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Title

First spectroscopic study of 51Ar by the (p,2p) reaction
Juhász M. M., Elekes Z., Sohler D., Utsuno Yutaka, Yoshida
Kazuki, Otsuka Takaharu, Ogata Kazuyuki, Doornenbal P.,
Obertelli A., Baba Hidetada, Browne F., Calvet D., Château F.,
Chen S., Chiga Nobuyuki, Corsi A., Cortés M. L., Delbart A.,
Gheller J.-M., Giganon A., Gillibert A., Hilaire C., Isobe T.,
Kobayashi Toshio, Kubota Yuki, Lapoux V., Motobayashi Toru,
Murray I., Otsu Hideaki, Panin V., Paul N., Rodriguez W., Sakurai
Hiroyoshi, Sasano Masaki, Steppenbeck D., Stuhl L., Sun Y. L.,

Author(s)Togano Yasuhiro, Uesaka Tomohiro, Wimmer K., Yoneda Kenichiro,
Achouri N. L., Aktas O., Aumann T., Chung L. X., Dombrádi Zs.,
Flavigny F., Franchoo S.,Gašparić I., Gerst R.-B., Gibelin J., Hahn
K. I., Kim D., Koiwai Takuma, Kondo Yosuke, Koseoglou P., Lee J.,
Lehr C., Linh B. D., Liu H. N., Lokotko T., MacCormick M.,
Moschner K., Nakamura Takashi, Park S. Y., Rossi D., Sahin E.,
Söderström P.-A., Takeuchi Satoshi, Törnqvist H., Vaquero V.,
Wagner V., Wang S., Werner V., Xu X., Yamada Hiroki, Yan D.,
Yang Z., Yasuda Masahiro, Zanetti L.

Citation
Text Version

Physics Letters B,814, p.136108_1-136108_8
Published Journal Article

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https://jopss.jaea.go.jp/search/servlet/search?5070832

DOI

https://doi.org/10.1016/j.physletb.2021.136108©2021 The Author(s). Published by Elsevier B.V. This is an open
Right

access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

Japan Atomic Energy Agency

Physics Letters B 814 (2021) 136108

Contents lists available at ScienceDirect

Physics Letters B
www.elsevier.com/locate/physletb

First spectroscopic study of 51 Ar by the (p,2p) reaction
M.M. Juhász a,b , Z. Elekes a,∗ , D. Sohler a , Y. Utsuno c,d , K. Yoshida d , T. Otsuka n,e,f ,K. Ogata g,h , P. Doornenbal n , A. Obertelli n,i,j , H. Baba n , F. Browne n , D. Calvet j , F. Château j ,S. Chen n,k,l , N. Chiga n , A. Corsi j , M.L. Cortés n , A. Delbart j , J.-M. Gheller j , A. Giganon j ,A. Gillibert j , C. Hilaire j , T. Isobe n , T. Kobayashi m , Y. Kubota n,o , V. Lapoux j ,T. Motobayashi n , I. Murray n,p , H. Otsu n , V. Panin n , N. Paul j , W. Rodriguez n,q,r ,H. Sakurai n,s , M. Sasano n , D. Steppenbeck n , L. Stuhl o , Y.L. Sun i,j , Y. Togano t , T. Uesaka n ,K. Wimmer s,n , K. Yoneda n , N.L. Achouri y , O. Aktas u , T. Aumann i,ab , L.X. Chung v ,Zs. Dombrádi a , F. Flavigny p , S. Franchoo p , I. Gašparić n,w , R.-B. Gerst x , J. Gibelin y ,K.I. Hahn z , D. Kim n,z , T. Koiwai s , Y. Kondo aa , P. Koseoglou i,ab , J. Lee l , C. Lehr i , B.D. Linh v ,H.N. Liu i,j,u , T. Lokotko l , M. MacCormick p , K. Moschner x , T. Nakamura aa , S.Y. Park z ,D. Rossi i,ab , E. Sahin ac , P.-A. Söderström n , S. Takeuchi aa , H. Törnqvist i,ab , V. Vaquero ad ,V. Wagner i , S. Wang ae , V. Werner i , X. Xu l , H. Yamada aa , D. Yan ae , Z. Yang n , M. Yasuda aa ,L. Zanetti iaAtomki, Eötvös Loránd Research Network (ELKH), P.O. Box 51, H-4001 Debrecen, Hungary
University of Debrecen, Egyetem tér 1, H-4032 Debrecen, HungarycCenter for Nuclear Study, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, JapandAdvanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japane
Department of Physics and Center for Nuclear Study, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japanf
Instituut voor Kern- en Stralingsfysica, Katholieke Universiteit Leuven, B-3001 Leuven, BelgiumgResearch Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japanh
Department of Physics, Osaka City University, Osaka 558-8585, Japani
Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germanyj
IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, FrancekState Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic of Chinal
Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kongm
Department of Physics, Tohoku University, Sendai 980-8578, Japann
RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, JapanoCenter for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japanp
Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, Franceq
Universidad Nacional de Colombia, Sede Bogota, Facultad de Ciencias, Departamento de Física, 111321, Bogotá, ColombiarPontiﬁcia Universidad Javeriana, Facultad de Ciencias, Departamento de Física, Bogotá, ColombiasDepartment of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japant
Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 172-8501, Japanu
Department of Physics, Royal Institute of Technology, SE-10691 Stockholm, Swedenv
Institute for Nuclear Science & Technology, VINATOM, P.O. Box 5T-160, Nghia Do, Hanoi, Viet Namw
Rud̄er Bošković Institute, Bijenička cesta 54, 10000 Zagreb, CroatiaxInstitut für Kernphysik, Universität zu Köln, D-50937 Cologne, Germanyy
LPC Caen, ENSICAEN, Université de Caen, CNRS/IN2P3, F-14050 Caen, Francez
Ewha Womans University, Seoul 120-750, Republic of Korea
aa
Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo, 152-8551, Japanab
GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germanyac
Department of Physics, University of Oslo, N-0316 Oslo, Norwayad
Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spainae
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People’s Republic of Chinab* Corresponding author.

