Structure of exotic nucleiStructure of exotic nucleiby large-scale shell modelby large-scale shell model

calculationscalculations

Yutaka Utsuno Yutaka Utsuno （宇都野 穣）（宇都野 穣）Japan Atomic Energy AgencyJapan Atomic Energy Agency

CollaboratorsCollaboratorsTakaharu Otsuka (Tokyo/RIKEN)Takaharu Otsuka (Tokyo/RIKEN)

Takahiro Mizusaki (Senshu)Takahiro Mizusaki (Senshu)Michio Honma (Aizu)Michio Honma (Aizu)

Yutaka Utsuno Yutaka Utsuno （宇都野 穣）（宇都野 穣）Japan Atomic Energy AgencyJapan Atomic Energy Agency

CollaboratorsCollaboratorsTakaharu Otsuka (Tokyo/RIKEN)Takaharu Otsuka (Tokyo/RIKEN)

Takahiro Mizusaki (Senshu)Takahiro Mizusaki (Senshu)Michio Honma (Aizu)Michio Honma (Aizu)

66thth China-Japan Joint Nuclear Physics Symposium May 16-20, 2006, Shanghai China-Japan Joint Nuclear Physics Symposium May 16-20, 2006, Shanghai 66thth China-Japan Joint Nuclear Physics Symposium May 16-20, 2006, Shanghai China-Japan Joint Nuclear Physics Symposium May 16-20, 2006, Shanghai

Exotic structure in N~20Exotic structure in N~20 • Disappearance of the N=20 magic number

– Example: Large B(E2) in 32Mg

• “Island of inversion”: conventionally standard picture– Normal (0p0h) vs. intruder (2p2h) – Restricted to nine nuclei over N=20– Not necessarily meaning the collapse of the N=20 shell gap

20

E.K. Warburton et al., Phys. Rev. C 41, 1147 (1990).

Mapping of the “island” from the Mapping of the “island” from the moments of Na isotopesmoments of Na isotopes

• Extensive Monte Carlo shell model (MCSM) study

• The onset of the intruder dominance must occur at N=19.

Y. Utsuno et al., Phys. Rev. C 70, 044315 (2004).

19

Implication to the shell structureImplication to the shell structure

“SDPF-M” interaction

Earlier onset needs narrower N=20 shell gap.

Strongly attractive T=0 d3/2-d5/2 monopole interaction provides uswith a unified shell evolution including the appearance of a newN=16 magic number (Ozawa et al.).

d3/2

d5/2

largest

smaller

difference incorrelation energy

Shell evolution from the viewpoint Shell evolution from the viewpoint of interactionof interaction

Tensor interaction

Works also between different l-orbits(making other shells change?)

T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, andY. Akaishi, Phys. Rev. Lett. 95, 232502 (2005).

Spin-isospin dependence

T. Otsuka, R. Fujimoto, Y. Utsuno, B.A. Brown, M. Honma, and T. Mizusaki, Phys. Rev. Lett. 87, 082502 (2001).

Primarily works within the same l-orbits(highly related to N=20 shell breaking)

From N~20 to N~28 regionFrom N~20 to N~28 region

• Our previous model space: not sufficient to describe the N~28 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

Monopole of T=0 tensorMonopole of T=0 tensor

i j GXPF1 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

• Tensor of GXPF1 (an empirically good interaction) is very close to .• Much weaker for potential interactions on the market (MK and FPD6) • is adopted as the T=0 tensor part (no free parameters).

(in MeV)

Tensor monopole interaction in sd shellTensor monopole interaction in sd shell

i j USD 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 by 1/2.• The difference supports the need for the modification in T=0 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 N=28 shell closure?

4242Si: a new magic nucleus?Si: a new magic nucleus?

• Various theoretical predictions– shell model: spherical or weakly d

eformed

– 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 nucleus1. low gamma-ray spectra in 43P

• large Z=14 shell gap?2. small cross section of two-proton

knockout (44S to 42Si)• different deformation?

No direct measurement such as 2+ has not been published.

Cross shell interaction with a Cross shell interaction with a proper tensor forceproper tensor force

• T=0 monopole compared to MK (in MeV)

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

central LS tensor total

MK -0.41 -0.03 -0.09 -0.53

present -0.37 -0.04 -0.24 -0.65

(Z=14 magic)

Vd3f7 vs. Vd3p3

(N=28 magic) d3 f7

p3

f7

d3

d5

This can affect the structure of a proposed magic nucleus 42

14Si28.

# present: a new cross shell interaction with (T=0) as the tensor part

Evolution of the proton shell from Evolution of the proton shell from N=20 to 28N=20 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 N=28 isotones for Z=15, 17, 19: sensitive to the s.p. state

Even-even N=28 isotonesEven-even N=28 isotones

(ep, en)=(1.3e, 0.5e) which is the same as USD’s

A prediction for “magic” A prediction for “magic” 4242SiSi

• Spherical minimum is very close in energy to the oblate deformed state• The 2+ level is thus sensitive to the N=28 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.)

~2 MeV by MK

SummarySummary

• According to a systematic shell-model study around N=20, 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 reproduce

d in a natural way and it significantly affects the magic structure in 42Si.