Ordering in Solid Hydrogen

Abstract

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 $M=0\mathrm{}$ and the other consisting of molecules $B$ in either of the states $M=\pm 1$, 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.