E-mail address: elekes@atomki.hu (Z. Elekes).

https://doi.org/10.1016/j.physletb.2021.136108
0370-2693/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP3 .

M.M. Juhász, Z. Elekes, D. Sohler et al.

a r t i c l e

i n f oArticle history:
Received 1 December 2020
Received in revised form 22 January 2021
Accepted 24 January 2021
Available online 27 January 2021
Editor: D.F. Geesaman
Keywords:
Proton knock-out reaction
γ -ray spectroscopy
Invariant mass method
Nuclear structure
Shell closure

Physics Letters B 814 (2021) 136108

a b s t r a c t
The nuclear structure of 51 Ar, an uncharted territory so far, was studied by the (p,2p) reaction using
γ -ray spectroscopy for the bound states and the invariant mass method for the unbound states. Twopeaks were detected in the γ -ray spectrum and six peaks were observed in the 50 Ar+n relative energy
spectrum. Comparing the results to our shell-model calculations, two bound and six unbound states
were established. Three of the unbound states could only be placed tentatively due to the low numberof counts in the relative energy spectrum of events associated with the decay through the ﬁrst excitedstate of 50 Ar. The low cross sections populating the two bound states of 51 Ar could be interpreted as aclear signature for the presence of signiﬁcant subshell closures at neutron numbers 32 and 34 in argon
isotopes. It was also revealed that due to the two valence holes, unbound collective states coexist withindividual-particle states in 51 Ar.
© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .

1. Introduction

an aluminum wedged degrader at the ﬁrst focal plane F1, locatedbetween the two dipole magnets D1 and D2 of BigRIPS. The constituents of the resulting cocktail beam were tagged between the
focal planes F3 and F7 by time of ﬂight, energy loss and magnetic
rigidity measurements. The TOF was determined by plastic scintillators at F3 and F7 [28], while  E was taken from a gas ionizationchamber at F7 [29]. The trajectory of the particles was monitored
by several sets of parallel plate avalanche counters (PPAC) at F3, F5
and F7 [30,31].
The excited states of 51 Ar were produced in nucleon removal
reactions using the MINOS device [32] which consisted of apolyethylene terephthalate cell ﬁlled with liquid hydrogen and acylindrical time projection chamber (TPC) placed downstream of
the focal plane F13. The effective target length was determined to
be 151(1) mm. The TPC chamber contained a gas mixture of argon,
CF4 and isobutane at room temperature and atmospheric pressure. Its length, inner diameter, and outer diameter were 300 mm,
80 mm, and 178.8 mm, respectively. The point of reaction was reconstructed either by using the scattered and the removed protons
or one of the protons and the projected trajectory of the radioactive ions (the former method was preferred when both data wereavailable) [33]. An overall eﬃciency of 95% and a resolution of
5 mm (FWHM) along the beam axis was achieved for the events
when at least one proton was recorded by the TPC.
The prompt γ rays were detected by the DALI2+ array [34]consisting of 226 NaI(Tl) scintillator crystals packed in cylindricallayers of 10-28 units around the liquid hydrogen target and a forward wall of 64 units. This arrangement provided a coverage ofpolar angles between 15◦ and 118◦ . The beam-like fragments leaving the target were analyzed by the SAMURAI spectrometer [35]based on B ρ ,  E, and TOF measurements. The B ρ values were
derived via trajectory determination by multiwire drift chambers
located upstream (FDC1) and downstream (FDC2) of the magnet
operated at a central magnetic ﬁeld of 2.7 T. Downstream of the
FDC2 a plastic scintillator wall consisting of 24 bars yielded the E and the TOF relative to a plastic detector at F13.
For the observation of excited states decaying by neutron emission, neutron TOF spectrometers NeuLAND and NEBULA wereplaced at 11 m and 14 m, respectively, downstream of the target at 0◦ [36]. NEBULA consisted of 120 plastic scintillator bars,
each with a dimension of 12 cm(W)×12 cm(D)×180 cm(H) arranged in two walls. Both walls consisted of two layers and were
equipped with an additional thin (1 cm) layer of plastic scintillators vetoing against the charged particles. The front face of thewalls were separated by a distance of 85 cm. 400 NeuLAND units
with a dimension of 5 cm(W)×5 cm(D)×250 cm(H) developed by
the R3 B collaboration [37] were placed upstream of NEBULA in 8
alternating horizontal and vertical layers to increase eﬃciency.

