Self-consistent theory of lattice distortion in solid p-H2, o-D2 and HD

A mean-field theory of the lattice distortion in J-even species of solid hydrogens and HD is developed. The Hamiltonian of the system includes contributions from two-body and three-body static energy, zero-point phonons, kinetic and potential Energies of quantum rotors and the lattice-rotation coupling. The Hamiltonian is described by two Order parameters: the deviation of the axial ratio, c/a, from its ideal value of root8/3 and the orientational order parameter. The coefficients of the Landau expansion of the free energy of the system in powers of these order parameters are calculated as a function of pressure and temperature. It is shown that the lattice distortion has a threshold behavior. As follows from preliminary numerical estimates, the lattice remains ideal up to the I-II phase transition.