Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Shell-model evaluation of beta-decay half-lives for N = 50 neutron
deﬁcient nuclei
M. Honma,∗1 T. Otsuka,∗2,∗3,∗4 T. Mizusaki,∗5 Y. Utsuno,∗6,∗3 N. Shimizu,∗3 and M. Hjorth-Jensen∗4,∗7,∗8
An accurate description of the structure of unstable nuclei has been one of the most challenging goals
in theoretical nuclear physics. A precise prediction ofvarious properties such as binding energies and transition strengths is important as an input of astrophysical simulations especially for nuclei that are beyond
the current experimental reach. The doubly-magic nucleus 100 Sn is one of the key nuclei for exploring theproton-rich extreme, and various theoretical as well as
experimental approaches have been made. In the previous report1) we presented the results of shell-model
calculations for the Gamow-Teller transition strength
distribution from 100 Sn. In this report, using the same
framework, the β-decay half-lives are evaluated for several proton-rich N =50 nuclei.
the adopted
adopted model
model space consists
As described inin,2)2), theof four single-particle orbits 1p1/2 , 0g9/2 , 1d5/2 and0g7/2 for both protons and neutrons. Because of thecomputational limitations, we need to employ a suitable truncation scheme. In the present calculation,
at most ﬁve particles are allowed to excite across theN or Z=50 shell gap relative to the naive ﬁlling conﬁgurations. The eﬀective interaction was determinedin a semi-empirical way. The starting Hamiltonian isderived microscopically3) based on the realistic N3 LOinteraction,and itit isis modifiedmodiﬁed byby iterative fits
ﬁts to theinteraction4)4), andexperimental energy data. For the purpose of the lifetime evaluation, we need to know the Q-value, but it
is not necessarily known experimentally. To test thereliability of the present scheme, the Q-values are also
evaluated theoretically. The β + -decay + electron capture processes through the Gamow-Teller transitions
are taken into account. The standard quenching factor 0.74 is used for the transition operator.
As shown in Fig.1, the shell-model results basicallyfollow the trends of the available experimental datafor both Q-values and the half-lives. However, a systematic deviation can be seen. The half-life is underestimated for Z ≤ 47 and overestimated for Z ≥ 48.
A part of this deviation is due to the inaccurate estimation of the Q-values, but even if the experimental
values are used, there still remain some discrepancies.

Probably this problem can be attributed to the insuﬃciency of the model space. In the present calculations,the possibly dominating transition πg9/2 → νg7/2 isfully taken into account, but some components suchas πd5/2 → νd3/2 are excluded, that are anticipated tocontribute to the states with higher excitation energies.
The more proton-rich, the larger the Q-value window,
and such components may have larger contribution.
More extensive calculation is necessary to conﬁrm thisinterpretation and improve the description.

∗1References

∗2
∗3
∗4
∗5
∗6
∗7
∗8

Center for Mathematical Sciences, University of Aizu
Department of Physics, University of Tokyo
Center for Nuclear Study, University of Tokyo
National Superconducting Cyclotron Laboratory, Michigan
State University
Institute of Natural Sciences, Senshu University
Advanced Science Research Center, Japan Atomic Energy
AgencyDepartment of Physics and Astronomy, Michigan State University
Department of Physics, University of Oslo

Qgs→gs (MeV)86420410
T1/2 (sec.)

310exp.
calc.

21011001043 44 45 46 47 48 49 50
proton number
Fig. 1. Comparison of (upper panel) Q-values (Qgs→gs ) and(lower panel) half-lives (T1/2 ) between the experimental data (symbols) and the shell-model results (lines)
for N = 50 nuclei with 43 ≤ Z ≤ 50. Experimental data are taken from Ref.5) The shell-model results
are obtained by using the eﬃcient shell-model code
6)
MSHELL64.
.
MSHELL646)

1) M. Honma
Honma etet al.,al.: RIKEN
RIKENAccel.
Accel. Prog.
Prog. Rep.
Rep. 48,48, 89 (2015).
(2015).
2) M. Honma
Honma etet al.,al.: RIKEN
RIKENAccel.
Accel. Prog.
Prog. Rep.
Rep. 47,47, 64 (2014).
(2014).
3) M. Hjorth-Jensen
al.: Phys.
Phys. Rep.
Rep. 261,261, 125
125 (1995).
(1995).
Hjorth-Jensen et al.,
4) D. R.
R. Entem
Entem etetal.:al., Phys.
Phys. Rev.
Rev. CC 68,68, 041001(R)041001(R) (2003).
(2003).
5) Data extracted
extracted usingusingthe
theNNDC
NNDCWorldWideWeb
WorldWideWeb
sitesite
ENSDF database.
database.
from the ENSDF
6) T. Mizusaki
Mizusaki etet al.,al.: MSHELL64
MSHELL64code
code(unpublished).
(unpublished).

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