Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Joint project for large-scale nuclear structure calculations
N. Shimizu,∗1 T. Otsuka,∗1,∗2 T. Togashi,∗1 N. Tsunoda,∗2 and Y. Utsuno∗1,∗3

∗1
∗2
∗3

cussed the deformation from the potential energy surfaces by the Q-constrained Hartree-Fock calculation.8)

Excitation energy [MeV]A joint project for large-scale nuclear structure calculations has been under way since the year 2001,
based on a collaboration agreement between RIKEN
Nishina Center and Center for Nuclear Study, the University of Tokyo. We maintain PC servers, one of whichhas 1TB main memory and is suitable for large-scale
nuclear shell-model calculations. In this project, we
performed various shell-model calculations of the nuclides that had been measured at the RIKEN RI Beam
Factory, such as 54 Ca, 34 Na, 35 Na, 37 Mg, 50 Ar, and55
Sc, under collaborations with many experimentalists.
1,2)
Since these collaborations are presented in other reports, we here introduce two theoretical achievementsof this project in 2013: The extended Kuo-Krenciglowa
method and the shell-model analysis of Cr isotopes.
Until recently, most shell-model calculations wereconfined to a single oscillator shell like the sd shellor the pf shell. However, recent interest in nuclei
away from the stability line requires larger shell-model
spaces. Because the derivation of microscopic effective interactions has been limited to degenerate model
spaces, there are both conceptual and practical limits to shell-model calculations that utilize those interactions. We develop a method to calculate effective
interactions for a nondegenerate model space, basedon the extended Kuo-Krenciglowa method, which is anatural extension of the conventional Kuo-Krenciglowa
method.3,4) We calculated effective interactions within(i) a single oscillator shell (a so-called degeneratemodel space) like the sd shell or the pf shell and (ii)
two major shells (nondegenerate model space) like thesdf 7p3 shell (sd shell, 0f7/2 and 1p3/2 ) or the pf g9 shell(pf shell and 0g9/2 ). We also calculated the energy levels of several nuclei that have two valence nucleons on
top of an inert core. Our results show that the present
method works excellently in shell-model spaces thatcomprise several oscillator shells as well as in a singleoscillator shell. This work is published in 2014.5)
The experimental observation in odd-mass neutronrich Cr isotopes revealed that the excitation energy of
9/2+
1 state decreases considerably with increasing neutron number.6) We performed shell-model calculations
for these Cr isotopes with pf g9d5 model space, which
consists of a full pf shell, 0g9/2 , 1d5/2 orbits, with acertain truncation. We introduced a new Hamiltonian,which is composed of the GXPF1Br effective interaction1) for the pf shell and VMU 7) for the rest of themodel space. The shell-model result agrees adequately
with experimental data, as shown in Fig.1. We also dis-

121110987
6
54 15/23 13/211/22 9/29/21 5/2-7/25/20 3/2-EXP

33/2+29/2+25/2+
19/217/217/215/215/213/211/29/2-9/27/25/25/23/2-

This work

33/2+
29/2+
25/2+

21/2+

21/2+

17/2+17/2+13/2+

13/2+9/2+9/2+

EXP

This work

Fig. 1. The level scheme of 57 Cr. The columns labeled‘EXP’ and ‘This work’ represent the experimental data
and the results of the shell-model calculation, respectively. The dashed lines denote the unassigned spinstates.

References
1) D. Steppenbeck et al.: Nature 502, 207 (2013).
2) T. Nakamura et al.: Phys. Rev. Lett. submitted.
3) T. T. S. Kuo and E. Osnes: Lecture Notes in Physics
Vol. 364 (Springer, Berlin, 1990).
4) K. Takayanagi: Nucl. Phys. A 852, 61 (2011); ibid.
Nucl. Phys. A 864, 91 (2011).
5) N. Tsunoda, K. Takayanagi, M. Hjorth-Jensen and T.
Otsuka: Phys. Rev. C, 89, 024313 (2014).
6) D. E. Appelbe et al.: Phys. Rev. C 67, 034309 (2003),
S. J. Freeman et al.: Phys. Rev. C 74, 064301 (2004),
A. N. Deacon et al.: Phys. Lett. B 622, 151 (2005).
7) T. Otsuka et al.: Phys. Rev. Lett. 104, 012501 (2010).
8) N. Shimizu et al.: Phys. Rev. C 85, 054301 (2012).

Center for Nuclear Study, University of Tokyo
Department of Physics, University of TokyoJapan Atomic Energy Agency- 55 -