Second random-phase approximation with the Gogny force: First applications

Abstract

We present the first applications of the second random-phase-approximation model with the finiterange Gogny interaction. We discuss the advantages of using such an interaction in this type of calculations where 2 particle-2 hole configurations are included. The results found in the present work confirm the well known general features of the second random-phase approximation spectra: we find a large shift, several MeV, of the response centroids to lower energies with respect to the corresponding random-phase-approximation values. As known, these results indicate that the effects of the 1 particle-1 hole/2 particle-2 hole and 2 particle-2 hole/2 particle-2 hole couplings are important. It has been found that the changes of the strength distributions with respect to the standard random-phase-approximation results are particularly large in the present case. This important effect is due to some large neutron-proton matrix elements of the interaction and indicates that these matrix elements (which do not contribute in the mean-field calculations employed in the conventional fit procedures of the force parameters) should be carefully constrained to perform calculations beyond the mean-field approach.

Structure and direct decay of Giant Monopole Resonances

“…The improvement of computational power has recently led to realistic applications of the SRPA both with phenomenological interactions [33][34][35] as well as forces derived from realistic two-body interactions [36]. A common feature of these calculations is that the monopole strength is shifted toward lower energies by several MeV as compared to standard RPA calculations.…”

“…For these nuclei, the independent (quasi)particle approach can only be used for qualitative studies. For lighter nuclei such as 16 O, however, comparison between SRPA and RPA calculations show that, although the position of the GMR peak is sensitive to the residual interaction, the total width is almost unaffected by the addition of 2p2h contributions [32][33][34][35][36]. It is possible, then, that in a first approximation, the direct decay of the GMR in 16 O can be described with continuum RPA or TDHF calculations.…”

“…When realistic interactions are used [36], it could indi-cate a possible role of missing three-body interactions. When effective interactions such as the Skyrme [33,34] or Gogny [35] interactions are used, this energy shift is shown to be strongly affected by large proton-neutron matrix elements of the residual interaction of the threehole-one-particle (3h1p) type, coupling 1p1h with 2p2h configurations [35]. Unfortunately, these terms of the residual interaction are not constrained in conventional fitting procedure of the effective interaction parameters.…”

Nuclear excitations as coupled one and two random-phase-approximation modes

“…Such applications provided a very strong modification (a large downwards energy shift) of the RPA excitation spectra, also for those collective states whose description within the RPA is rather good. This was obtained for collective nuclear excitations with Skyrme and Gogny forces [14,15], as well as with an interaction derived from the Argonne V18 nucleon-nucleon potential with the unitary correlation operator method [16]. In the case of metallic clusters, within the jellium model [4], the modifications found when passing from RPA to SRPA are very large [17] and completely spoil the quality of the RPA results concerning the dipole strength distribution.…”

Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

“…Despite this success, the necessity of increasing the accuracy of theoretical predictions in some cases has motivated several groups to formulate beyond-mean-field models, which explicitly include more correlations in their formal scheme. Several directions have been explored, for instance: projection techniques in the framework of the generator coordinate method [2][3][4][5]; second randomphase approximation (SRPA) calculations with Skyrme and Gogny forces [6,7], as well as with an interaction derived from a realistic force [8]; particle-vibration coupling (PVC) techniques with the Skyrme interaction [9,10] and with a relativistic Lagrangian [11]; multiparticlemultihole configuration mixing (mpmhCM) methods with both Skyrme [12] and Gogny [13] forces.…”