Working on the origin of the elements, Maria Goeppert-Mayerand Edward Teller discovered a speciﬁc pattern and special numbers in atomic nuclei later named magic by Eugene Wigner. In
this context Goeppert-Mayer published her important work on theclosed shells [1,2] which paved the way to a fertile ﬁeld of nuclear
physics. It was soon realized that these magic numbers were notstatic, the location of single-particle states might change, and as aconsequence magicity could appear at numbers different from theconventional ones in certain regions of nuclei [3–5]. In the past
decades concerted experimental and theoretical efforts have been
made to uncover the change of magicity and its underlying mechanisms [6].
Based on the indirect (energy of the ﬁrst 2+ state, reduced transition strength, etc.) and direct (for example, two-neutron separation energy) indicators of magicity substantial experimental data
were collected which supported a new magic number at N = 32
for Cr [7,8], Ti [9,10], Sc [11], Ca [12–14], K [15], and Ar [16] isotopes. However, contrary results were also published for Ti [17]isotopes showing the limitation of the indicators. In addition, apossible subshell closure at the neutron number 34 was also predicted as early as about 20 years ago [18]. This magicity did not
manifest itself in Cr [8,7], Ti [9,19] and Sc [20] isotopes, however
few experiments indicated its presence in Ca [21–23] and Ar [24]isotopes.
The low-lying structure of 53 Ca, located between N = 32 andN = 34 was investigated by β -decay [25], multi-nucleon knock-out[21] and neutron knock-out [23] reactions. The observed lowest−
two excited states (3/2−
1 , 5/21 ) were interpreted by promoting aneutron to a higher orbital across the sizable shell gaps at 32 and34, respectively. By removing two protons from 53 Ca we arrive at
51
Ar, which is a similar outstanding case to test the magicity of theneutron numbers 32 and 34. Therefore, we have studied 51 Ar forthe ﬁrst time by the (p,2p) reaction in order to map its low-lying
excited states.
2. Experiment
The experiment was performed at the Radioactive Isotope Beam
Factory operated by the RIKEN Nishina Center and the Center for
Nuclear Study of the University of Tokyo. A beam of 70 Zn ions
was produced at an energy of 345 MeV/u and at a beam intensity of 240 pnA by the accelerator complex. This primary stablebeam collided with a 9 Be production target of 10 mm thickness
placed at the entrance of the BigRIPS separator [26] forming radioactive nuclei by fragmentation. The selection of ions of interest
was performed by the B ρ −  E − T O F method (B ρ : magnetic
rigidity,  E: energy loss, TOF: time of ﬂight) [27] using slits and2

