the pion-induced strangeness production and
from [96] for the strangeness exchange with kaons. In the next step, the
decision if the produced leads to the formation of a hypersource is taken
based on phase space coalescence in the final state of the initial collision,
i.e., at points in time well beyond their production. A hypersource therefore
corresponds to an excited hypernucleus after the collision phase and before
the statistical decay phase. If the baryon density at the location of the
exceeds the cutoff density of $\rho_{\mathrm{c}}=0.01\,\rho_{0}$, it is
attributed to a hypersource, similarly to all other baryons fulfilling the
condition. For this hypersource, the total energy is then calculated as the
sum over the particles’ momenta and the mean field potentials at their
locations.
To extract the excitation energy of the hypersource, the mass of the
respective ground state nucleus has to be subtracted from the determined total
energy by assuming a modified Bethe-Weizsäcker mass formula for hypernuclei,
which is fitted to experimental data on hypernuclear binding and separation
energies [97]. This typically leads to excitation energies in the order of 0
to 6 MeV/nucleon, as depicted in Fig. 2.

Figure 2: Distribution of the excitation energy Eex of the hypersources as simulated by GiBUU. The connecting lines guide the eye and a vertical offset is included for better visibility, as indicated in parentheses. Table 1: Simulated statistics of the antiproton annihilations in GiBUU. Hypersources (HS) are excited hypernuclei, which are defined by phase-space coalescence. Only statistical uncertainties are presented. The initial sample for each nucleus includes 250,000 collisions. Nucleus | annihilations |  s |  rate in $\%$ | HSs | HS rate in $\%$ | HS per
---|---|---|---|---|---|---
[16][]O | 223,344 | 3,039 $\pm$ 55 | 1.36 $\pm$ 0.02 | 601 $\pm$ 25 | 0.27 $\pm$ 0.01 | 0.198
[40][]Ar | 231,893 | 4,007 $\pm$ 63 | 1.73 $\pm$ 0.03 | 1,325 $\pm$ 36 | 0.57 $\pm$ 0.02 | 0.331
[84][]Kr | 249,731 | 5,566 $\pm$ 75 | 2.23 $\pm$ 0.03 | 2,435 $\pm$ 49 | 0.98 $\pm$ 0.02 | 0.437
[132][]Xe | 249,858 | 6,032 $\pm$ 78 | 2.41 $\pm$ 0.03 | 2,915 $\pm$ 54 | 1.17 $\pm$ 0.02 | 0.483

In ABLA++, the hypersources and their excitation energies are then used as an
input to determine their deexcitation via fission or evaporation of either
protons, neutrons or other light particles based on the Weisskopf formalism
[98] and finally gammas until a ground state hypernucleus is reached. The code
has been used to validate the deexcitation and evaporation of residues [99,
100] following the fission of [181][]Ta [101] and [208][]Pb [102, 103, 104,
105], and recently to investigate the hypernuclear formation in nucleon-
induced spallation reactions [106, 107, 108]. The latter was made possible by
implementation of the Bethe-Weizsäcker mass formula and its hypernuclear
extension, which allows the calculation of particle separation energies as the
difference in binding energy of the initial (hyper-)nucleus and the residual
(hyper-)nucleus after a potential evaporation. Besides the excitation energy
and baryon content, the momentum, kinetic energy and angular momentum of the
hypersource have to be provided. The latter is not directly accessible in
GiBUU. It is assumed that low angular momentum states are predominantly
populated, so that $J=2$ was set for all deexcitation processes.

