Establishing the dominance of the closed-shell configuration in 54Ca

Y. Utsuno1), K. Yoshida1), S. Chen2), and J. Lee2) for the SEASTAR collaboration
1): Advanced Theoretical Physics Gr., JAEA 2): Univ. Hong Kong

One of the interesting properties of nuclei far from  stability
is the modification of the shell structure. For stable nuclei, theconventional nuclear magic numbers, 2, 8, 20, 28, 50, 82, areknown to occur. These numbers arise from the shell structure
produced by the Woods-Saxon (or harmonic-oscillator) potential
with a strong spin-orbit interaction introduced. For unstable
nuclei, on the other hand, it is known that some of those magic
numbers disappear and that new magic numbers emerge instead.
For instance, the N=20 magic number breaks down for neutronrich nuclei around 32Mg, whose first excited levels are much
lower than those of other N=20 isotones. It is also widely
accepted that a new magic number N=16 appears for 24O on thebasis of its high first excited level and the large binding energy
compared to surrounding nuclei.
What is the driving force of such changing shell structure inneutron-rich nuclei? One of the most probable candidates is thetensor force [1]. The tensor force provides attraction between aproton in the j> orbital (j=l+1/2) and a neutron in the j’< orbital(j’=l’-1/2), and also repulsion between a proton in the j> orbital
and a neutron in the j’> orbital. Therefore, as the proton j> orbital
is filled, the spin-orbit splitting of the neutron l’ orbitals reduces.
In other words, the neutron spin-orbit splitting is enhanced withdecreasing protons in the j> orbital. One of the actual cases ispresented in Fig. 1. Since Ca isotopes have almost no proton
fractions in the f7/2 orbital, their neutron spin-orbit splitting ispredicted to be larger than that of Ni isotopes, thus locating theneutron f5/2 orbital high and producing new subshell gaps (ormagic numbers if they are large enough) at N=32 and N=34.
The occurrence of the N=34 magic number in neutron-richnuclei was proposed in 2001 [2]. While the existence of the large
shell gap at N=32 was found in the 1980s, no experimental
information on the shell gap at N=34 had been available until themeasurement of the first excited level in 54Ca was reported in2013 [3]. The measured quantity, 2.04 MeV, is larger than that ofsingly-magic nuclei such as 42,44,46,50Ca, but is smaller than thatof doubly magic nuclei 40,48Ca. Although the occurrence of a new
magic number N=34 was concluded in Ref. [3], moreexperimental information is needed to establish its magic nature.
The most direct way to prove the magic nature is, by definition,
to show the dominance of the closed-shell configuration. This342p2p1/2

1/2

32
2p2p3/2

1f 7/2

1f 7/2
Niproton3/2

Caneutron

protonneutronFig. 1 Schematic illustration of the appearance of the N=32 and N=34
magic numbers in Ca isotopes due to the tensor force. Taken from [1].

(a)

f5/2

(b)

f5/2

p1/2

p1/2

p3/2

p3/2

Fig. 2 Illustration of the neutron (a) closed-shell and (b) 2p-2h excitedconfigurations for 54Ca.

idea is realized in Ref. [4] using a single-neutron knockout
reaction 54Ca(p, pn)53Ca performed at RIBF in RIKEN incombination with up-to-date nuclear reaction and structure
theories. This experiment is a part of the SEASTAR campaignthat aims at probing changing shell structures in neutron-richnuclei, and our theory group is deeply involved in submitting theexperimental proposal [5]. The outline of this study is illustrated
in Fig. 2. If one assumes the ground state of 54Ca is composed of
the closed-shell configuration alone, either a neutron in p1/2 or p3/2
can be knocked out for producing low-lying states of 53Ca [seeFig. 2(a)]. On the other hand, an f5/2 neutron can be knocked out
from the configuration with 2p-2h excitations involved [see Fig.
2(b)], which mostly goes to the 5/2-1 state in 53Ca. Thus, the crosssection to produce the 5/2-1 state is the key quantity to assessing
the magic nature of 54Ca.
Experimental details of this study are described in Ref. [3]. The
measured cross section to produce the 5/2-1 state is 1.0(3) mb. By
using the reaction calculation based on the distorted wave
impulse approximation (DWIA), this cross section is converted
to the spectroscopic factor, which characterizes the occupation of
the orbital of interest. The deduced spectroscopic factor
C2S=0.24(7) is in good agreement with that obtained from ourshell-model calculation, C2S=0.19, indicating the closed-shellprobability 1-0.24(7)/2=0.88(4) derived under a simple but
reasonable nuclear-structure assumption. The nearly ninetypercent close-shell probability thus derived is large enough toclaim the occurrence of the new N=34 magic number in 54Ca.
We stress that quantifying the spectroscopic factor and theclosed-shell probability carried out in this study would beimpossible without the highly descriptive power of the DWIA
calculation. This theory has recently been extended to probing α
clustering through the α knockout (p, pα) reaction [6].
References[1] T. Otsuka, A. Gade, O. Sorlin, T. Suzuki, and Y. Utsuno,Rev. Mod. Phys. 92, 015002 (2020).
[2] T. Otsuka, R. Fujimoto, Y. Utsuno et al., Phys. Rev. Lett.
87, 082502 (2001).
[3] D. Steppenbeck et al., Nature 502, 207 (2013).
[4] S. Chen et al., Phys. Rev. Lett. 123, 142501 (2019).
[5] P. Doornenbal et al., Proposal to the 16th RIBF NP-PAC
meeting, NP1512-SAMURAI39R2 (2015).
[6] Y. Yoshida et al., Phys. Rev. C 100, 044601 (2019).