Measurement of conversion electrons with the $^{208}Pb(p,n)^{208}Bi$ reaction and derivation of the shell model proton neutron hole interaction from the properties of $^{208}Bi$

Conversion electrons from 208Bi have been measured using singles and coincidence techniques with the 208Pb(p,n)208Bi reaction at 9 MeV. The new information on multipolarities and spins complements that available from recent gamma-gamma-coincidence studies with the same reaction [Boutachkov et al., Nucl. Phys. A768, 22 (2006)]. The results on electromagnetic decays taken together with information on spectroscopic factors from earlier single-particle transfer reaction measurements represent an extensive data set on the properties of the one-proton one-neutron-hole states below 3 MeV, a spectrum which is virtually complete. Comparison of the experimental observables, namely, energies, spectroscopic factors, and gamma-branching ratios, with those calculated within the shell model allows extraction of the matrix elements of the shell model residual interaction. More than 100 diagonal and nondiagonal elements can be determined in this way, through a least squares fit to the experimental data. This adjustment of the interaction significantly affects the calculated properties of the gamma-ray transitions. Nevertheless, the matrix elements thus obtained are remarkably similar to those of a realistic interaction calculated from free-nucleon scattering. Characteristic features of the interaction are discussed.