##  3 Yields

Based on previous experimental and simulation studies on strangeness
production in antiproton annihilations, the expected rate of production is in
the order of about 1 $\%$ to 3 $\%$ per annihilation, depending on the target
nucleus [76, 77, 109, 110]. As the annihilations treated in the following
simulations occur on the nuclear surface, it is expected that not all s will
be captured by the residual nucleus to form an excited hypersource. Thus, to
get an overview over the accessible range of hypernuclei after deexcitation, a
sufficient number of annihilations has to be considered.
For each target nucleus, about 250,000 initial collisions were simulated. Due
to the peripheral initialization with large collision impact parameter, an
annihilation occurs in about 90 to 95 % of all collisions, while otherwise the
antiproton simply passes the nucleus without an interaction. The amount of
simulated annihilations and production rates of baryons and hypersources per
annihilation are presented in Table 1. The rate of baryons is consistent with
the previous measurements with stopped antiproton beams at LEAR [71, 72], and
between 20 $\%$ to 50 $\%$ of the hyperons can form a hypersource after
interacting with the residual nucleus, while the capture probability increases
with the number of residual nucleons. To estimate the statistical uncertainty
of the yields, we assume that the production of baryons and hypersources
follows a Poisson distribution, as all simulations are performed within the
standard parallel-ensemble method over the same time interval [83].
Typically, a few protons and neutrons are evaporated by the initial
annihilation, leading to a high abundance of hypersources with baryon mass
numbers close to the initial nucleus. The excitation energies range from 0 up
to 10 MeV/nucleon with a mean value of about 1.5 MeV/nucleon for [132][]Xe,
1.9 MeV/nucleon for [84][]Kr, 2.4 MeV/nucleon for [40][]Xe, and 4.2
MeV/nucleon for [16][]O. This mean excitation energy per nucleon scales
approximately inversely with the square root of the ratio of baryon numbers,
leading to a total excitation energy that scales up with the square root of
the baryon numbers. The absolute values for the excitation energies are
comparable with other production approaches for hypernuclei, such as
relativistic light ion collisions [111]. As the typical nucleon separation
energy is about 10-15 MeV and the alpha particle removal energy is about 35
MeV, most hypersources will deexcite via the emission of a few alpha particles
and several nucleons, leading to overall lighter ground state hypernuclei.
Figure 3 depicts the dependence of the hypersource mass number before the
deexcitation and the final ground state hypernucleus mass number depending on
the initial excitation energy per nucleon for the case of [40][]Ar. While low
excitation energies up to about 3 MeV/nucleon lead to the production of heavy
g.s. hypernuclei, the emission channel becomes accessible for higher
excitation energies, leading to free hyperons ($A=1$) in the final state of
the deexcitation.

Figure 3: Dependence of the final g.s. hypernuclei on the initial excitation energy of the corresponding hypersource derived from GiBUU for the case of [40][]Ar. Figure 4: Yields of different hypernuclear isotopes per annihilation on the respective target nucleus. The landscape of already investigated hypernuclei is shaded in gray [112]. Table 2: Most abundant g.s. hypernuclei after deexcitation in ABLA++ for the four reference nuclei. [16][]O |  [40][]Ar |  [84][]Kr |  [132][]Xe
---|---|---|---
nucleus | rate in $10^{-5}$ | nucleus | rate in $10^{-5}$ | nucleus | rate in $10^{-5}$ | nucleus | rate in $10^{-5}$
[10][]B | 9 $\pm$ 2 |  [29][]Al | 19 $\pm$ 3 |  [65][]Cu | 28 $\pm$ 3 |  [109][]Ag | 21 $\pm$ 3
[7][]Li | 8 $\pm$ 2 |  [32][]Si | 15 $\pm$ 3 |  [72][]Ge | 24 $\pm$ 3 |  [113][]In | 19 $\pm$ 3
[10][]Be | 7 $\pm$ 2 |  [28][]Al | 15 $\pm$ 3 |  [71][]Ga | 21 $\pm$ 3 |  [104][]Pd | 18 $\pm$ 3
[11][]B | 6 $\pm$ 2 |  [31][]Al | 13 $\pm$ 2 |  [69][]Ga | 20 $\pm$ 3 |  [106][]Pd | 16 $\pm$ 3
[9][]Be | 5 $\pm$ 2 |  [28][]Mg | 13 $\pm$ 2 |  [62][]Ni | 19 $\pm$ 3 |  [107][]Ag | 16 $\pm$ 3

