Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 53

Quenching factor of Gamow-Teller and spin dipole resonances†
L. -G. Cao,∗1 S. -S. Zhang,∗2 and H. Sagawa∗3,∗4

Ex =0

Ex =0

where Ex (max) is taken to be 30 MeV in the GT case.
The quenching factor qf = 0.64 corresponds to a renormalization factor of qRF = 0.80 for the GT transition
operator to retain the empirical sum rule value.
The calculated SD strength for 48 Ca is shown in Fig. 1.
†∗1
∗2
∗3
∗4Condensed from the article in Phys. Rev. C 100, 054324(2019)
School of Mathematics and Physics, North China ElectricPower University
School of Physics and Nuclear Energy Engineering, Beihang
UniversityRIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

- 69 -

6-1

SGT- (MeV )

5448

Exp.
SAMi
SAMi(qf=0.64)
SAMi-T
SAMi-T(qf=0.64)

Ca

3
2
100-1

15

220

10

SSD- (fm MeV )Spin-isospin excitations provide a unique opportunity
to study the spin correlations in nuclei. The GamowTeller (GT) transition is the simplest with both spin
and isospin transfers by one unit. The next simplest is
spin-dipole (SD) excitations, which involve the orbital
angular momentum transfer by one unit together withspin and isospin transfer. The quenching of the total
GT strength from the model-independent sum rule has
prompted theoretical studies of possible mechanisms,
ranging from conventional conﬁguration mixing to anadmixture of ∆-hole states. Experimental investigationsof the (p, n) and (n, p) reactions using the multipole decomposition (MD) technique have identiﬁed not only theGT strength but also a considerable amount of broadly
distributed L = 1 SD strength at excitation energies
beyond the GT peak.
We study GT and SD states in four doubly magic
nuclei 48 Ca, 90 Zr, 132 Sn, and 208 Pb by using the selfconsistent Hartree-Fock+random-phase approximation(RPA) model with/without tensor interactions. We
adopt the modern energy density functions (EDFs)
SAMi and SAMi-T for the theoretical study. The latterhas tensor terms determined from Bruckner HF calculations with the AV18 interaction.
The GT strength is shown in Fig. 1 for the t− channel of 48 Ca. The main experimental GT resonance wasfound experimentally at Ex ∼10 MeV, in addition to asmall peak at Ex = 3 MeV in 48 Ca. The results calculated with SAMi reproduce well the main peak, but thelow-energy strength is predicted 1 MeV lower than theexperimental one. SAMi-T gives essentially the same
results for the main peak, but reproduces better the excitation energy for the small lower energy peak. The
integrated GT strength from Ex = 0 → 25 MeV is 15.3,
which is 64% of the GT sum rule. The calculated results exhaust almost 100% of the sum rule up to Ex =20 MeV. The quenching factor for the transition strengthis deﬁned as/ Ex (max)Ex (max)∑∑
qf =B(GT : Ex )exp
B(GT )cal ,51015E (MeV)

2025Exp.
SAMi
SAMi(qf=0.66)
SAMi-T
SAMi-T(qf=0.73)
48
Ca Total

500

1020E (MeV)

3040Fig. 1. RPA strength functions of 48 Ca for the t− channel ofGT and SD resonances. The solid circles are the experimental data taken from Ref. 1). The short-dotted (shortdashed) and solid (dashed-dotted) lines are the theoretical results without and with a quenching factor given by
the SAMi (SAMi-T) EDF, respectively.

The tensor interactions have substantial eﬀects on theSD response, and the eﬀect is diﬀerent for each multipole. As a net eﬀect, the main peak at Ex ∼23 MeV isshifted to a lower energy by 1 MeV by the tensor eﬀect,
which provides a better description of the experimental
strength distributions of SD for 48 Ca.
The quenching eﬀect is modest for the SD strength.
In 48 Ca, the qf value is 0.66 (0.73) for the SD with theSAMi (SAMi-T) EDF. In 90 Zr, the GT needs qf = 0.7,
while the SD shows qf = 0.8. The feature of quenchingis the same for 208 Pb; qf = 0.65 for the GT and qf =0.78(0.80) for the SD with the SAMi (SAMi-T) EDF.
In conclusion, the quenching eﬀect is modest for theSD strength with the quenching factor qf ∼ 0.8 compared with that for GT, for which qf ∼ (0.55 − 0.69),
which is consistent with the quenching value obtained
from the GT beta decay processes in nuclei with A < 50.
This diﬀerence in the eﬀective quenching factors between
GT and SD should be implemented in future theoreticalstudies of double beta decay probabilities.
Reference1) K. Yako et al., Phys. Rev. Lett. 103, 012503 (2009) andprivate communications.