Shell-Model Theory ofPb206

Abstract

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.Electric quadrupole transition rates are shown to be describable in terms of a neutron effective charge. The effective charge is about $1.15e$ and the same in ${\mathrm{Pb}}^{206}$ as in ${\mathrm{Pb}}^{207}$. Other calculated quantities in good agreement with experiment are the relative cross sections to final $p$ states in the ${\mathrm{Pb}}^{206}(d, p){\mathrm{Pb}}^{207}$ reaction and the difference in binding energies of the last neutron in ${\mathrm{Pb}}^{206}$ and ${\mathrm{Pb}}^{207}$. The results are shown to be insensitive to substantial amounts of triplet-odd force, either attractive or repulsive.