Theory of Solid Hydrogen Mixture. I. Distribution of Local Order Parameters, NMR Line Shapes and Relaxation Times

Abstract

The ortho-para mixture of solid H₂ is studied theoretically for fcc lattices of finite size, assuming EQQ interaction. The excitation spectrum is calculated by using the Hartree ground-state obtained numerically. The lowest excitation energy decreases with decrease of ortho concentration X, and vanishes at X∼0.55. The distribution of the local order parameters (LOP) is obtained in comparison with NMR line shape. Importance of the quantum effect is pointed out for the distribution of LOP which broadens rapidly with decrease of X. The relaxation time T₁ is also studied as a function of NMR frequency shift, manifesting that ortho-H₂ with smaller value of order parameter relaxes more rapidly in the quadrupolar glass region.