Regularization of zero-range effective interactions in finite nuclei

Abstract

The problem of the divergences which arise in beyond mean-field calculations, when a zero-range effective interaction is employed, has not been much considered so far. Some of us have proposed, quite recently, a scheme to regularize a zero-range Skyrme-type force when it is employed to calculate the total energy, at second-order perturbation theory level, in uniform matter. Although this scheme looked promising, the extension for finite nuclei is not straightforward. We introduce such procedure in the current paper, by proposing a regularization procedure that is similar, in spirit, to the one employed to extract the so-called V_{\rm low-k} from the bare force. Although this has been suggested already by B.G. Carlsson and collaborators, the novelty of our work consists in setting on equal footing uniform matter and finite nuclei; in particular, we show how the interactions that have been regularized in uniform matter behave when they are used in a finite nucleus with the corresponding cutoff. We also address the problem of the validity of the perturbative approach in finite nuclei for the total energy.

Accepted in Phys. Rev. C (https://journals.aps.org/prc/accepted/4207aPfaIc313f02133c78b61b9c320e0a4e115d5)

References in corpus (9)

• Energy density functional study of nuclear matrix elements for neutrinoless $\beta \beta$ decay
• Relativistic quasiparticle time blocking approximation. Dipole response of open-shell nuclei
• Covariant theory of particle-vibrational coupling and its effect on the single-particle spectrum
• A microscopic benchmark-study of triaxiality in low-lying states of 76Kr
• The Gamow-Teller response within Skyrme random-phase approximation plus particle-vibration coupling
• Variational multiparticle-multihole configuration mixing method applied to pairing correlations in nuclei
• Beyond-mean-field theories with zero-range effective interactions. A way to handle the ultraviolet divergence
• Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei
• Self-consistent microscopic description of neutron scattering by ${}^{16}$O based on the continuum particle-vibration coupling method