ARE Q-BOSONS SUITABLE FOR THE DESCRIPTION OF CORRELATED FERMION PAIRS

In a single-j shell we consider fermion pair and multipole operators coupled to zero angular momentum. The commutation relations of these operators can be satisfied up to first-order corrections by suitably defined q-bosons, onto which the fermion pair operators are mapped. After performing the same mapping to a simple pairing Hamiltonian, we prove that the pairing energies are also correctly reproduced up to the same order. The small parameter used (T = ln Q) is found to be inversely proportional to the size of the shell.