Multipole transitions to determine lifetimes and polarizabilities in Mg-like ions from $\mathrm{Si}{}^{2+}$ to $\mathrm{Fm}{}^{88+}$

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 $3s3p{}^3{P}_2$ 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 $1s^{2}2s^{2}2p^6$ 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 $Z=14–100$.

Figure 1

Second-order contributions for multipole matrix elements in Mg-like ions as a function of $Z$.

Figure 2

Line strengths for $E2,M1$, and $M2$ transitions in Mg-like ions as a function of $Z$.

Figure 3

Transition rates for the lifetime of the $3s3p{}^3{P}_2$ level in Mg-like ions as a function of $Z$.

Figure 4

Ground-state dipole polarizability in Mg-like ions as a function of $Z$. The values of polarizability presented here are in units of $a_0^3$, where $a_0=0.052918$ nm is the Bohr radius.

Figure 5

Ground-state quadrupole polarizability in Mg-like ions as a function of $Z$. The values of polarizability presented here are in units of $a_0^3$, where $a_0=0.052918$ nm is the Bohr radius.

Figure 6

Ground-state octupole polarizability in Mg-like ions as a function of $Z$. The values of polarizability presented here are in units of $a_0^3$, where $a_0=0.052918$ nm is the Bohr radius.