Commutators method for boson mapping in the seniority scheme

A new approximate method for carrying out the boson mapping in the seniority scheme is described, in which the boson expansions of the pair and multipole operators are determined by satisfying the commutation relations for the associated Lie algebra. The method is illustrated for the single-j shell-model algebra SO(2(2j + 1)). The calculation is successively carried out to lowest and to next-higher order, the latter exhibiting the necessity of including g-bosons in the calculation in order to reach algebraic consistency. Agreement with the exact result of Ginocchio for j = 3/2 is established to the order considered. (orig.)