Extended commutator method for boson mapping in the seniority scheme: Two non-degenerate-j shells with vertical strokej1-j2vertical stroke=2

The commutator method of Bonatsos, Klein and Li for approximate boson mapping in the seniority scheme, previously illustrated for the single-j shell-model algebra SO(2(2j+1)), has been extended in order to be applicable to the case of many non-degenerate-j shells, and the physically interesting case of two shells with vertical strokej1-j2vertical stroke=2 has been studied in detail. The most important new feature of this work is that bosons corresponding to pairs of two fermions each of which belongs to a different shell have been included in the calculation. (These bosons had been omitted in previous work using the Otsuka-Arima-Iachello method.) The calculation is successively carried out to lowest and to next-higher order, the latter exhibiting the necessity of including f- and g-bosons (both of positive parity) in the calculation in order to reach algebraic consistency. (orig.)