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Abstract
.Recently, a new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M*, has been presented. We investigate the possible existence of spurious finite-size instabilities of this new Gogny force by repeating a study that we have already performed for the most commonly used parameterizations (D1, D1S, D1N, D1M) of the Gogny force. This study is based on a fully antisymmetrized random phase approximation (RPA) calculation of the nuclear matter response functions employing the continued fraction technique. It turns out that this new Gogny interaction is affected by spurious finite-size instabilities in the scalar isovector channel; hence, unphysical results are expected in the calculation of properties of nuclei, like neutron and proton densities, if this D1M* force is used. The conclusions from this study are then, for the first time, tested against mean-field calculations in a coordinate representation for several nuclei. Unphysical results for several nuclei are also obtained with the D1N parameterization of the Gogny force. These observations strongly advocate for the use of the linear response formalism to detect and avoid finite-size instabilities during the fit of the parameters of Gogny interactions as it is already done for some Skyrme forces.
Highlights
A new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M∗, has been presented
To study the possible onset of finite-size instabilities, we start by repeating here the same study as the one published in ref. [12] where we developed a fully-antisymmetrized random phase approximation (RPA) calculation of ρc/ρ0 ρc/ρ0
In the left panel of fig. 1, we show the critical densities in the three spin-isospin (S, T ) channels (0, 1), (1, 1) and (1, 0) as a function of the transferred momentum q for the D1M∗ force
Summary
A new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M∗, has been presented. Beyond these evaluations performed by the authors, it is interesting to check the behavior of this newly adjusted interaction with respect to the development of finite-size instabilities, since it was pointed out that they can be hidden by the use of a representation of the quasiparticle wave functions on a limited number of harmonic oscillator shells [11] whereas these instabilities can develop when the calculation is performed on a mesh.
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