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

The quon algebra, which interpolates between the Bose and Fermi algebras an d depends on a free parameter q, is used to generate a Marumori mapping of the quadrupole-quadrupole Hamiltonian, for a single j-shell. This Hamiltoni an is then diagonatized for a system composed of six fermions and its eigen values are compared with the ones obtained from the counterpart fermionic H amiltonian and with another usual boson expansion method. The deformed mapp ing is shown to require a larger basis than the usual Marumori method for t he diagonalization of the Hamiltonian. The low-lying levels of the spectrum obtained from the fermionic calculation in the SD subspace can be reproduc ed with our mapping for some selected j-shells.