M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

Approximately 200 particles hit the liquid hydrogen cell every
second while the intensity of the 52 K ions was about 6 pps. The
mean kinetic energy of the 52 K particles at the entrance of the target was measured to be 260 MeV/u, losing an average 83 MeV/u
while passing through the liquid hydrogen. 894 and 4002 eventswere counted in the 52 K(p,2p)51 Ar and 52 K(p,2p)51 Ar→50 Ar+n reaction channels, respectively.
3. Results and discussion
All the crystals of the DALI2+ array were calibrated for energy
several times during the experiment using 60 Co, 137 Cs, and 88 Y
radioactive sources, which allowed a correction for the gain shiftof the detectors (<0.4%). In order to increase the photopeak eﬃciency of the setup, an addback procedure was applied during theanalysis. This combined the hits in adjacent units (<15 cm) originating from a single γ ray undergoing Compton-scattering and/or
pair production. The Doppler-correction of the emitted γ rays was
performed using the vertex position determined by a tracking algorithm for protons in the TPC. The change of the drift velocity in
the TPC was monitored during the experiment and was taken into
account in the analysis.
Fig. 1 shows the Doppler-corrected experimental γ -ray spectra for 51 Ar fragments. In the upper panel, there was no selection
on the incoming beam, so all the reaction channels were included
while the lower panel shows the events for the 52 K(p,2p)51 Ar
reaction channel. Three peaks seem to be present in the upper
panel, the positions of which were determined at 809(16) keV,
963(9) keV, and 1180(9) keV by ﬁtting the spectrum with Gaussianfunctions plus a double-exponential background. The uncertainties originated from the statistics and the uncertainty due to theenergy calibration (5 keV). The peaks at 963 keV and 1180 keV
also appear for the 52 K(p,2p)51 Ar reaction channel but the peak at
809 keV is barely visible.
In order to further analyze the spectra, separate simulations were performed for the three transitions with the GEANT4
code [38]. The resulting response functions were added together
with individual scaling parameters plus a double-exponential background. The total ﬁts are presented by red lines (including threepeaks) in Fig. 1 while the backgrounds are plotted by blue lines.
The statistical conﬁdence of the peaks were determined to be 2.5σ ,8.7σ and 9.5σ for the three peaks in the upper panel, which indicates that the peak at 809 keV might not be real. For the lower
panel, the conﬁdence of this peak is even lower (1.0σ ) and the χυ2values showed that the spectra could be ﬁtted with an assumption of only two peaks (green line in Fig. 1). Therefore, the peak at
809 keV was not considered further.
Due to the low statistics, γ γ matrices could not be used toconclude coincidences for the γ rays, therefore we assumed thatboth transitions connected each an excited state and the groundstate establishing two levels at energies of 963 keV and 1180 keV.
The parallel placement of the γ rays is supported by the low
neutron separation energy of 51 Ar (S n = 1.4(7) MeV from mass
systematics [39], S n = 1.57 MeV from our shell-model calculation).
For the 52 K(p,2p)51 Ar reaction channel, the inclusive cross section
was determined to be 0.62(2) mb while the exclusive cross section was extracted to be 0.046(14) mb and 0.102(18) mb for the
963-keV and the 1180-keV states, respectively.
The unbound excited states of 51 Ar populated by the (p,2p) reaction were derived by reconstructing the relative energy (E rel ) of
the 50 Ar+neutron system. This energy is simply the difference between the invariant mass before and after the decay while the energy of the excited states can be calculated by adding the neutron
separation energy of 51 Ar. For the relative energy, the momentumof the 50 Ar ions were determined by the SAMURAI spectrometerand the momentum of the neutron by the NEBULA+NeuLAND TOF

Fig. 1. Doppler-corrected γ -ray spectra for 51 Ar using vertex reconstruction (requiring only a single proton in the TPC) and addback procedure (upper panel:
all reaction channels, lower panel: 52 K(p,2p)51 Ar reaction channel). The data witherror bars and shaded area represent the experimental spectrum, the red andgreen lines are the simulations including three and two peaks, respectively, plus
a double-exponential background, and the latter function (exponential background)is also plotted separately as a blue line.

spectrometer. The TOF calibration was performed using the γ -ray
ﬂash arriving at the spectrometer from the target before the neutrons. The unbound excited states of 51 Ar could decay in a waythat either the ground state or the excited states of 50 Ar were produced. For the latter case, the emitted γ rays were also taken into
account in order to correctly reconstruct the excited levels of 51 Ar.
The resulting relative energy spectra are shown in Fig. 2 where
the counts were corrected for the neutron detection eﬃciency of
the NEBULA+NeuLAND setup (55% at 100 keV, 20% at 5 MeV).
The upper panel includes all the events from the decay of unbound states in 51 Ar while the lower panel was prepared with agate on the E γ = 1.178 MeV transition between the ﬁrst excitedstate and the ground state of 50 Ar [16]. The resonances appearing
in the spectra were ﬁtted with Breit-Wigner functions [40] (linesof light green, light blue, magenta, cyan, dark green, dark blue)
according to the R-matrix theory [41]. The particular form of thefunctions included a central resonance energy parameter (E 0 ), an
energy-dependent apparent width parameter ( ), an orbital angular momentum parameter of the resonance (l), and a scaling
factor. On the other hand, a non-resonant contribution to the spectra could also arise which was modeled by a Maxwellian function(black line) [42] and added to the ﬁnal ﬁtting function (red line).
As a result, six resonances were identiﬁed the parameters ofwhich are listed in Table 1. The best ﬁt (χυ2 = 0.99) achieved
with the l values in the Table, however, these could not be used
for a deﬁnitive assignment since similar goodness of ﬁt could be
gained by different sets of orbital angular momentum parameters. In the lower panel only four peaks (271 keV, 1040 keV,
1494 keV, 1883 keV) out of the observed six seem to appear.
This spectrum was ﬁtted in a manner similar to the above men3

