Asymmetry potential for sub-Coulomb-energy protons interacting withZr90

Abstract

The depth of the asymmetry potential for nucleons interacting with $^{90}\mathrm{Zr}$ is obtained at sub-Coulomb proton energies, from the observed isospin splitting of the $3{s}_{\frac{1}{2}}$ proton single-particle resonance. The splitting is described by the Lane model with an asymmetry potential depth of 31.4 MeV and with other parameters adopted from analyses of measured, sub-Coulomb energy $^{92,94}\mathrm{Zr}(p, n)$ and ($p, p$) cross sections. The resulting value of 31.4 MeV is significantly larger than the value obtained at higher energies by proton-scattering and charge-exchange measurements, indicating that the asymmetry potential must be energy dependent. The present result and the results at higher energies are shown to be in excellent agreement with the energy-dependent asymmetry potential of Giannini et al.NUCLEAR REACTIONS Lane model analysis of isospin splitting of $3{s}_{\frac{1}{2}}$ proton state in $^{90}\mathrm{Zr}$+$p$ deduced asymmetry potential depth.