Ⅱ-2. Nuclear Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Fully self-consistent study of charge-exchange resonances and theirimpact on the symmetry energy parameters†
X. Roca-Maza,∗1,∗2 Li-Gang Cao,∗3 G. Colò,∗1,∗2 and H. Sagawa∗4,∗5
A comprehensive eﬀort is currently being devoted
to the determination of the nuclear symmetry energy,
particularly concerning its density dependence. The
symmetry energy is deﬁned starting from the nuclear
matter equation of state. The energy per particle ina uniform system characterized by a density ρ and a
relative neutron-proton asymmetry β ≡ (ρn − ρp ) /ρcan be estimated by expanding up to second order inβ asEE(ρ, β) = (ρ, β = 0) + S(ρ)β 2 .
AA(1)This truncation has been found to be accurate for densities up to 2ρ0 , where ρ0 is the saturation density.
In this work, the basic idea is to use nuclear energy density functionals (EDFs) that provide diﬀerent values for J, L and the neutron skin, and calculate the energy diﬀerence between the anti-analog giant dipole resonance (AGDR) and isobaric analog state(IAS), EAGDR − EIAS in 208 Pb. After checking the existence of the above mentioned linear correlations, one
can employ the experimental value for the energy difference EAGDR − EIAS and deduce the corresponding
values of J, L and the neutron skin. Here, we haveachieved three improvements with our self-consistentmodel and its analysis: (i) the two-body spin-orbit interaction had not been taken into account in Ref.1)1,,
while we adopt its exact form in the present study;(ii) we have checked the eﬀect of implementing the exact Coulomb exchange; and (iii) we have checked theextraction method of the energy centroid of AGDR
from the charge-exchange random phase approximation (RPA) calculations.

Fig. 1. (Color online) Energy diﬀerence EAGDR − EIAS ofAGDR and IAS as a function of the neutron-skin thickness, obtained by using the SAMi-J family of Skyrme
functionals. The calculated values are presented as solidcircles. Two diﬀerent experimental data2,3) are also
shown as solid (magenta) and dashed (blue) lines, respectively. The arrows indicate the neutron skin constrained by these experimental data. We also display results obtained with the covariant DD-ME Lagrangiansof Ref.3)3..

We calculate the energy diﬀerence between AGDRand IAS energies and the impact on the symmetryenergy and neutron skin in the fully self-consistenttheory. The calculated results are shown in Fig. 1
together with the experimental results and the theoretical results obtained by means of relativistic meanﬁeld (RMF) calculations with the DD-ME eﬀective Lagrangian introduced in Ref.3)3.. We obtained the neutron skin from the correlation plot in Fig. 1 as 0.239± 0.038 fm from experimental data of J. Yasuda etal.2) and 0.216 ± 0.010 fm from experimental data of
A. Krasznahorkay et al.3) . These values give the symmetry energy coeﬃcients J and L as listed in Table 1.
The ﬁnal results for the symmetry energy parameters
J and L are changed by 10% at most compared withthe previous analysis and tend to be slightly closer tothe empirical values obtained in other analyses in theliterature. There are still open problems, such as obtaining a better agreement with the experimental energy of IAS in 208 Pb and the strong correlation of theIAS energy with the neutron skin, in which the variation of the IAS energy is larger than expected fromthe change of the charge radii within the family.

†References

Table 1. Allowed range for J, L and the neutron skin whenexperimental data from both Refs.2)2 and3)3 are considered. The estimates from the previous calculations ofRef.1)1 and from the current work are compared.

JLΔRnp∗1∗2∗3∗4∗5Ref. 1
30.7 – 37.7 MeV
72.7 – 144.3 MeV
0.192 – 0.316 fm

Present work
31.2 – 35.4 MeV
75.2 – 122.4 MeV
0.201 – 0.277 fm

Condensed from the article in Phys. Rev. C94, 044313(2016)
Dipartimento di Fisica, Università degli Studi di Milano
Istituto Nazionale di Fisica Nucleare (INFN), Milano
School of Mathematics and Physics, North China ElectricPower University, Beijing
RIKEN Nishina Center
Center for Mathematics and Physics, University of Aizu

- 101 -1) L. G. Cao, X. Roca-Moza, G. Colò, H. Sagawa, Phys.
Rev. C92, 034308 (2015).
2) J. Yasuda et al., Prog. Theor. Exp. Phys. 2013, 063D02(2013).
3) A. Krasznahorkay et al., Phys. Lett. B720, 428 (2013);
arXiv: 1311.1456 (2013).