RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-2. Nuclear Physics (Theory)

Joint project for large-scale nuclear structure calculations in 2014
N. Shimizu,∗1 T. Otsuka, ∗1,∗2 T. Togashi,∗1 N. Tsunoda,∗2 and Y. Utsuno∗1,∗3
A joint project for large-scale nuclear structure calculations has been promoted since the year 2002 basedon a collaboration agreement between the RIKEN Accelerator Research Facility (currently RIKEN NishinaCenter) and the Center for Nuclear Study, the University of Tokyo. Currently, we maintain 16 PC servers
with Intel CPUs for large-scale nuclear shell-model calculations. One of the servers has 40 CPU cores and1TB main memory. Based on this project, we performed shell-model calculations of the various nuclides
which had been measured at the RIKEN RI Beam Factory, such as 31 Ne, 33 Mg, and 50 Ar under collaborations with many experimentalists.1) Since the resultsof these collaborations are presented in other reports,
here we introduce four theoretical achievements of thisproject in 2014: development of a shell-model code,shell-model analyses of the isomeric states of 43,44 S
and high-spin states of neutron-rich Cr, Fe isotopes,
and an application of the extended Kuo-Krenciglowa(EKK) method in understanding the island of inversion.
We developed a new code, named “KSHELL” forlarge-scale shell-model calculations on state-of-the-art
supercomputers2) . In nuclear shell-model calculations,
we solve an eigenvalue problem of the Hamiltonian
matrix, whose dimension tends to be huge, by including many-body correlations fully inside the model
space. The newly developed code enables us to solve
this eigenvalue problem by using many CPU cores efﬁciently.
We have investigated the structure of exotic nuclei
in the N ∼ 28 region, which attracts much attention in experimental studies using RIBF. In our mostrecent work3) , we focus on the nature of exotic isomeric states in neutron-rich S isotopes, in particular+44 4)
strongly hindered E2 decay from 4+S .
1 and 21 inThis study is based on shell-model calculations using
the SDPF-MU interaction5) which was developed inthis joint project. In order to extract intrinsic statesfrom the shell model, we carry out the variation afterangular-momentum projection (AM-VAP). The AMVAP calculation shows that the 4+
1 level is dominatedby a K = 4 intrinsic state and that this is the origin
44of the strong E2 hindrance. The 4+
S is the1 level inlightest high-K isomer among the ones ever identiﬁedin the A ∼ 100, A ∼ 130, A ∼ 180, and A ∼ 250
regions.
We have performed large-scale shell model calculations for natural- and unnatural-parity states in Cr and∗1∗2∗3

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

Fe isotopes with N ≤ 356) . Unnatural positive-parity
states in odd-mass Cr and Fe nuclei with N ≤ 35 wereobserved experimentally from low-lying energy levels
to high-spin ones. These states are dominated by oneparticle one-hole excitation across the N = 40 shellgap. The model space of our calculation is composedof f p-shell + 0g9/2 + 1d5/2 orbits with the truncation
allowing 1h̄ω excitation of a neutron. It eﬀectively describes and predicts the energy levels up to the highspin states. The eﬀective single-particle energies ofν0g9/2 in Cr and Fe isotopes are rather constant in theregion with N ≤ 35. This indicates that the sharp
drop of the 9/2+
1 levels in this mass region, which isdiscussed as an indication of the evolution of ν0g9/2 , isexplained by the Fermi surface approaching the ν0g9/2
orbit with the increase of neutron number.
Investigation of the neutron-rich nuclei starting fromthe fundamental nuclear force has been accomplishedby the newly constructed EKK method7) . To construct
the eﬀective interaction for the shell model startingfrom the nuclear force, we usually utilize the manybody perturbation theory, but the standard perturbation theory ends up with a series of divergences whenapplied to a large shell-model space, for example, themodel space spanned by two major shells. The EKK
method avoids a divergence with a re-summation of
the perturbative series and makes it possible to construct the eﬀective interaction for more than one major
shell. We constructed the eﬀective interaction for thesdpf -shell, starting from the N3LO interaction with
the EKK method. The contribution from the threebody force is also added as eﬀective two-body interactions. We found that this interaction consistently
describes the ground state energies and low-lying levels of even-even nuclei (O, Ne, Mg, Si isotopes). In
particular, the disappearance of the N = 20 gap ofNe, Mg isotopes and the restoration of the N = 20
gap of Si and S isotopes are well described.
References
1) T. Nakamura et al.: Phys. Rev. Lett. 112, 142501(2014).
2) N. Shimizu, arXiv:1310.5431 [nucl-th].
3) Y. Utsuno, N. Shimizu, T. Otsuka, T. Yoshida, and Y.
Tsunoda: Phys. Rev. Lett. 114, 032501 (2015).
4) D. Gonzalez et al.: Phys. Rev. C 83, 061305(R) (2011).
5) Y. Utsuno, T. Otsuka, B. A. Brown, M. Honma, T.
Mizusaki, and N. Shimizu: Phys. Rev. C 86, 051301(R)(2012).
6) T. Togashi, N. Shimizu, Y. Utsuno, T. Otsuka, and M.
Honma: Phys. Rev. C 91, 024320 (2015).
7) N. Tsunoda, K. Takayanagi, M. H.-Jensen, and T. Otsuka: Phys. Rev. C 89, 024313 (2014).

- 96 -完全版2014_本文.indd 96

15/10/16 17:45