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)

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Cited by in corpus (6)

• Time-dependent density-functional description of nuclear dynamics
• Effective density functionals beyond mean field
• Towards a self-consistent dynamical nuclear model
• Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms
• Extension and parameterization of high-order density dependence in Skyrme forces
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory