Multipole (E1, M1, E2, M2, E3, M3) transition wavelengths and rates   between 3l5l' excited and ground states in nickel-like ions
  A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections and includes corrections from negative energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) transitions between 3l5l' excited and ground states in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s22s22p63s23p63d10} Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for nickellike tungsten (Z = 74). The contributions from negative-energy states are included in the second-order E1, M1, E2 M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas. 
U. I. Safronova, A. S. Safronova, P. Beiersdorfer