Figure 4 summarizes the yield of ground state hypernuclei after the
deexcitation simulation in ABLA++ relative to an annihilation process. For
each initial nucleus, a predominant region of production arises with
production rates of 1 to 2 per mille for several hyperisotopes indicated by
red-shaded colors, indicating that a wide range of so-far undiscovered
hypernuclei becomes accessible.
Similarly to the total excitation energy, the difference of the initial
nucleus baryon number and the high production g.s. hypernuclei baryon number
rises with the square root of the initial baryon numbers. In Table 2 the five
most abundant g.s. hypernuclei and their simulated production rates are
summarized for each target nucleus. Combining the yields from all four initial
nuclei, over 200 new hypernuclei in the medium-mass region of the hypernuclear
chart are accessible. We underline here that an experimental method to tag and
identify produced hypernuclei still needs to be implemented. While this work
focuses on the prediction of production yields, effort towards an experimental
implementation are ongoing.
The rate of production for a hypernucleus of interest reaches up to a few
$10^{-4}$ per annihilation. Consequently, at least tens of millions
antiproton-nucleus annihilations have to be considered to provide sufficient
statistics for a significant measurement. Such conditions can be reached at
the extra-low energy antiproton (ELENA) ring of CERN [113], where up to 107
antiprotons/bunch are provided every 120 seconds, so that a measurement of a
specific hypernucleus could be performed within a few hours for the considered
stable reference nuclei. The properties of the produced hypernuclei, e.g.
their ground state mass, can then be accessed based on their mesonic weak
decay via an invariant mass measurement. While the light hypernuclei produced
from oxygen decay predominantly via meson emission, the non-mesonic decay N
$\rightarrow$ NN is dominant for the heavier hypernuclei originating from
argon, krypton and xenon [114, 115].
The authors have been made aware of a recent first implementation of
antiproton annihilations at rest and in-flight within the INCL nuclear cascade
transport code, integrated inside GEANT4 [116]. When available, a comparison
of this model’s predictions to the present work for hypernuclei production
would be of interest.

Table 3: Statistics of the strangeness production from antiproton annihilations in GiBUU assuming only strangeness exchange (SE) or non-strange meson interactions (NSMI). Nucleus | open channel | annihilations |  s |  rate in $\%$ | HSs | HS rate in $\%$
---|---|---|---|---|---|---
[40][]Ar | SE | 9,230 | 180 $\pm$ 13 | 1.95 $\pm$ 0.15 | 66 $\pm$ 8 | 0.71 $\pm$ 0.09
NSMI | 9,217 | 50 $\pm$ 7 | 0.54 $\pm$ 0.08 | 14 $\pm$ 4 | 0.15 $\pm$ 0.04
[84][]Kr | SE | 9,994 | 230 $\pm$ 15 | 2.30 $\pm$ 0.15 | 102 $\pm$ 10 | 1.02 $\pm$ 0.10
NSMI | 9,995 | 89 $\pm$ 9 | 0.89 $\pm$ 0.09 | 22 $\pm$ 5 | 0.22 $\pm$ 0.05

###  3.1 Strangeness Production Mechanism

To investigate how the baryons are produced subsequently to the initial
annihilation in GiBUU, the cross sections for strangeness exchange reactions
of nucleons with kaons and the strangeness production by pions as well as and
mesons have been set to zero separately.
The two target nuclei [40][]Ar and [84][]Kr have been considered to examine
the ratio of the production channels for different masses of target nuclei.
For all simulations, the and production channels are considered together due
to the strong coupling between the two baryons. The simulations were performed
with similar initial conditions. The resulting baryon and hypersource
production rates are summarized in Table 3.
For both nuclei, the strangeness exchange with primary kaons is the dominant
and hypersource production mechanism, contributing to about 82 %, while the
remaining 18 % are produced via nucleon non-strange meson interactions. The
baryons produced in a strangeness exchange reaction have a probability of
about 40 to 50 % to be created in a low-momentum state which allows the
attribution to a hypersource, while only about 25 % of the produced by pion
interactions can be captured by the residual nucleus.

###  3.2 Isospin dependence

Figure 5: Impact of the initial target nucleus on the yields along different
hyperisotopic chains. The neutron-deficient [124][]Xe favors the production of
lighter and more neutron-deficient isotopes in the [][]Mo and [][]Pd chains ,
while [132][]Xe provides high yields in neutron-rich and heavy isotopes along
the [][]Pd and [][]Sn chains.

