Observation of Pair Interaction between Ortho Molecules in SolidH2

A study of the electric quadrupole-quadrupole (EQQ) interaction between ortho-${\mathrm{H}}_2$ molecules in solid ${\mathrm{H}}_2$ is presented. This work consists in recording and interpreting the pair spectrum of proton nuclear magnetic resonance for low ortho-${\mathrm{H}}_2$ concentrations. In the theoretical part of this paper, a calculation of the absorption spectrum for an isolated pair of ortho molecules is presented, and the temperature dependence of this spectrum is derived as a function of the rotational states of the isolated ortho pair. Furthermore, the results of similar calculations on the absorption spectrum of isolated triangles of ortho-${\mathrm{H}}_2$ molecules in solid ${\mathrm{H}}_2$ are briefly discussed. This spectrum is expected to be less pronounced than the pair spectrum and to be mostly responsible for a broad absorption background. The experimental work, carried out at temperatures between 0.45 and 14°K on several low ortho-${\mathrm{H}}_2$ concentrations shows the maxima expected from theory. From the analysis of the results, and assuming the interactions between molecules to be purely EQQ, the coupling constant $\frac{\Gamma }{k_B}=\frac{6e^2{Q}^2}{25R^5{k}_B}$ is found to be 0.82°K. This value is smaller than that expected for the solid rigid lattice, where $\frac{\Gamma }{k_B}=1.00\mathrm{}$°K. One also obtains from the analysis a dipolar coupling constant $d=54.5\mathrm{}$ kHz which is smaller than that measured for the free ${\mathrm{H}}_2$ molecule, where $d=57.7\mathrm{}$ kHz. It is suggested that the departures both in $\Gamma$ and in $d$ from expectations are caused by the interactions between lattice vibrations and rotations, since solid ${\mathrm{H}}_2$ will behave more like a quantum crystal with large zero-point motion than like a classical rigid crystal.