The energies of the ground np states and the lowest ns and nd states in neutral
B, Al, Ga, In and Tl are obtained by using relativistic many-body perturbation
theory (RMBPT) method. First-, second-, third-order, and 'all order' Coulomb
energies and first- and second-order Breit energies are calculated.
Transition matrix elements provide another test of quality of atomic-structure
calculations and another measure of the size of correlation corrections.
Reduced matrix elements of the dipole operator in first-, second-, third- and
'all order'- perturbation theory between low-lying states of B~I, Al~I, Ga~I,
In~I, and Tl~I are presented. Second-order matrix element are extended to include
all high-order correction associated with the random-phase approximation (RPA).
These second-order calculations are practically gauge independent. The third-order
matrix elements include (RPA) plus Bruekner-orbital, structural radiation, and normalization correction. Results for a limited number states are obtained in the relativistic single-double (SD) approximation, where single and double excitations of Dirac-Fock wave functions are included to 'all orders' in perturbation theory. Using SD wave functions, accurate values are obtained for energies of the lowest states and for the possible electric-dipole matrix elements between these states. With the aid of the SD wave functions, we also determine transition rates and oscillator strengths together with lifetimes levels. These calculations provide a theoretical benchmark for comparison with experiment and theory.