For the simulations presented above, the most abundant isotope of each
reference target nucleus was taken into account. However, there are other
stable isotopes of, e.g., argon and xenon, which can be considered for the
production of more neutron-deficient hypernuclei due to a lower neutron number
in the initial target nucleus. In the following, simulations are presented for
[36][]Ar and [124][]Xe and the hypernuclear yields are compared to the results
of [40][]Ar and [132][]Xe, respectively. While the overall production rate of
hypernuclei remains similar, the yields of individual hyperisotopes shift
according to the initial neutron number. Figure 5 summarizes the yields of
different ground state hypernuclei along different isotopic chains based on
annihilations on [124][]Xe and [132][]Xe. While the heavier and neutron-rich
target isotope favors the production of high $Z$ and high $N$ hypernuclei
along the [][]Sn chain, the neutron-deficient target favors the production of
more neutron- and proton-deficient hypernuclei along the [][]Mo chain. A
similar trend is also observed for the case of argon isotopes, with higher
yields of [][]Si isotopes for [40][]Ar and a strong abundance of the [][]Mg
chain for [36][]Ar. To cover an as wide range of the hypernuclear chart as
possible, it is thus useful to consider the full range of stable target
isotopes.

##  4 Conclusion

The production of single -hypernuclei from the peripheral annihilation of a
captured antiproton following the formation of antiprotonic atoms has been
investigated systematically. We report on Monte-Carlo simulations within the
GiBUU transport framework, while the deexcitation of hyperfragments is
performed with the ABLA++ code. The sites of annihilations are derived by
fitting to the overlap of the nuclear density with analytical radial
antiprotonic orbital wavefunctions from QED. Following the initial
annihilation, the produced mesons interact with the residual nucleus and
produce hyperons in about 1 $\%$ to 3 $\%$ of annihilations, consistent with
previous measurements. The hyperons are predominantly produced via direct
strangeness exchange with primary kaons produced from annihilations in
$\sim$80 % of the cases, while pion-induced strangeness production contri-
butes to the remaining $\sim$20 %. The produced hyperons may then be captured
by the residual nucleons to form an excited hypersource based on phase-space
coalescence, where the hypersource rate per increases with the initial nucleus
mass number from about 20 $\%$ for [16][]O to about 50 $\%$ for [132][]Xe. The
deexcitation via evaporation of the excited hypersources determines the yields
and isotopic composition of ground state hypernuclei. The production rates of
specific g.s. hypernuclei reach up to a few $10^{-4}$ per annihilation. While
the statistical uncertainties of the presented results for the production
rates in GiBUU are guided by the number of initial annihilations simulated,
the uncertainties of the yields extracted from ABLA++ originate predominantly
from the uncertainty of the assumed hypernuclear binding energies and the
corresponding excitation energies. While this uncertainty might shift the
yields of individual hyperisotopes, the overall conclusion in terms of range
of accessible hypernuclei based on antiprotonic annihilations does remain.
The reported results based on peripheral annihilations of antiprotons on
nuclei indicate that a wide range of ground state hypernuclei can be populated
with competitive yields. By considering different stable target isotopes, long
hyperisotopic chains can be populated. Additional information about
hypernuclear properties and the underlying N and NN interactions could be
gained by investigating their weak decay. This work, along with the software
framework used, constitutes a first step towards exploring the feasibility of
a dedicated experiment at the ELENA accelerator at CERN.

Acknowledgements This work was supported by the European Research Council
through the ERC grant PUMA-726276 and the Alexander-von-Hum-boldt foundation.
We thank Meytal Duer for discussions on the content and the proof-reading of
the manuscript as well as Jean-Christophe David for his comments. J.L. R.-S.
is grateful for the support provided by the ’Ramón y Cajal’ program under
Grant No. RYC2021-031989-I.

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##  Appendix A Annihilation Branching Ratios

Branching ratios of final states for antiproton-proton annihilations (left)
and antiproton-neutron annihilations (right). In case of non-strange final
states, only channels with at least 2 $\%$ probability are depicted, and for
kaonic final states with at least 0.1 %.

