Shell-Model Theory ofPb206

A detailed nuclear shell model calculation of the energy levels and gamma-ray transition rates in ${\mathrm{Pb}}^{206}$ is carried through. For pure singlet two-body forces with the same effective range and strength as for the low-energy two-body system, energy level agreement is good—for 13 known levels, the mean discrepancy between theory and experiment is 0.057 Mev. For singlet forces 75% as strong as for the low-energy two-body system, plus weak coupling to collective vibration, the energy level agreement is somewhat better—the mean discrepancy between theory and experiment is 0.035 Mev per level. In the latter theory, the strength of collective motion is determined from the known Coulomb excitation cross section in ${\mathrm{Pb}}^{206}$. In either theory, the calculated transition rates are in qualitative accord with experiment, but quantitative agreement is lacking.