A phenomenological spin-orbit and nuclear potential for ²⁰⁸Pb

Abstract:

A local, state-independent nuclear single-particle potential for ²⁰⁸Pb was developed by suitably shaping the nuclear central term and the related spin-orbit term of Thomas type. The aim was to reproduce accurately the excitation energies of the known single-particle states in ²⁰⁷Tl, ²⁰⁷Pb, ²⁰⁹Bi and ²⁰⁹Pb as well as the recently observed dependence of the spin-orbit splittings on angular momentum ℓ and principal quantum number n. As result, a set of orthogonal proton and neutron wave functions was obtained which were used for a consistent reanalysis of proton and neutron single-particle transfer reactions on ²⁰⁸Pb. The quality of the description of measured angular distributions is comparable with that obtained originally with individual “best fit” potentials. The resulting single-particle spectroscopic factors amount on the average to S≈ 0.7. Single-particle densities derived from these wave functions are in qualitative agreement with measured charge and mass densities for ²⁰⁸Pb.