Antiproton - Proton
---
Final State | Probability in $\%$
$\rho^{+}\rho^{-}$ | 3.37
$\pi^{+}\pi^{-}\pi^{0}$ | 2.34
$\pi^{+}\pi^{-}\rho^{0}$ | 2.02
$\pi^{+}\pi^{0}\rho^{-}$ | 2.02
$\pi^{-}\pi^{0}\rho^{+}$ | 2.02
$\pi^{+}\pi^{-}\omega$ | 3.03
$\pi^{+}\pi^{-}\pi^{0}\omega$ | 2.84
$\pi^{+}\pi^{+}\pi^{-}\pi^{-}$ | 2.74
$\pi^{+}\pi^{-}\pi^{0}\pi^{0}$ | 3.89
$\pi^{+}\pi^{+}\pi^{-}\rho^{-}$ | 2.58
$\pi^{+}\pi^{-}\pi^{-}\rho^{+}$ | 2.58
$\pi^{+}\pi^{-}\pi^{0}\rho^{0}$ | 6.29
$\pi^{+}\pi^{0}\pi^{0}\rho^{-}$ | 5.05
$\pi^{-}\pi^{0}\pi^{0}\rho^{+}$ | 5.05
$\pi^{+}\pi^{+}\pi^{-}\pi^{-}\pi^{0}$ | 2.61
$\pi^{+}\pi^{-}\pi^{0}\pi^{0}\omega$ | 2.58
$\pi^{+}\pi^{+}\pi^{+}\pi^{-}\pi^{-}\pi^{-}$ | 2.83
$\pi^{+}\pi^{+}\pi^{-}\pi^{-}\pi^{0}\pi^{0}$ | 9.76
$\pi^{+}\pi^{-}\pi^{0}\pi^{0}\pi^{0}\pi^{0}$ | 2.68
$K^{*+}K^{*-}$ | 0.225
$K^{*0}\bar{K}^{*0}$ | 0.225
$K^{0}\bar{K}^{0}\pi^{0}$ | 0.146
$K^{+}K^{-}\pi^{0}$ | 0.146
$K^{0}K^{-}\pi^{+}$ | 0.142
$\bar{K}^{0}K^{+}\pi^{-}$ | 0.142
$K^{0}\bar{K}^{0}\omega$ | 0.232
$K^{+}K^{-}\omega$ | 0.232
$K^{0}\bar{K}^{0}\rho^{0}$ | 0.202
$K^{+}K^{-}\rho^{0}$ | 0.202
$K^{0}K^{-}\rho^{+}$ | 0.234
$\bar{K}^{0}K^{+}\rho^{-}$ | 0.234
$K^{*+}\bar{K}^{0}\pi^{-}$ | 0.23
$K^{*-}K^{0}\pi^{+}$ | 0.23

Antiproton - Neutron
---
Final State | Probability in $\%$
$\rho^{-}\rho^{0}$ | 3.51
$\rho^{-}\eta$ | 2.27
$\rho^{-}\omega$ | 3.51
$\pi^{+}\pi^{-}\pi^{-}$ | 2.86
$\pi^{+}\pi^{-}\rho^{-}$ | 3.62
$\pi^{-}\pi^{0}\rho^{0}$ | 5.61
$\pi^{0}\pi^{0}\rho^{-}$ | 3.51
$\pi^{-}\rho^{+}\rho^{-}$ | 2.09
$\pi^{-}\pi^{0}\omega$ | 5.05
$\pi^{+}\pi^{-}\pi^{-}\omega$ | 10.52
$\pi^{-}\pi^{0}\pi^{0}\omega$ | 7.01
$\pi^{+}\pi^{-}\pi^{-}\pi^{0}$ | 5.51
$\pi^{+}\pi^{-}\pi^{-}\pi^{0}\pi^{0}$ | 2.72
$\pi^{+}\pi^{+}\pi^{-}\pi^{-}\pi^{-}\pi^{0}$ | 8.33
$\pi^{+}\pi^{-}\pi^{-}\pi^{0}\pi^{0}\pi^{0}$ | 6.67
$K^{0}K^{-}$ | 0.147
$K^{*-}K^{*0}$ | 0.184
$K^{0}K^{-}\pi^{0}$ | 0.316
$K^{0}\bar{K}^{0}\pi^{-}$ | 0.432
$K^{+}K^{-}\pi^{-}$ | 0.513
$K^{0}K^{-}\omega$ | 0.35
$K^{0}K^{-}\rho^{0}$ | 0.15
$K^{0}\bar{K}^{0}\rho^{-}$ | 0.77
$K^{+}K^{-}\rho^{-}$ | 0.77
$K^{*-}K^{0}\pi^{0}$ | 0.245
$K^{*0}K^{-}\pi^{0}$ | 0.245
$K^{*0}\bar{K}^{0}\pi^{-}$ | 0.13
$\bar{K}^{*0}K^{0}\pi^{-}$ | 0.13
$K^{*+}K^{-}\pi^{-}$ | 0.154
$K^{*-}K^{+}\pi^{-}$ | 0.154