Correlation and relativistic effects for the $4f-\mathit{nl}$ and $5p-\mathit{nl}$ multipole transitions in Er-like tungsten

Wavelengths, transition rates, and line strengths are calculated for the multipole ($E1$, $M1$, $E2$, $M2$, $E3$, and $M3$) transitions between the excited [Cd]$4f^{13}5p^6\mathit{nl}$, [Cd]$4f^{14}5p^5\mathit{nl}$ configurations and the ground [Cd]$4f^{14}5p^6$ state in Er-like ${\mathrm{W}}^{6+}$ ion ([Cd]=[Kr]$4d^{10}5s^2$). In particular, the relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in this hole-particle system. This method is based on the relativistic many-body perturbation theory that agrees with multiconfiguration Dirac-Fock (MCDF) calculations in lowest order, and includes all second-order correlation corrections and corrections from negative-energy states. The calculations start from a [Cd]$4f^{14}5p^6$ Dirac-Fock (DF) potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the multipole matrix elements needed for calculations of other atomic properties such as line strengths and transition rates. In addition, core multipole polarizability is evaluated in random-phase and DF approximations. The comparison with available data is demonstrated.

Figure 1

Dirac-Fock binding energies of the $4f_j$, $5s_{1/2}$, and $5p_j$ orbitals as a function of $Z$.

Figure 2

DF valence energies of the $5d_j$, $6p_j$, $6s_{1/2}$ orbitals as a function of $Z$.