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Extension of the Brinkman-Rice picture and the Mott transition

In order to explain the metal-Mott-insulator transition, the Brinkman-Rice (BR) picture is extended. In the case of less than one as well as one electron per atom, the on-site Coulomb repulsion is given by U={kappa}{rho}^2U_c by averaging the electron charge per atom over all atomic sites, where {kappa} is the correlation strength of U, {rho} is the band filling factor, and U_c is the critical on-site Coulomb energy. The effective mass of a quasiparticle is found to be m*/m=1/{1-{kappa}^2{rho}^4} for 0<{kappa}{rho}^2<1 and seems to follow the heat capacity data of Sr_{1-x}La_xTiO_3 and YBa_2Cu_3O_{7-delta} at {kappa}=1 and 0<{kappa}{rho}^2<1. The Mott transition of the first order occurs at {kappa}{rho}^2=1 and a band-type metal-insulator transition takes place at {kappa}{rho}^2=0. This Mott transition is compared with that in the d=infinity Hubbard model. The effective mass for 2D-DOS instead of the vHs can be used for the mechanism of high T_c superconductivity.