Theory of the Ortho-Para Conversion in Solid Hydrogen

The rate of ortho-para conversion in solid hydrogen (H 2 ) is calculated taking two kinds of interactions between ortho-molecules into consideration: interaction between the nuclear spins of one molecule and those of the other molecule and interaction between the rotational magnetic moment of one molecule and the nuclear spins of other molecule. When an ortho-molecule converts into a para molecule, the rotational energy of the former is emitted as lattice phonons; we take the Debye model for the lattice vibrations and find that the dominant process is the emission of two phonons. The result for the rate of conversion (including a small effect arising from the emission of three phonons) is 1.94 percent per hour, which is comparable with the observed value of 1.75 percent per hour due to Cremer and of 0.9 percent per hour obtained recently by Hill. Further, the effect of a small amount of oxygen dissolved in solid hydrogen is treated and curves for the increase in average concentration as functions of time are plotted for various values of the oxygen concentration and of the initial ortho concentration. They are compared with preliminary measurements made in Tōhoku University.

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