Excitation energies of particle-hole states in 208Pb and the surface delta interaction

The schematic shell model without residual interaction (SSM) assumes the same excitation energy for all spins in each particle-hole configuration multiplet. In ²⁰⁸Pb, more than forty states are known to contain almost the full strength of a single particle-hole configuration. The experimental excitation energy for a state with a certain spin differs from the energy predicted by the SSM by ?0.2 to +0.6 MeV. The multiplet splitting is calculated with the surface delta interaction; it corresponds to the diagonal matrix element of the residual interaction in the SSM. For states containing more than 90% strength of a certain configuration and for the centroid of several completely observed configurations, the calculated multiplet splitting often approximates the experimental excitation energy within 30 keV. The strong mixing within some pairs of states containing the full strengths of two configurations is explained.