Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Joint project for large-scale nuclear structure calculations in 2016
N. Shimizu,∗1 N. Tsunoda,∗1 T. Miyagi,∗2 S. Yoshida,∗2 T. Abe,∗2 T. Otsuka∗2,∗1 and Y. Utsuno∗3,∗1

∗1
∗2
∗3

Center for Nuclear Study, the University of Tokyo
Department of Physics, the University of TokyoJapan Atomic Energy Agency- 103 -

1.5

Ex (MeV)A joint project for large-scale nuclear structure calculations has been promoted since 2002 based on acollaboration agreement between the RIKEN Accelerator Research Facility (currently RIKEN Nishina Center) and the Center for Nuclear Study, the Universityof Tokyo. Currently, we maintain 16 PC servers withIntel CPUs for large-scale nuclear shell-model calculations. Based on this project, we performed shellmodel calculations of the various nuclides that havebeen measured or are proposed to be measured at theRIKEN RI Beam Factory and other facilities, such as
38,40 48
P Ca, 55 Ca, 128 Cd, 130 Sn, and 132 Sn, under various collaborations with many experimentalists.1) Inparallel, we have performed several theoretical studies for understanding nuclear structure. Among them,
we brieﬂy show three theoretical achievements: the sophisticated perturbation theory for constructing shellmodel interaction2,3) shell-model study of the beta decay of neutron-rich 13 ≤ Z ≤ 18 nuclei,4) and thedevelopment of the unitary-model-operator approach(UMOA).5)
We have developed a novel many-body perturbation method to derive the eﬀective interaction for shellmodel calculations. Our new theory (extended KuoKrenciglowa method) can handle an arbitrary model
space, such as two major shells,
shells2)2), unlike conventional
standard theory (KK method). Then, we derived anew eﬀective interaction for the sd + pf shell, startingfrom the nuclear force based on chiral eﬀective ﬁeld
theory and Fujita-Miyazawa three-body force. With
this interaction, we succeeded in describing the nuclear
shell structure around the region so-called “island ofinversion,” where the breaking of the N = 20 shell gap
is important. In this year, we further investigated thephysics around the “island of inversion” and clariﬁed
the long-standing problem of how the sd-to-pf excitations occur in Mg isotopes with distinct diﬀerencesfrom conventional approaches. As an example, Fig. 1
shows the low-lying states of 31 Mg, where energy levels of positive and negative parity states are quite nearand conﬁguration mixing related to the N = 20 gap
is important. We can see that experimental values arereproduced better than in other shell model studies.3)
Using the EKK method, we have also started investigating nuclei in other regions.
In order to discuss the systematic properties of beta
decay of neutron-rich nuclei, we performed large-scale
shell-model calculations and obtained the GamowTeller transition for the 78 nuclei with 13 ≤ Z ≤ 18(a) exp.

(b) present (c) sdpf-m (d) sdpf-U
3/2+
5/2-

1.0

(5/2+)(3/2+)

0.5(7/2-)

0.0(3/2-)(3/2+)
1/2+-mix

3/23/2+
1/2+

1/2+3/23/2+
7/2-

Mg

(e) AMD

5/2+
3/27/2-31

3/2+
5/27/23/21/2+
3/2+3/2-

3/2+1/2+

Fig. 1. Energy levels of 31 Mg, (a) experimental values,(b) present work, (c) sdpf-m, (d) sdpf-U-mix and (e)AMD+GCM calculation.

1,4)
and 22 ≤N ≤≤34.
341,4). In this calculation, the SDPF≤NMU interaction was adopted.6) Shell-model results ofthe beta-decay half lives and delayed neutron emission
rates remarkably agree with experimental data. This
indicates the validity of large-scale shell-model calculations for nuclei in the neutron rich region.
The UMOA was developed and extended in order to investigate the medium- and heavy-mass nuclei
based on the underlying nuclear interactions.5) In theUMOA, we construct the eﬀective Hamiltonian which
does not induce the 1-particle-1-hole and 2-particle-2hole excitations. We have calculated the ground-stateenergies and radii with the similarity-renormalization7)transformed nucleon-nucleon
nucleon-nucleon(NN)(N N )interactions
interactionsgroup transformed7)
closed-shellnuclei
nucleiacrossacrossthethenuclear
nuclear chart
chart up
forforthetheclosed-shellto lead region. The converged results can be obtained
when we take 15 major shells as a model space. Our resulting energies and radii are unrealistically overboundand smaller than the experimental data, respectively.
We have found that the neutron-skin thicknesses areinsensitive to the choice of resolution scale for the N N
interaction and can be determined uniquely. For aquantitative understanding, it is necessary to include
the three-nucleon-force eﬀect which cannot be treatedin the current UMOA framework. In such a situation,
we are extending the UMOA framework and are carrying out benchmark calculations for light nuclei.

References
1) V. Tripathi et al., Phys. Rev. C 95, 024308 (2017).
2) N. Tsunoda et al., Phys. Rev. C 89, 024313 (2014).
3) N. Tsunoda, T. Otsuka, N. Shimizu, M. H.-Jensen, K.
Takayanagi, T. Suzuki, Phys. Rev. C 95, 021304(R)(2017).
4) S. Yoshida, oral presentation, CNS summer school 2016(2016).
5) T. Miyagi, T. Abe, R. Okamoto, T. Otsuka, Prog.
Theor. Exp. Phys. 2015 041D01 (2015).
6) Y. Utsuno et al., Phys. Rev. C 86, 051301(R) (2012).
7) S. K. Bogner et al., Phys. Rev. C 75, 061001 (2007).