Fermions and bosons in a double-well potential

The boson-fermion model, describing a mixture of fermions and bosons is analyzed on a small, two-site lattice. The model includes all the on-site Coulomb-type interactions between bosons, between fermions and between fermions and bosons. Additionally, the Hamiltonian includes a term that describes a conversion of a pair of opposite-spin fermions into a boson and vice versa. We show how this conversion depends on the model parameters

H2H_2 and (H2)2(H_2)_2 molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters

The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron--ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to the solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for $2 \times H_2$ rectangular configurations.Comment: 14 pages, 14 figures, 6 table