Orientational Ordering in Solid Hydrogen

A model for solid orthohydrogen in the temperature range of the observed second-order transition is considered. The lattice structure is taken to be hexagonal close packed and the quadrupole-quadrupole interaction energy is minimized with respect to parameters defining a self-consistent set of one-particle rotational wave functions, with $J=1\mathrm{}$. Values of the ground-state energy are deduced when, respectively, (i) all lattice sites are equivalent, and (ii) superlattice ordering occurs in planes perpendicular to an axis of threefold symmetry of the crystal. In the latter case, a zeroth-order statistical treatment of the free energy is given using an orthogonal set of rotational wave functions, approximately consistent with the ground-state wave functions. It is found that a second-order transition occurs at 2.9°K and that the change in entropy per orthohydrogen molecule over the transition range is k ln3, in accordance with experiment.