Multipole transitions to determine lifetimes and polarizabilities in Mg-like ions from Si2+ to Fm88+

Abstract

The relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate the multipole ($E1,M1,E2,M2$, and $E3$) matrix elements to determine the $3s3p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{2}$ lifetime and multipole polarizabilities in Mg-like ions. The electric multipole matrix elements are determined in length and velocity forms. The calculations start from a $1{s}^{2}2{s}^{2}2{p}^{6}$ Dirac-Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients, and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order multipole matrix elements to ensure gauge independence of transition amplitudes. The details of our calculations of the multipole polarizabilities are illustrated for Mg-like $\mathrm{Si}{}^{2+}$, $\mathrm{Fe}{}^{14+}$, $\mathrm{Kr}{}^{24+}$, $\mathrm{Mo}{}^{30+}$, $\mathrm{Xe}{}^{42+}$, and $\mathrm{W}{}^{62+}$ ions. Our RMBPT results are compared with available theoretical results and experimental measurements. Trends of the line strengths, transition rates, and contributions in the ground-state multipole polarizabilities as functions of $Z$ are illustrated graphically in Mg-like ions with $Z=14--100$.