M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

E 5x = S n + 1494 keV + 1178 keV = S n + 2672 keV and E 6x = S n +1883 keV + 1178 keV = S n + 3061 keV. The exclusive cross sections
for the six states were obtained to be 0.93(12) mb, 1.54(24) mb,
1.56(20) mb, 0.35(12) mb, 0.7(3) mb and 0.23(9) mb, respectively.
To compare the experimental ﬁndings with theory, shell-model
calculations were performed in the sd-pf valence space employing effective interactions of SDPF-MUs Hamiltonian introduced inRef. [43] which is based on the SDPF-MU Hamiltonian [44,45]
ﬁne-tuned to take into account experimental data in this regionof nuclei, such as 49 K [46,47], 51 K, 53 K [43] and 54 Ca [21]. This
new SDPF-MUs Hamiltonian includes a shift of the original T = 0
central force monopole strength between the proton s1/2 and neutron p 1/2 orbitals as well as between the proton s1/2 and neutron
p 3/2 orbitals in order to better describe the experimental resultsfor 51 K and 53 K. Additionally, the neutron f 52/2 pairing matrix ele-ment was also shifted a little to better match the 2+ energies in
the Ca isotopes. The spin/parity of the ground state of 52 K was
not unambiguously determined experimentally. A β -decay study
excluded the 0− , and proposed the 2− assignment [48] but the
1− was also found to be possible by our shell-model calculations.
Therefore, when dealing with the (p,2p) reaction, both the 1− andthe 2− scenarios were considered.
The output of the shell-model calculations regarding the leveland decay scheme is shown in the left part of Fig. 3. The characteristics of the theoretical states are listed in Table 2. Since theneutron separation energy is not known for 51 Ar, the calculated
theoretical value of 1.57 MeV is plotted in Fig. 3, and the energyof the experimental states are also placed relative to this Sn . It
is worth noting that the mass systematics gives a similar S n of
1.4(7) MeV [39].
To compare the exclusive cross sections deduced from the experiment, we calculated the single-particle cross sections for the(p,2p) reaction within the distorted wave impulse approximation (DWIA) framework [49]. The single-particle wave function
and the nuclear density were obtained by the Bohr-Mottelson
single-particle potential [50]. The optical potentials for the distorted waves in the initial and ﬁnal channels were constructed by
the microscopic folding model [51] with the Melbourne g-matrix
interaction [52] and the calculated nuclear density. The spin-orbit
part of each distorting potential was disregarded, which introduced
an uncertainty of about 5% for the cross sections. As for the pp interaction, the Franey-Love effective interaction [53] was adopted.
These theoretical cross sections were combined with the spectroscopic factors of our shell-model calculations and averaged overthe beam energy covered by our target similar to the experimental exclusive cross sections. The resulting theoretical cross sections
with J π = 2− (52 K g.s.) for the relevant states are listed in Table 3
and also indicated next to the levels in Fig. 3.
The shell-model calculations provide two bound excited states(975 keV, 1117 keV) which are very close in energy to the proposed observed levels (963 keV, 1180 keV). Moreover, the calculated cross sections are also in a fair agreement with the experimental ones. This suggests that our assumption, i.e., the observed
transitions do not form a cascade but are parallel to each other, isvalid. The small experimental cross sections (46 μb, 102 μb) showthat these states are dominated by neutron excitations across theshell gaps at neutron numbers 32 and 34 since they are weakly
populated by the (p,2p) reaction. Likewise, the observed inclusive
cross section of 0.62(2) mb and the theoretical one of 1.15 mb
agree reasonably well. However, we note that an assignment opposite to the one in Fig. 3 can not be excluded for the two boundstates, i.e., J π = 5/2−
1 might belong to the observed 963-level andJ π = 3/2−
1 to the observed 1180-level. This good match between
the experimental results and the shell-model predictions suggeststhat the shell gaps at N = 32 and N = 34 are indeed large, as implied by the shell-model calculations, which is illustrated in Fig. 4

Fig. 2. Relative energy spectra for 51 Ar corrected for the energy-dependent neutron
detection eﬃciency including all the events from the decay of the excited states(upper panel) and only those events which were in coincidence with the transition
between the ﬁrst excited state and the ground state of 50 Ar (lower panel). The datawith error bars and shaded area represent the experimental spectrum. The red line
represents a ﬁt of Breit-Wigner functions (light green, light blue, magenta, cyan,dark green, dark blue) plus a background modeled by a Maxwell function. For the ﬁt
in the lower panel, the Breit-Wigner widths and positions were ﬁxed to the values
taken from the ﬁt in the upper panel.

