## Abstract

For a random distribution of *NX* impurities over the *N* sites of a close-packed lattice, the average size of clusters of impurities connected by nn separations is finite for *X* ≲ 20%, as discussed in section 3.4. At sufficiently low concentrations *X*, it is therefore appropriate to analyze the properties of these solids in terms of *clusters* containing small numbers of *J* = 1 molecules, such as singles, nn pairs, triples with at least two nn separations, etc.^{1, 2} The *distribution* of the impurities over the lattice may be *random*, as realized after quick freezing of a liquid sample, or may correspond to the true *equilibrium* distribution, attained after a time long compared to the diffusion time constant. Valuable information on various cluster properties has been obtained from measurements of the specific heat of solid H_{2}, D_{2}, and their mixtures for *J* = 1 concentrations in the range 0.1–1%.^{2–4} The finer details of the *effective interaction* between the *J* = 1 impurities have been revealed by the Raman,^{5} NMR,^{6},^{7} and microwave (MW)^{8} *spectroscopy of pairs of J* = 1 *molecules*.

## Keywords

Partition Function Induce Dipole Moment Solid Hydrogen Rigid Lattice Pair Frame## Preview

Unable to display preview. Download preview PDF.

## References

- 1.T. Nakamura, On the quenching of molecular rotation of ortho-hydrogen in solid state,
*Progr. Thwor. Phys. (Kyoto)***44**, 135–150 (1955).ADSCrossRefGoogle Scholar - 2.R. J. Roberts and J. G. Daunt, Specific heats of solid hydrogen, solid deuterium, and solid mixtures of hydrogen and deuterium,
*J. Low Temp. Phys.***6**, 97–129 (1972).ADSCrossRefGoogle Scholar - 3.R. J. Roberts and J. G. Daunt, Anomalous specific heat of solid deuterium below 0.6 K,
*J. Low Temp. Phys.***16**, 405–408 (1974).ADSCrossRefGoogle Scholar - 4.R. J. Roberts, E. Rojas, and J. G. Daunt, Low-temperature quadrupole and crystalline field effects in the specific heat of solid D
_{2},*J. Low Temp. Phys.***24**, 265–273 (1976).ADSCrossRefGoogle Scholar - 5.I. F. Silvera, W. N. Hardy, and J. P. McTague, Direct observation of isolated
*J*= 1 pairs in solid deuterium and hydrogen by Raman scattering,*Phys. Rev.***B4**, 2724–2733 (1971).ADSGoogle Scholar - 6.A. Brooks Harris, L. I. Amstutz, H. Meyer, and S. M. Myers, Observation of pair interaction between orthomolecules in solid H
_{2},*Phys. Rev.***175**, 603–609 (1968).ADSCrossRefGoogle Scholar - 7.R. Schweizer, S. Washburn, and H. Meyer, NMR studies of single crystals of H
_{2}:11. The spectrum of isolated ortho-H_{2}pairs,*J. Low Temp. Phys.***37**, 309–341 (1979).ADSCrossRefGoogle Scholar - 8.W. N. Hardy, A. J. Berlinsky, and A. B. Harris, Microwave absorption by ortho-H
_{2}pairs in solid hydrogen,*Can. J. Phys.***55**, 1150–1179 (1977).ADSCrossRefGoogle Scholar - 9.A. Brooks Harris, Interactions between molecules in solid hydrogen,
*Phys. Rev.***Bl**, 1881–1902 (1970).ADSGoogle Scholar - 10.H. Miyagi, Energy levels of triangular clusters of ortho-hydrogen molecules due to quadrupole interaction in crystals,
*Progr. Theor. Phys. (Kyoto)***40**, 1448–1449 (1968).ADSCrossRefGoogle Scholar - 11.H. Meyer, Comments on two recent papers on solid H
_{2},*Phys. Rev.***187**, 1173–1174 (1969).ADSCrossRefGoogle Scholar - 12.J. F. Jarvis, H. Meyer, and D. Ramm, Measurement of (
*∂pP/∂T*)_{v}and related properties in solidified gases. IE Solid H_{2}.*Phys. Rev.***178**, 1461–1471 (1969).ADSCrossRefGoogle Scholar - 13.I. F. Silvera, The solid molecular hydrogens in the condensed phase: Fundamentals and static properties,
*Rer. Mod. Phys.***52**, 393–452 (1980).ADSCrossRefGoogle Scholar - 14.A. B. Harris, A. J. Berlinsky, and W. N. Hardy, Interactions between ortho-H
_{2}molecules in nearly pure para-H_{2},*Can. J. Phys.***55**, 1180–1210 (1977).ADSCrossRefGoogle Scholar - 15.B. W. Statt, W. N. Hardy, and R. Jochemsen, Observation of new lines in the microwave spectrum of ortho-H
_{2}pairs in solid hydrogen,*Can. J. Phys.***58**, 1326–1340 (1980).ADSGoogle Scholar - 16.S. Luryi and J. Van Kranendonk, Renormalized interactions in solid hydrogen and analysis of the ortho-pair level structure.
*Can.J. Phys.***57**, 307–326 (1979).ADSCrossRefGoogle Scholar - 17.B. W. Statt and W. N. Hardy, Line broadening mechanisms of the ortho-H
_{2}pair spectrum,*Can. J. Phys.***58**, 1341–1355 (1980).ADSGoogle Scholar - 18.S. Washburn, R. Schweizer, and H. Meyer, NMR studies on single crystals of H
_{2}: III. Dynamic effects,*J. Low Temp. Phys.***40**, 187–205 (1980).ADSCrossRefGoogle Scholar - 19.V. V. Goldman, Short-range correlations in quantum crystals and motional renormalization of anisotropic interactions in solid hydrogen as a function of density,
*Phys. Rev.***B20**, 4478–4481 (1979).ADSGoogle Scholar