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

TL;DR

This paper develops a non-perturbative method to incorporate particle-phonon coupling effects into calculations of odd-even double mass differences in semi-magic nuclei, improving agreement with experimental data.

Contribution

A novel method for including particle-phonon coupling effects in DMD calculations without perturbation theory, using Dyson equation solutions for semi-magic nuclei.

Findings

Improved agreement with experimental DMD data for lead isotopes.

Significant impact of PC corrections on theoretical predictions.

Method applicable to other 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 $\delta \Sigma^{\rm PC}$ 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 $\delta \Sigma^{\rm PC}$ 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 $\Sigma(\epsilon){=}\Sigma_0{+}\delta \Sigma^{\rm PC}(\epsilon)$ 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.