Table 1
Resonance parameters determined by ﬁtting the spectrum of the52
K(p,2p)51 Ar→50 Ar+n reaction channel. E 0 is the central resonance energy,
is the energy-dependent apparent width, l is the deduced orbital angular momentum of the resonance. The statistical conﬁdence (C ) of the peaks is also
indicated.
E0
(keV)

(keV)

92(4)
271(13)1040(12)1449(35)
1883(56)2386(43)

69(11)
272(37)324(37)361(156)297(120)391(172)

l

C

0
0
1
3
1
1

41.5σ
35.2σ
47.8σ
17.4σ
7.9σ
13.3σ

tioned one but keeping E 0 ,and l ﬁxed to the values derived
from the ﬁt of the spectrum in the upper panel. The χυ2 = 1.50
value shows that our proposal of four resonances might be valid,
however, the spectrum could also be ﬁtted well with an assumption of three (271 keV, 1040 keV, 1494 keV) or even ﬁve(271 keV, 1040 keV, 1494 keV, 1883 keV, 2386 keV) peaks. In conclusion, this analysis unambiguously establishes an excited stateat E 1x = S n + 92 keV decaying to the ground state of 50 Ar andtwo states at E 2x = S n + 271 keV + 1178 keV = S n + 1449 keV
and E 3x = S n + 1040 keV + 1178 keV = S n + 2218 keV decaying
through the ﬁrst excited state in 50 Ar (1178 keV [16]). Due tothe low statistics in the lower panel of Fig. 2, we can only tentatively establish the three other states at E 4x = S n + 2386 keV,4

M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

Fig. 3. Partial level and decay scheme of 51 Ar up to the expected two-neutron separation energy of 5.6(7) MeV [39]. The two observed bound excited states with their decay
and relative γ -ray intensities corrected for the eﬃciency of the DALI2+ array are shown below the neutron separation energy of 1570 keV taken from our shell-model
calculation. Three further unbound excited states were also established by the experiment and three tentatively placed excited states are also plotted with dashed lines
together with their decay either to the ground state or the ﬁrst excited states of 50 Ar. The numbers on the right hand side of the levels indicate the extracted exclusive crosssection in the 52 K(p,2p)51 Ar reaction. The experimental data are compared with our shell-model calculations with J π = 2− (52 K g.s.). The calculated γ -ray branching ratios
are also written next to the downward arrows. Only those states are displayed for which the calculated (p,2p) cross section is above 0.1 mb. The four lowest excited statesobserved in the experiment could be matched with counterparts in the shell-model level scheme but it should be noted that the two bound states can also be assigned
inversely to the theoretical ones. The cross section values left hand side of the theoretical levels were derived from the spectroscopic factors and the theoretical single-particle
cross sections.

−and E 2x to the theoretical 5/2−
2 and 5/26 levels, respectively basedon the observed large cross sections (0.93(12) mb, 1.54(24) mb)
comparable to the theoretical ones. Regarding the calculated unbound 3/2− levels, it can be seen that all of them show somewhat
more proton dominance over the 3/2−
1 one based on the L z valstateisnotablebecause the z-component
ues. Besides, the 3/2−
7
(taking J z = J ) of its spin (S z ) is also large. This also shows up in
the calculated substantial cross section (0.85 mb). The energy andthe cross section of the observed state (E 3x , 1.56(20) mb) indicatethat it might be the counterpart of the theoretical 3/2−
7 level however, due to the resolution in E rel , it cannot be excluded that someother nearby theoretical levels contribute. The collective property−of the mentioned higher-lying states (especially for 5/2−
2 , 5/26 )can also be seen by comparing their calculated B ( E2) values of
53 e2 fm4 and 14 e2 fm4 to that of the individual-particle 5/2−
1state of only 5 e2 fm4 . Such a collective behavior is also present
for several higher-lying 3/2− states but not so emphasized. For
the remaining three other observed states, no corresponding theoretical levels can be determined because their energy is uncertain

for the N = 32 isotones. As protons are removed from the proton f 7/2 orbital, the neutron f 5/2 orbital increases rapidly. The
neutron p 3/2 and p 1/2 orbitals also moderately increase keeping
their energy splitting nearly constant, and as a consequence subshell gaps at neutron numbers 32 and 34 emerge in Ca and Ar
isotopes.
It is noted that the J π = 1− (52 K g.s.) scenario gives similar
results with a particular difference in the calculated cross section
value of 709 μb for the 5/2−
1 level contradicting the experimental
data, which supports the 2− assignment for the ground state of
52
K.
Looking at the characteristics of the calculated unbound states−in Table 2, it is obvious that the 5/2−
2 and 5/26 levels signiﬁcantly−
differ from the 5/21 level (and from the other calculated 5/2− levels) if we consider the z-component (taking J z = J ) of their angular momentum (L z ) values. For these two unbound states, the large
L z values indicate signiﬁcant proton contribution to the excitation, which is also reﬂected in the sizable calculated cross sections(2.64 mb, 1.97 mb). We propose to assign our observed states at E 1x5

M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

Table 2The z-component (taking J z = J ) of spin (S z ) and of angular momentum (L z ) together with the occupation number of nucleon orbitals for the theoretical states (E theor ) fromour shell-model calculations. Only those excited states are shown for which the theoretical (p,2p) cross section exceeds 0.1 mb.
E theor
(MeV)

