  Relativistic many-body perturbation theory is applied to study properties of
ions of the francium isoelectronic sequence. Specifically, energies of the 7s,
7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are
calculated through third order; reduced matrix elements, oscillator strengths,
transition rates, and lifetimes are determined for 7s - 7p, 7p - 6d, and 6d -
5f electric-dipole transitions; and 7s - 6d, 7s - 5f, and 5f_5/2 - 5f_7/2
multipole matrix elements are evaluated to obtain the lifetimes of low-lying
excited states. Moreover, for the ions Z = 87 - 92 calculations are also
carried out using the relativistic all-order single-double method, in which
single and double excitations of Dirac-Fock wave functions are included to all
orders in perturbation theory. With the aid of the SD wave functions, we obtain
accurate values of energies, transition rates, oscillator strengths, and the
lifetimes of these six ions. Ground state scalar polarizabilities in Fr I, Ra
II, Ac III, and Th IV are calculated using relativistic third-order and
all-order methods. Ground state scalar polarizabilities for other Fr-like ions
are calculated using a relativistic second-order method. These calculations
provide a theoretical benchmark for comparison with experiment and theory.
