Low-lying spectroscopy of a few even-even silicon isotopes investigated with the multiparticle-multihole Gogny energy density functional

Abstract

A multiconfiguration microscopic method has been applied with the Gogny effective interaction to the calculation of low-lying positive-parity states in even-even 26−32 Si isotopes. The aim of the study is to compare the results of this approach with those of a standard method of GCM type and to get insight into the predictive power of multiconfiguration methods employed with effective nucleonnucleon force taylored to mean-field calculations. It is found that the multiconfiguration approach leads to an excellent description of the low-lying spectroscopy of 26 Si, 28 Si and 32 Si, but gives a systematic energy shift in 30 Si. A careful analysis of this phenomenon shows that this discrepancy originates from too large proton-neutron matrix elements supplied by the Gogny interaction at the level of the approximate resolution of the multiparticle-multihole configuration mixing method done in the present study. These proton-neutron matrix elements enter in the definition of both singleparticle orbital energies and coupling matrix elements. Finally, a statistical analysis of highly excited configurations in 28 Si is performed, revealing exponential convergence in agreement with previous work in the context of the shell model approach. This latter result provides strong arguments towards an implicit treatment of highly excited configurations.

Quantum chaos and thermalization in isolated systems of interacting particles

“…We can note that in realistic nuclear calculations the uniformity of the eigenstates is indeed observed: the dispersion (3.6) is practically the same for all many-body states originating from the same occupation of single-particle orbitals, both in standard shell-model examples [1] and in the modern multi-configurational approach [75].…”

Nuclear level density: Shell-model approach

“…The first moment (2) is the diagonal matrix element of the Hamiltonian averaged over the partition, while the second moment (3) is the sum of squared offdiagonal elements along one line of the Hamiltonian matrix, again averaged over the lines corresponding to the partition. It is known that the dispersion for each basis state very weakly fluctuates within a partition [6,38] even prior to the next averaging. The second moment includes all interactions coupling the partitions.…”

Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

“…On the other hand, EDF underlying interactions can be used to perform SM diagonalizations [17,18] and multipole decompositions [1]. Furthermore, self-consistent mean-field analyses of single-particle energies in the deformed basis with Nilsson-like plots are routinely done to understand qualitatively the orbits that play a role for a given nucleus.…”