Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semimagic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by S. A. 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)μN and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratios g_L~(ph) of all low-lying phonons in ~(208)Pb. 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.
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