Calculations of electric and magnetic nuclear excitations beyond mean field
Final Report Abstract
The project aimed at a systematic improvement and exploration of the phononcoupling model in connection with self-consistent calculations based on the Skyrme energy-density functional. The phonon-coupling model includes complex many-body configurations beyond the standard random-phase approximation for computing nuclear excitation properties. It does so in efficient manner by concentrating on a small selection of strongly contributing excited states (=phonons). This simplification raises three problems: 1) double counting of correlation diagrams, 2) violation of Pauli principle, and 3) proper exhaustion of essential contributions. The development part of the project worked on solutions for these three problems. Problem 1, double counting, is solved by a regularization scheme which which subtracts the stationary part of the correlation diagram because this is assumed to be already contained in the Skyrme energy-density functional. Problem 2 and 3 are closely related and are handled by optimizing the space of active phonons. We have extensively studied the trends of giant resonance energies in dependence of the choice of phonons and found a region where the results are stable against variation of the cutoff recipe. Taking this as the working point for applications, we have studied giant resonances (isoscalar monopole, isovector dipole, isoscalar quadrupole) and low lying collective vibrations in a variety of doubly magic nuclei from 16 O to 208 Pb. The correlations introduced with the phonon-coupling model lead to small, but not ignorable, shifts of the resonance energies and large enhancement of the widths of the resonances. Furthermore, the results were found to depend sensitively on the actual Skyrme parametrization. Thus resonance energies can be added as experimental information confining the choice of Skyrme parametrizations. It is a particularly comforting result that those parametrizations which reproduce the peak positions deliver also the correct width. Nonetheless, there remains an open problem for future research: we have not yet identified a parametrization which provides an equally good description for all giant resonance modes. Besides this main stream of development, we have worked out two sideprojects and published their results: first, the relation of the self-consistent description to the empirical Landau-Migdal modeling, and second, a review of Green’s function methods on nuclear physics.
