Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 51 (2018)

Shell-model description of magnetic dipole bands in 105 Sn
M. Honma,∗1 T. Otsuka,∗2,∗3,∗4,∗5 T. Mizusaki,∗6 Y. Utsuno,∗7,∗8 N. Shimizu,∗8 and M. Hjorth-Jensen∗4,∗9,∗10
Because of the well-developed shell closure at N ,Z = 50, Sn isotopes have often been studied using theshell model by considering only valence neutrons. However, several states have been observed in light Sn isotopes that would be described by the conﬁgurations witha broken 100 Sn core. One interesting example is thehigh-spin regular band that decays mainly by M1 transitions.1) This band has been interpreted by the “shearsmechanism” using the tilted-axis cranking model.2) In
this report, we present the results of our trial to describe this magnetic dipole band using the shell model,
taking 105 Sn as an example.
The adopted model space consists of the proton(0g9/2 , 1d5/2 , 0g7/2 ) orbits and the neutron (1d5/2 ,0g7/2 , 0h11/2 , 2s1/2 , 1d3/2 ) orbits. The eﬀective interaction is prepared by combining the SNBG13) interaction as neutron-neutron and proton-proton part, theP1GD5G34) interaction for proton-neutron part among
the relevant orbits if deﬁned, and for the rest parts themicroscopic interaction5) based on the realistic N3 LO
interaction.6) The bare single-particle energies (SPEs)for the neutron orbits are adjusted so as to reproduce
the eﬀective SPEs obtained by the SNBG1 interaction
at 114 Sn. The SPE of the proton 0g9/2 orbit is takenfrom the P1GD5G3 interaction, and the rest are deter12

mined so that the eﬀective SPEs agree with those ofthe neutrons at 100 Sn. In order to ensure the computational feasibility, up to 5 nucleons are allowed to excite
into the proton (1d5/2 , 0g7/2 ) orbits or neutron (0h11/2 ,2s1/2 , 1d3/2 ) orbits.
The calculated band structure is shown in Fig. 1. One
can ﬁnd reasonable agreement between the experimental data and the shell-model results. The E2 and M1
transition probabilities are calculated by using the effective charge ep = 1.6, en = 0.8, and the eﬀective
spin g-factors g eﬀ = 0.74g free . The calculated nega−−
tive parity band 43/2−
1 -41/21 -39/21 -· · · decays mainlyby M1 transitions, consistently with the experiment.
The typical B(M 1) value within the band is ∼ 1µ2N ,while the B(E2) value is at most 0.08e2 b2 , indicating the M1 dominance. In addition to this band, theshell-model results give a positive-parity M1-dominant+++
band 39/2+
2 -37/23 -35/22 -· · ·, on top of the 23/22 state.
The dominant conﬁgurations in the calculated wave
functions are π(g9/2 )−1 (g7/2 )1 ν(g7/2 d5/2 )4 (h11/2 )1 andπ(g9/2 )−1 (g7/2 )1 ν(g7/2 d5/2 )5 relative to the 100 Sn closed
core for the negative and the positive parity bands, respectively. However, the purity of these conﬁgurations
is gradually lost for lower spin states, and the feature of
the “shears mechanism,” i.e., a rapid decrease of B(M 1)with increasing spin, is not clear.

105Sn+

39/22

−

−

10(41/2 )−(37/2 )−Ex (MeV)8(33/2 )−(29/2 )−

(29/2 )
6−

(25/2 )+

4+

(21/2 )+(19/2 )+20(23/2 )−
(21/2 )+(21/2 ) (19/2+)−(17/2 )−

(27/2 )

+

33/21

−

(31/2 )

+

29/21

−

(27/2 )

+

25/21

−

+

21/21+

17/21+

13/21+

9/21+(7/2 )−

37/21+

−

+

41/21

35/22

(35/2 )

(23/2 )−−+−

(39/2 )

(17/2 ) (15/2+)+(15/2 )(13/2 )++
(13/2)+(9/2 ) (11/2 )(5/2 )+
37/23(43/2 )+

5/21+

23/21++
21/22

19/21+
15/21+
11/21+

7/21

experiment+13/22+
9/22+
5/22+

31/21+

27/21+
23/22+

19/22+

15/22−

33/21−

29/22−

25/22

31/21−
27/21−

23/21−

21/21−−

29/21−

25/21

43/21−

39/21−

35/21−
31/22−
27/22−
23/23−− 19/217/2
1−
13/21 1−
15/21−
11/21

shell modelFig. 1. Energy levels of 105 Sn. The experimental data are taken from Refs. 1, 7). The shell-model results
are obtained using the code MSHELL64.8) The width of the arrow drawn in the shell-model results
is proportional to the branching ratio.
∗1Center for Mathematical Sciences, University of Aizu
RIKEN Nishina Center∗3 Department of Physics, University of Tokyo∗4 National Superconducting Cyclotron Laboratory, Michigan
State University∗5 Instituut voor Kern- en Stralingsfysica, KU Leuven∗6 Institute of Natural Sciences, Senshu University∗7 Advanced Science Research Center, Japan Atomic Energy
Agency∗8 Center for Nuclear Study, University of Tokyo∗9 Department of Physics and Astronomy, Michigan State University∗10 Department of Physics, University of Oslo∗2- 95 -References
1) G. de Angelis et al., Nucl. Phys. 654, 659c (1999).
2) S. Frauendorf, Nucl. Phys. 557, 259c (1993).
3) M. Honma et al., RIKEN Accel. Prog. Rep. 45, 35 (2012).
4) M. Honma at al., RIKEN Accel. Prog. Rep. 47, 64 (2014).
5) M. Hjorth-Jensen et al., Phys. Rep. 261, 125 (1995).
6) D. R. Entem et al., Phys. Rev. C 68, 041001(R) (2003).
7) Data extracted using the NNDC WorldWideWeb sitefrom the ENSDF database.
8) T. Mizusaki et al., MSHELL64 code (unpublished).