Matrix elements of the Breit Hamiltonian

A formulation has been developed for the evaluation of the matrix representation, in sets of ‖${\mathrm{SM}}_S$ ${\mathrm{LM}}_L$), ‖${\mathrm{SLJM}}_J$), or ‖${\mathrm{JIFM}}_F$) functions (as required), of the complete atomic Hamiltonian operator consisting of the electronic, the SL-nonsplitting (specific mass, mass variation, Darwin, spin-spin contact, and orbit-orbit) correction terms, and the fine- (spin-orbit and spin-spin dipole) and hyperfine-structure (magnetic dipole, electric quadrupole, and magnetic octupole) interactions. This formulation may be easily implemented in a computer program, appropriate for the accurate evaluation of the energy levels of any atomic system.