Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Tensor force and shape evolution of Si isotopes in
Skyrme-Hartree-Fock model†
A. Li,∗1 X. -R. Zhou,∗1 and H. Sagawa∗2,∗3
state using weak nucleon pairing may stem from awell-known fact that the pairing interaction forms theJ = 0+ pairs of identical particles that have spherically symmetric wave functions. As a result, nuclei
tend to be more spherical when a strong pairing coupling exists between neutrons and protons as in thecases of T22 and T44; otherwise nuclei are more likely
to be deformed, as in the cases of T24, T64, and T66.
This suggests that the resulting shape of a nucleus issensitive to the nucleon pairing in this nucleus, andthe experimentally determined deformed shape of 30 Si
suggests that a relatively weak paring correlation ispresent in the Skyrme eﬀective forces T24, T64 andT66. We also notice that a large tensor force present
in T64 and T66 tends to produce a deep energy surface; i.e., the tensor force exerts a dramatic eﬀect thatmaintains a deformed ground state in 30 Si. The eﬀectof the tensor force is also observed in 32 Si as shownin the right panel of Fig. 1. Its shape is predicted to
be spherical using T22, T24, and T44 but oblate using
T64 and T66 with large tensor forces. The sphericalresult in the ﬁrst three cases is obviously not consistent
with experiments, and the shape change from spherical to oblate when introducing a large tensor force isintriguing.
In summary, we used the DSHF model to investigate
the shape evolution of the quadruple deformation of Si
isotopic nuclei. We found interesting manifestations ofthe tensor force and pairing eﬀect in several isotopic
nuclei, such as 30 Si and 32 Si. The eﬀect of tensor force
is observed when we compare the predicted shape of32
Si using increasing tensor forces in the HF energy
density. The tensor-force-driven deformation in these
nuclei should be investigated in more details because
it may result in a further improvement of many theoretical models or parameterizations toward a better
description of theories on the shell structures of nuclei
in general, such as the shell model and SHF model.

In the present study, we focus on the tensor effect on the shape evolution of Si isotopes. We determined whether the tensor-force-driven deformation
is present in neutron-rich Si isotopes, especially 30 Siwith a possible N = 16 subshell, because some models (e.g., the FRDM) predicted a spherical shape forthese nuclei1) while their large B(E2) values suggested
a deformed nature2) . For this purpose, we use thedeformed Skyrme-Hartree-Fock model (DSHF)3) withBCS approximation for the nucleon pairing. We showin Fig. 1 the energy curves of 30 Si (left panel) and32
Si (right panel) as a function of the quadruple deformation parameter β2 using the Skyrme interactions
with tensor terms T22, T24, T44, T64, and T664) .
The energy minima are indicated with triangles. 30 Si
is suggested to be deformed, but T22 and T44 withrelatively large pairing strengths (∼ 1000 MeV) failto give deformed energy minima. In contrary, a deformed ground state can be achieved using the T24,
T64 and T66 parametrization with a small pairingstrength (∼ 800 MeV). Moreover, the predicted oblate
shape of these nuclei is consistent with the recent RMF
result5) . A possibility of achieving a deformed ground

References
1) T.R. Werner et al., Nucl. Phys. A597 327 (1996).
2) R. W. Ibbotson et al., Phys. Rev. Lett. 80, 2081 (1998).
3) D. Vautherin, Phys. Rev. C 7, 296 (1973).
4) T. Lesinski et al., Phys. Rev. C 76, 014312 (2007).
5) Z. P. Li, J. M. Yao, D. Vretenar, T. Niksic, H. Chen,and J. Meng, Phys. Rev. C84, 054304 (2011).

Fig. 1. (Color online) Energy curves of 30 Si (left panel) and32Si (right panel) as a function of the quadruple deformation parameter β2 using the Skyrme interactions
T22, T24, T44, T64, and T66. The energy minima areindicated with triangles.
†∗1
∗2
∗3

Condensed from the article in Prog. Theor. Exp. Phys.
063D03(2013)
Department of Astronomy and Institute of TheoreticalPhysics and Astrophysics, Xiamen University
RIKEN Nishina Center
University of Aizu

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