Electric dipole polarizability in208Pb: Insights from the droplet model

Abstract

We study the electric dipole polarizability α D in 208 Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean-field models. We adopt the droplet model as a guide to better understand the correlations between α D and other isovector observables. Insights from the droplet model suggest that the product of α D and the nuclear symmetry energy at saturation density J is much better correlated with the neutron skin thickness r np of 208 Pb than the polarizability alone. Correlations of α D J with r np and with the symmetry energy slope parameter L suggest that α D J is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of the nuclear energy density functional by comparing our theoretical predictions against measurements of both α D and the parity-violating asymmetry in 208 Pb. We find that the recent experimental determination of α D in 208 Pb in combination with the range for the symmetry energy at saturation density J = [31 ± (2) est ] MeV suggests r np ( 208 Pb) = 0.165 ± (0.009) expt ± (0.013) theor ± (0.021) est fm and L = 43 ± (6) expt ± (8) theor ± (12) est MeV.

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, andRoca-Maza1, Viñas2, Centelles3 et al. 2015Phys. Rev. CSelf Cite238322563View full textAdd to dashboardCite

“…Therefore, Eq. (5) suggests that the product α D J-rather than α D alone-is strongly correlated to the neutron skin thickness of the nucleus [20]. Although inspired by the droplet model, the strong correlation α D J-∆r np in 208 Pb was validated in Ref.…”

“…As elaborated in great detail in Ref. [20], the simplicity of the DM allows one to relate the electric dipole polarizability to the neutron skin thickness in a nearly analytical way. Indeed, neglecting corrections to the neutron skin thickness due to both the Coulomb field and the surface diffuseness, one finds…”

“…Although inspired by the droplet model, the strong correlation α D J-∆r np in 208 Pb was validated in Ref. [20] by performing self-consistent mean-field plus RPA calculations for both neutron skin thickness and electric dipole polarizability using a rather large and representative set of non-relativistic and relativistic models. As a consequence of this correlation, a high precision measurement of the electric dipole polarizability of a nucleus provides critical information on its neutron skin thickness-if J was known.…”

“…In a subsequent systematic study performed with a large ensemble of both nonrelativistic and relativistic EDFs, a neutron skin thickness ∆r np = 0.168±0.022 fm was estimated [19]. By using relations deduced from the Droplet Model (DM), it was noted that the neutron skin thickness is correlated more strongly with the product of the electric dipole polarizability and the symmetry energy coefficient at saturation density (J), than to the dipole polarizability alone [20]. Using this correlation-and some plausible estimates for J-a value of ∆r np = 0.165 ± 0.026 fm was obtained [20].…”

“…By using relations deduced from the Droplet Model (DM), it was noted that the neutron skin thickness is correlated more strongly with the product of the electric dipole polarizability and the symmetry energy coefficient at saturation density (J), than to the dipole polarizability alone [20]. Using this correlation-and some plausible estimates for J-a value of ∆r np = 0.165 ± 0.026 fm was obtained [20]. Given the strong correlation between the neutron skin thickness of 208 Pb and the slope L of the symmetry energy at saturation density, these results favor a relatively soft symmetry energy with L 40 MeV, even though with fairly large error bars.…”