Phonon-particle coupling effects in odd-even double mass differences of semi-magic nuclei

Abstract

A method is developed to consider the particle-phonon coupling (PC) effects in the calculation of the odd-even double mass differences (DMD) in semi-magic nuclei starting from the free $NN$-potential. The PC correction $\delta {\Sigma }^{\mathrm{PC}}$ to the mass operator $\Sigma$ is found in $g_L^2$-approximation, $g_L$ being the vertex of creating the $L$-phonon. The tadpole term of the operator $\delta {\Sigma }^{\mathrm{PC}}$ is taken into account. The method is based on a direct, without any use of the perturbation theory, solution of the Dyson equation with the mass operator $\Sigma (ϵ)={\Sigma }_0+\delta {\Sigma }^{\mathrm{PC}}(ϵ)$ for finding the single-particle energies and $Z$-factors. In its turn, they are used as an input for finding different PC corrections to the DMD values. Results for a chain of even semi-magic nuclei ${}^{200-206}$Pb show that the inclusion of the PC corrections makes agreement with the experimental data significantly better.

Comments: 6 pages, 2 figures, 3 tables; ; v2 -- small corrections in the text; to be published in JETP Letters