Abstract
The boson-fermion interaction in the interacting boson-fermion model-2 (IBFM-2) is derived in a systematic and general form from a quadrupole-quadrupole force using several nondegenerate levels. The boson-fermion quadrupole operator employed is obtained from the boson-fermion image of the one nucleon transfer operator which in turn can be calculated following two alternative schemes: the Otsuka-Arima-Iachello and generalized Holstein-Primakoff schemes. Four different terms (two quadrupole and two exchange) were obtained. Application of the new expressions to a single-$j$ model is studied and analyzed.
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