Structure of exotic nuclei by large-scale shell model calculations

1
Structure of exotic nucleiby large-scale shell
modelcalculations

• Yutaka Utsuno (??? ?)
• Japan Atomic Energy Agency
• Collaborators
• Takaharu Otsuka (Tokyo/RIKEN)
• Takahiro Mizusaki (Senshu)
• Michio Honma (Aizu)

6th China-Japan Joint Nuclear Physics Symposium
May 16-20, 2006, Shanghai
2
Exotic structure in N20

• Disappearance of the N20 magic number
• Example Large B(E2) in 32Mg
• Island of inversion conventionally standard
  picture
• Normal (0p0h) vs. intruder (2p2h)
• Restricted to nine nuclei over N20
• Not necessarily meaning the collapse of the N20
  shell gap

20
E.K. Warburton et al., Phys. Rev. C 41, 1147
(1990).
3
Mapping of the island from the moments of Na
isotopes

• Extensive Monte Carlo shell model (MCSM) study
• The onset of the intruder dominance must occur at
  N19.

19
Y. Utsuno et al., Phys. Rev. C 70, 044315 (2004).
4
Implication to the shell structure
SDPF-M interaction
difference in correlation energy
d3/2
largest
smaller
Earlier onset needs narrower N20 shell gap.
d5/2
Strongly attractive T0 d3/2-d5/2 monopole
interaction provides uswith a unified shell
evolution including the appearance of a new N16
magic number (Ozawa et al.).
5
Shell evolution from the viewpoint of interaction
Tensor interaction
Spin-isospin dependence
T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe,
and Y. Akaishi, Phys. Rev. Lett. 95, 232502
(2005).
T. Otsuka, R. Fujimoto, Y. Utsuno, B.A. Brown,
M. Honma, and T. Mizusaki, Phys. Rev. Lett. 87,
082502 (2001).
Works also between different l-orbits (making
other shells change?)
Primarily works within the same l-orbits (highly
related to N20 shell breaking)
6
From N20 to N28 region

• Our previous model space not sufficient to
  describe the N28 region (upper pf orbits are
  lacking)
• SDPF-M interaction phenomenological treatment
  for the monopole interaction by shifting 0.3 MeV
  for the d3/2-d5/2 channel from USD
• Extending the model space to the full sd-pf shell
• Shell evolution with high predictive power
• First stage cross shell interaction

7
Monopole of T0 tensor
i j GXPF1 pr MK KB KB3 FPD6
f7 f7 0.223 0.210 0.080 0.176 0.202 0.071
f7 p3 0.036 0.035 0.013 0.047 0.047 0.012
f7 f5 -0.335 -0.315 -0.120 -0.265 -0.303 -0.107
f7 p1 -0.073 -0.070 -0.026 -0.095 -0.095 -0.023
p3 p3 0.092 0.150 0.064 0.070 0.070 -0.002
p3 f5 -0.048 -0.046 -0.017 -0.063 -0.063 -0.016
p3 p1 -0.229 -0.376 -0.160 -0.174 -0.174 0.005
f5 f5 0.382 0.360 0.137 0.302 0.346 0.122
f5 p1 0.097 0.093 0.034 0.126 0.126 0.031
p1 p1 0.306 0.501 0.213 0.232 0.232 -0.008
(in MeV)

• Tensor of GXPF1 (an empirically good
  interaction) is very close to pr.
• Much weaker for potential interactions on the
  market (MK and FPD6)
• pr is adopted as the T0 tensor part (no free
  parameters).

8
Tensor monopole interaction in sd shell
i j USD pr Kuo SDPOTA
d5 d5 0.36 0.69 0.72 0.26
d5 d3 -0.30 -0.57 -0.60 -0.22
d3 d3 0.17 0.33 0.34 0.13
(in MeV)

• The tensor in USD is weaker than pr by 1/2.
• The difference supports the need for the
  modification in T0 d3/2-d5/2 monopole adopted
  in the SDPF-M interaction.
• An sd-pf interaction with a proper tensor
  interaction appears to make it possible to give
  a unified picture about the isoscalar shell
  evolution in the region.
• What about effect on the N28 shell closure?

9
42Si a new magic nucleus?

• Various theoretical predictions
• shell model spherical or weakly deformed
• Skyrme HF(B) soft ranging from spherical to
  oblate
• Gogny oblate
• RMF oblate
• Most theoretical works pay attention to the
  neutron shell structure (related to loosely bound
  p orbit).
• Effect of the proton shell?

• evidence for magic nucleus
• low gamma-ray spectra in 43P
• large Z14 shell gap?
• small cross section of two-protonknockout (44S
  to 42Si)
• different deformation?
• No direct measurement such as 2 has not been
  published.

10
Cross shell interaction with a proper tensor force

• T0 monopole compared to MK (in MeV)

f7
central LS tensor total
MK 0.04 0.01 -0.19 -0.14
present 0.13 0.01 -0.52 -0.38
Vf7d3 vs. Vf7d5
d3
(Z14 magic)
d5
p3
central LS tensor total
MK -0.41 -0.03 -0.09 -0.53
present -0.37 -0.04 -0.24 -0.65
Vd3f7 vs. Vd3p3
f7
d3
(N28 magic)
This can affect the structure of a proposed magic
nucleus 4214Si28.
present a new cross shell interaction with
(T0) pr as the tensor part
11
Evolution of the proton shell from N20 to 28

• The Nature paper (J. Fridmann et al, Nature 435,
  922 (2005)) claims that the observation of a 184
  keV gamma-ray in 43P is a strong evidence for the
  magicity of the 42Si core.
• odd-even N28 isotones for Z15, 17, 19
  sensitive to the s.p. state

12
Even-even N28 isotones
(ep, en)(1.3e, 0.5e) which is the same as USDs
13
A prediction for magic 42Si
2 MeV by MK

• Spherical minimum is very close in energy to the
  oblate deformed state
• The 2 level is thus sensitive to the N28 shell
  gap.(Only a few hundred keV smaller gap makes
  the level lower than 1 MeV)
• Further lower 2 ? (report by Azaiez and Dombradi
  at SENUF06.)

14
Summary

• According to a systematic shell-model study
  around N20, the shell evolution from stable to
  unstable nuclei must occur from the
  electromagnetic moment etc.
• Its origin, i.e., the strong dependence of the
  monopole interaction on spin/isospin, can be
  quantitatively accounted for by the tensor force.
• Using a proper tensor interaction as the
  shell-model interaction, we have started to
  construct a full sd-pf shell model interaction.
• The proton shell evolution about d3/2 and s1/2 is
  reproduced in a natural way and it significantly
  affects the magic structure in 42Si.