A phenomenological spin-orbit and nuclear potential for $\chem{^{208}Pb}$

G. Mairle; P. Grabmayr

doi:doi:10.1007/s100500070016

2020 Impact factor 3.043

Hadrons and Nuclei

Eur. Phys. J. A 9, 313-326

A phenomenological spin-orbit and nuclear potential for $\ensuremath{\mathsf{^{208}Pb}}$

G. Mairle¹ - P. Grabmayr²

¹ Universität Mannheim, Germany
² Physikalisches Institut, Universität Tübingen, Germany

Received: 12 September 2000
Communicated by P. Schuck

Abstract
A local, state-independent nuclear single-particle potential for $\ensuremath{\mathsf{^{208}Pb}}$ 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 $\ensuremath{\mathsf{^{207}Tl}}$ , $\ensuremath{\mathsf{^{207}Pb}}$ , $\ensuremath{\mathsf{^{209}Bi}}$ and $\ensuremath{\mathsf{^{209}Pb}}$ as well as the recently observed dependence of the spin-orbit splittings on angular momentum $\ell$ 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 $\ensuremath{\mathsf{^{208}Pb}}$ . 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 $S\approx$ 0.7. Single- particle densities derived from these wave functions are in qualitative agreement with measured charge and mass densities for $\ensuremath{\mathsf{^{208}Pb}}$ .