Boson mapping for a single j-shell within the quon statistics

The quon algebra, which interpolates between the Bose and Fermi algebras and depends on a free parameter q, is used to generate a Marumori mapping of the quadrupole-quadrupole Hamiltonian, for a single j-shell. This Hamiltonian is then diagonalized for a system composed of six fermions and its eigenvalues are compared with the ones obtained from the counterpart fermionic Hamiltonian and with another usual boson expansion method. The deformed mapping is shown to require a larger basis than the usual Marumori method for the diagonalization of the Hamiltonian. The low-lying levels of the spectrum obtained from the fermionic calculation in the SD subspace can be reproduced with our mapping for some selected j-shells. (author)