Origin of the neutron skin thickness ofPb208in nuclear mean-field models

Abstract

We study whether the neutron skin thickness r np of 208 Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to r np arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in r np of 208 Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that r np of 208 Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of r np of 208 Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of r np . We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208 Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208 Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208 Pb nucleon densities.

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, andRoca-Maza1, Viñas2, Centelles3 et al. 2015Phys. Rev. CSelf Cite233322563View full textAdd to dashboardCite

“…For a given heavy nucleus such as 208 Pb, the various correction terms, as well as r 2 , computed using many different successful EDFs have very similar values [37]. Therefore, Eq.…”

“…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. Moreover, by invoking the well-known correlation between ∆r np and L [33,[37][38][39], important constraints on the density dependence of the symmetry energy may also be obtained. Finally, based on the established correlation between the neutron-skin thickness of two neutron-rich nuclei [38,40,41], we anticipate that the tight correlation between α D J and ∆r np observed in 208 Pb will extend to other medium-to heavy-mass nuclei.…”

Density dependence of the nuclear symmetry energy from measurements of neutron radii in nuclei

“…(10). That is, we perform the exact phase shift analysis of the Dirac equation [69,68,37] [α·p +V ± (r)]ψ ± = Eψ ±…”

“…We solve the scattering problem in the distorted wave Born approximation (DWBA) [68,38,37] for realistic calculations of the parity violating asymmetry defined in Eq. (10).…”

Current Status of Nuclear Physics Research

“…Collective vibrations of nuclei are also a good tool to investigate the symmetry energy. Some features of neutron rich nuclei are also though to be very sensitive to the the symmetry energy, such as their neutron skin ∆r = r p − r n , where r p(n) is the proton (neutron) matter distribution [289,290]. Collective vibrations in neutron-rich nuclei at low energies are usually so-called Pigmy Resonances or Ikeda resonances [188,191,[291][292][293].…”