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

TL;DR

This study applies a multiconfiguration microscopic method with the Gogny interaction to analyze low-lying states in silicon isotopes, showing high accuracy for some isotopes and revealing insights into the method's predictive power and limitations.

Contribution

It demonstrates the effectiveness of multiconfiguration methods with Gogny interaction for silicon isotopes and analyzes the convergence and residual interaction effects.

Findings

Excellent description of $^{26}$Si, $^{28}$Si, and $^{32}$Si spectra.

Systematic energy shift observed in $^{30}$Si due to residual interaction.

Exponential convergence of highly excited configurations in $^{28}$Si.

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 $^{26-28}$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 nucleon-nucleon 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 matrix elements in the proton-neutron residual interaction supplied by the Gogny interaction. 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.