Including particle-vibration coupling in the Fayans functional. Odd-even mass differences of semi-magic nuclei

TL;DR

This paper introduces a method to incorporate particle-vibration coupling into the Fayans functional to improve predictions of odd-even mass differences in semi-magic nuclei, showing significant accuracy improvements for lead isotopes.

Contribution

A new approach to evaluate particle-phonon coupling corrections within the Fayans functional for better nuclear mass difference predictions.

Findings

Improved agreement with experimental data for lead isotopes.

Partial success in tin isotopes with better results for addition modes.

Discrepancies in removal modes highlight ongoing challenges.

Abstract

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ makes agreement of the theory with the experimental data significantly better. For the tin chain, the situation is not so definite. In this case, the PC corrections make agreement better in the case of the addition mode but they spoil the agreement for the removal mode. We discuss the reason of such a discrepancy.