Jπ

0

1/2−
1

0.975

3/2−
1

1.117

5/2−
1

1.826

5/2−
2

2.088

3/2−
2

2.884

5/2−
3

3.181

5/2−
4

3.268

3/2−
4

3.368

3/2−
5

3.459

5/2−
6

3.980

9/2−
2

3.981

5/2−
7

4.087

3/2−
7

4.137

9/2−
3

4.141

5/2−
8

4.229

3/2−
8

4.363

3/2−
9

4.527

3/2−
10

4.988

9/2−
6

5.361

9/2−
8

Nucleon
type

Sz

π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν
π
ν

−0.004−0.131−0.0140.243−0.009−0.181−0.046−0.185−0.0160.131−0.0070.062−0.036−0.073−0.091
0.095−0.0330.059−0.081−0.132−0.037−0.066−0.016−0.002−0.2190.025−0.0190.153−0.010−0.171−0.1740.067−0.0480.033−0.0600.102−0.067−0.135−0.004−0.068

Lz

0.025
0.610
0.216
1.055
0.199
2.491
1.439
1.291
0.785
0.599
0.344
2.101
0.373
2.236
0.924
0.572
0.848
0.626
1.269
1.443
1.261
3.342
0.914
1.605
0.908
0.787
1.043
3.323
0.616
2.065
0.798
0.810
0.368
1.147
0.367
1.090
1.068
3.635
0.707
3.865

Orbits
d5/2

d3/2

s1/2

f 7/2

f 5/2

p 3/2

p 1/2

5.83
6
5.82
6
5.78
6
5.83
6
5.77
6
5.79
6
5.79
6
5.83
6
5.85
6
5.86
6
5.78
6
5.82
6
5.85
6
5.76
6
5.81
6
5.87
6
5.81
6
5.89
6
5.78
6
5.73
6

2.46
4
2.65
4
2.66
4
2.68
4
2.80
4
2.73
4
2.66
4
2.60
4
2.61
4
2.67
4
2.59
4
2.75
4
2.89
4
2.74
4
2.75
4
2.75
4
2.80
4
2.88
4
2.57
4
2.70
4

1.72
2
1.53
2
1.56
2
1.49
2
1.43
2
1.48
2
1.55
2
1.57
2
1.54
2
1.47
2
1.63
2
1.43
2
1.26
2
1.51
2
1.44
2
1.38
2
1.39
2
1.23
2
1.65
2
1.57
2

0
7.78
0
7.69
0
7.58
0
7.69
0
7.42
0
7.53
0
7.43
0
7.59
0
7.70
0
7.67
0
7.46
0
7.53
0
7.54
0
7.20
0
7.46
0
7.63
0
7.51
0
7.75
0
7.60
0
7.30

0
0.40
0
0.47
0
1.22
0
0.68
0
1.53
0
1.43
0
1.25
0
0.91
0
0.88
0
0.83
0
1.28
0
1.14
0
1.26
0
1.75
0
1.38
0
0.92
0
1.23
0
0.66
0
1.35
0
1.73

0
3.77
0
3.18
0
3.25
0
3.59
0
3.23
0
3.03
0
3.34
0
3.44
0
3.09
0
3.53
0
3.42
0
3.10
0
3.33
0
3.11
0
3.03
0
3.37
0
3.01
0
3.23
0
3.23
0
3.09

0
1.04
0
1.67
0
0.95
0
1.04
0
0.82
0
1.01
0
0.99
0
1.05
0
1.33
0
0.97
0
0.85
0
1.22
0
0.87
0
0.94
0
1.14
0
1.09
0
1.25
0
1.36
0
0.82
0
0.87

4. Summary
The 51 Ar, lying between the possible N = 32 and N = 34 subshell closures predicted by theoretical calculations and suggested
by some earlier experimental works, was studied via the (p,2p) reaction. Its low-lying level structure, unexplored until now, was established using γ -ray spectroscopy and the invariant mass method.
The observed two bound states were populated very weakly which
is a clear indication that they are mainly formed by promoting aneutron across the shell gaps at N = 32 and N = 34. Therefore,
this is in line with the previous results [16,24], i.e., the subshells
gaps at N = 32 and N = 34 are substantial in argon isotopes.
Some of the detected unbound states were populated with large
cross sections, which turned out to have collective behavior according to our shell model calculations. This means that 51 Ar is anatomic nucleus in which individual-particle and collective states
coexist.
Fig. 4. Change of effective single-particle orbitals at N = 32 as the proton number
decreases toward the dripline.

Declaration of competing interest

due to their questionable existence in the E rel spectrum in coincidence with the 1178-keV γ ray in 50 Ar as well as the density oftheoretical states at high energies.

The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared toinﬂuence the work reported in this paper.
6M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

Table 3
Theoretical level energies (E theor ), spectroscopic factors, exclusive cross sections for the reaction52
K(p,2p)51 Ar (σtheor ) in comparison with experimental level energies (E expt ) and cross sections (σexpt )up to the expected two neutron separation energy of 5.6(7) MeV [39]. The level energies and spectroscopic factors originate from our shell-model calculations with J π = 2− (52 K g.s.) while the crosssections are obtained by combining the DWIA cross sections and the spectroscopic factors. The uncertainty in the DWIA framework and its input is about 20% as discussed in Ref. [49]. Only those excitedstates are shown for which the theoretical (p,2p) cross section exceeds 0.1 mb. Regarding the experimental data, four states could be matched with theoretical levels. However, the assignments of thelowest two excited states are ambiguous since they can be swapped.
E theor
(MeV)

Jπ

0

1/2−
1

0.975

3/2−
1

1.117

5/2−
1

1.826

5/2−
2

2.088

3/2−
2

2.884

5/2−
3

3.181

5/2−
4

3.268

3/2−
4

3.368

3/2−
5

3.459

5/2−
6

3.980
3.981

9/2−
2
5/2−
7

4.087

3/2−
7

4.137
4.141

9/2−
3
5/2−
8

4.229

3/2−
8

4.363

3/2−
9

4.527

3/2−
10

4.988
5.361

9/2−
6
9/2−
8

σtheorSpectroscopic factor

<0.01
0.37
<0.01
0.04
0.02
0.07
<0.01
<0.01
0.01
0.67
0.38
0.06
0.01
0.01
<0.01
0.14
0.01
<0.01
0.37
0.03
<0.01
0.13
<0.01
<0.01
0.09
0.01
<0.01
0.49
0.31
<0.09
<0.01
0.03
0.11
<0.01
0.02
0.28
0.05
<0.01
0.08
0.03
<0.01
<0.01
0.15
<0.01
<0.01
0.06
<0.01
<0.01
0.11
0.08
0.09

d5/2
d3/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d3/2
s1/2
d5/2
d5/2

E expt
(MeV)

σexpt

(mb)
0.82

0

0.47(3)0.149

0.963(9)0.046(14)0.177

1.180(9)0.102(18)2.64

S n + 0.092(4)0.93(12)

S n + 1.449(35)1.54(24)

(mb)

0.17

0.33

0.86

0.28

0.23

1.97

0.20
0.38

0.85

0.11
0.28

0.44

0.20

0.36

0.19
0.20

Acknowledgements

support of Marie Skłodowska-Curie Individual Fellowship (H2020MSCA-IF-2015-705023) from the European Union and the support
from the Helmholtz International Center for FAIR. H. N. L. acknowledges the support from the Enhanced Eurotalents program(PCOFUND-GA-2013-600382) co-funded by CEA and the European
Union. T. A., C. L., D. R., H. T., V. W., L. Z., H. N. L., V. W. and A. O.
acknowledge the support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project No. 279384907SFB 1245. R. B. G. acknowledges the support from the DFG underGrant No. BL 1513/1-1. Y. L. S. and A. O. acknowledge the support from the Alexander von Humboldt Foundation. B. D. L. andWe are very grateful to the RIKEN Nishina Center accelerator staff for providing the stable beam and to the BigRIPS teamfor the smooth operation of the secondary beams. The development of the MINOS device has been supported by the European
Research Council through the ERC Grant No. MINOS-258567. F. B.
was supported by the RIKEN Special Postdoctoral Researcher Program. K. O. acknowledges the support by Grant-in-Aid for ScientiﬁcResearch JP16K05352. Y. U. acknowledges the support by Grantin-Aid for Scientiﬁc Research 20K03981. Y. L. S. acknowledges the7M.M. Juhász, Z. Elekes, D. Sohler et al.

Physics Letters B 814 (2021) 136108

L. X. C. acknowledge the support from the Vietnam Ministry of Science and Technology under Grant No. ÐTCB.01/21/VKHKTHN. I. G.
has been supported by HIC for FAIR and HRZZ under project No.
1257 and 7194. K. I. H., D. K. and S. Y. P. acknowledge the support from the NRF grant funded by the Korea government (No.
2017R1A2B2012382 and 2019M7A1A1033186). F. B. acknowledge
the support from the RIKEN Special Postdoctoral Researcher Program. D. S. and Z. E. were supported by projects No. GINOP-2.3.315-2016-00034 and No. K128947. V. V. acknowledges support fromthe Spanish Ministerio de Economía y Competitividad under Contract No. FPA2017-84756-C4-2-P. V. W. and P. K. acknowledge thesupport from BMBF grants 05P15RDFN1 and 05P19RDFN1. P. K. acknowledges support from HGS-HIRe. This work was also supported
by NKFIH (114454).

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