  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.
