M1 resonance in 208Pb within the self-consistent phonon-coupling model

The main goal of the paper is to investigate the experimentally observed spectral fragmentation of the isovector M1 resonance in Pb-208 within a self-consistent model based on an energy-density functional (EDF) of the Skyrme type. This fragmentation is not reproduced in a conventional one-particle-one-hole (1p1h) random-phase approximation (RPA) and thus has to be investigated in the framework of models including complex configurations. However, previously applied models of this type were not self-consistent. In the present work, we use a recently developed renormalized version of the self-consistent time-blocking approximation (RenTBA) in which 1p1h circle times phonon configurations are included on top of the RPA 1p1h configurations. We have investigated several parameter sets of modified Skyrme EDFs which were fitted within the RenTBA and RPA to reproduce the basic experimental characteristics of the low-energy M1 excitations in Pb-208. We have found as a necessary condition for producing the appropriate fragmentation of the M1 resonance in 208Pb that the minimum energy of the intermediate 1p1h circle times phonon configurations comes close to the mean energy of the M1 resonance. We present also results of the RenTBA and RPA calculations for the first excited states of the natural parity modes in Pb-208 obtained with the modified parametrizations.