Phonon coupling effects in magnetic moments of magic and semi-magic nuclei

TL;DR

This paper investigates phonon coupling corrections to magnetic moments in magic and semi-magic nuclei using a self-consistent theoretical framework, revealing that these corrections are generally small in magic nuclei but more significant in non-magic ones.

Contribution

The study develops a model separating regular and non-regular phonon coupling contributions, including tadpole terms, and provides a method to account for higher order effects within the Theory of Finite Fermi Systems.

Findings

PC corrections cancel each other in magic nuclei, making total correction negligible.

In non-magic nuclei, PC corrections are noticeable and typically negative, improving data agreement.

Calculated phonon gyromagnetic ratios show close agreement with models for some states, but significant differences for others.

Abstract

Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semi-magic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by Fayans et al. The perturbation theory in g_L^2 is used where g_L is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g_L^2 accuracy. An approximate method is suggested to take into account higher order terms in g_L^2. Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of -(0.1 - 0.5) \mu_N and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratio g_L^{ph} of all low-lying phonons in 208Pb. For the 3^-_1 state it is rather close to the Bohr-Mottelson model prediction whereas for other L-phonons, two 5^- and six positive parity states, the difference from the Bohr-Mottelson values is significant.