Contribution of the $4f$-core-excited states in determination of atomic properties in the Promethium Isoelectronic Sequence

The atomic properties of Pm-like ions were comprehensively studied using relativistic atomic codes with the main emphasis on W ion. Excitation energies of the $4f^{14}nl$ (with $nl$ = $5s$, $6s$, $5p$, $6p$, $5d$, $6d$, and $5f$) states in Pm-like ions with nuclear charge $Z$ ranging from 74 to 100 are evaluated within the framework of relativistic many-body theory (RMBPT). First- and second-order Coulomb energies and first- and second-order Breit corrections to the energies are calculated. The important question of what is the ground state in Pm-like ions was answered. Properties of the $4f$-core-excited states are evaluated using the multiconfiguration relativistic Hebrew University Lawrence Livermore Atomic Code (HULLAC code) and the Hartree-Fock-Relativistic method (COWAN code). Our large scale calculations includes the following set of configurations: $4f^{14}5s$, $4f^{14}5p$, $4f^{13}5s^2$, $4f^{13}5p^2$, $4f^{13}5s5p$, $4f^{12}5s^25p$, $4f^{12}5s5p^2$, and $4f^{12}5p^3$. Excitation energies, transition rates, and lifetimes in Pm-like tungsten are evaluated with additional inclusion of the $4f^{11}5s^25p^2$, $4f^{11}5s5p^3$, $4f^{10}5s^25p^3$, and $4f^{10}5s5p^4$ configurations. Wavelengths of the $5s-5p$ transitions are obtained by the COWAN, HULLAC, and RMBPT codes.