Correlations and effective potential in the ground state of a one-dimensional model for solid helium and deuterium

The ground-state energyE can be calculated exactly by the transfer-integral method if the total wave function is assumed to be a product of single-particle functions and nearest-neighbor correlation functionsf. The variation ofE with respect tof for fixed leads to a Schrödinger equation for the relative motion of two particles which is coupled to the transfer integral equation by an effective potential V. For the case of a Gaussian the optimalf, the one- and two-particle probability amplitudes, and other quantities are computed by iteration of the Schrödinger equation with the transfer integral equation until self-consistency is achieved. The minimum ofE as a function of the Gaussian width is obtained for different values of the lattice parameter. The shape of V andf is discussed. The self-consistentf describes both short- and long-range correlations.