Ordering in Solid Hydrogen

It is shown that in the case of the model for solid ortho-hydrogen considered, the ground-state superlattice structure, produced by the electrostatic quadrupole interactions, may be derived exactly. It consists essentially of two unequal sublattices: one consisting of molecules A in the state $M=0$ and the other consisting of molecules B in either of the states M=±1, the latter being twice as many as the former. The configuration on each triangular plane, normal to the axis of symmetry of the lattice, is such that each A molecule is surrounded by six B molecules, and each B molecule is surrounded by three A molecules and three B molecules. The transition temperature of the system is found to be 5.8^∘{}K in the zeroth approximation and 3^∘{}K in a tetrahedral approximation, the latter being in agreement with the experimental estimate.