II-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Energy-weighted sum rule for Gamow-Teller giant resonances inhigh-spin isomeric states of N = Z nuclei†
M. Sasano,∗1 H. Sagawa,∗1,∗2 T. Suzuki,∗3,∗4 and M. Honma∗2
Among collective modes,1) the Gamow-Teller (GT)
giant resonance is an interesting excitation mode. It isa 0 h̄ω excitation that is characterized by the quantumnumber changes in the orbital angular momentum(∆L = 0), spin (∆S = 1), and isospin (∆T = 1).
It is induced by the transition operator στ .
Recently, an experimental project was proposed tomeasure the GT transitions from the 52 Fe(12+ ) highspin isomeric state provided as an RI beam.2) Inspiredby this, herein, we derived an energy-weighted sum
rule (EWSR) to estimate the energies of GT giant resonances in high-spin isomeric (HSI) states in N = Z
nuclei and evaluated the spin and isospin residual interactions by comparing the EWSR with the shell model
calculations.
The sum rules provide a reliable tool for evaluating
the natures of giant resonances. In the calculations ofsum rules, the contributions from all the ﬁnal states
are summed up. Therefore, the sum-rule values solelydepend on the properties of the initial ground state
and the Hamiltonian of the system, but they are notsensitive to the details of the ﬁnal states. Roughly
speaking, the non-energy-weighted sum rule (NEWSR)
provides a criterion for the collectivity of the observed
resonances, while the EWSR provides a measure of theinteraction strength driving the oscillation.
By dividing EWSR with NEWSR, the average energy of the resonance can be derived. We found that,with the simple Bohr-Mottelson Hamiltonian,3) the average energy relation is written as
ν=−1
ν=−1EGT− EM1=4

κστ − κσ⟨i |S0 | i⟩ .
Ainstead of κστ −κσ , κστ −κτ appears. The GT energies
in high-spin isomers with N = Z have diﬀerent sensitivies from those in N > Z 0+ nuclei. This is because
these states have diﬀerent symmetries in the spin andisospin space.
We used the newly derived energy relation to analyze the results of the shell model calculations for theGT transition from 52 Fe(12+ ) and 94 Ag(21+ ) N = Z
high spin isomers. In the shell-model calculations, theeﬀective interactions, GXPF1J5) and PIGD5G36) wereused for Fe and Ag, respectively. From the analysis,κστ − κσ was derived as 20.4–20.5 MeV. By assuminga κστ value of 23 MeV, the strength of the spin residual interaction, κσ was deduced as 2.5 MeV. Thus, wedemonstrated that the GT energies in high spin isomers are useful for evaluating the short-range part ofthe spin residual interaction, which is important to describe the onset of the pion condensation in nuclearmatter.
We thank Haozhao Liang for the valuable discussions.
This work was supported in part by
JSPS KAKENHI (Grant Numbers JP19K03858 andJP19K03855).
References

1) M. N. Harakeh, A. M. van der Woude, Giant Resonances, (Oxford University Press, Oxford, 2001).
2) K. Yako et al., private communications.
3) A. Bohr, B. R. Mottelson, Nuclear Structure SingleParticle Motion, Vol.I, (Benjamin, New York 1969).
4) T. Suzuki, Phys. Lett. B 104, 92–94 (1981); T. Suzuki,Nucl. Phys. A 379, 110–124 (1982).
5) M. Honma et al., J. Phys. Conf. Series 20, 002 (2005).
6) M. Honma et al., RIKEN Accel. Prog. Rep. 48, 77(2015).

(1)

Here, κστ and κσ are the spin-isospin and spin coupling
constants used in the hamiltonian. A is the mass numν=−1
ν=−1
ber of the nucleus. ⟨i |S0 | i⟩, and EGTand EM1
correspond to the expectation value of the spin excess
along the elongation axis of the nucleus, the averageenergies of the GT and M1 transitions, respectively.
This relation is analogous to the average energy relation derived in Ref. 4) for N > Z 0+ nuclei. In thelatter case, the left-hand side of the relation is the energy diﬀerence between the GT giant resonance andthe isobaric analog state. ⟨i |S0 | i⟩ in the right-handside is replaced with the neutron excess N − Z. Thus,
†
∗1
∗2
∗3
∗4

Condensed from the article in Phys. Rev. C 103, 014308(2021)RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu
Department of Physics, College of Humanities and Science,Nihon University
National Astronomical Observatory of Japan- 45 -1