Theory of -Transition in Solid Hydrogen

Abstract

A theory of A-transition in solid hydrogen is developed on the basis of quadrupole-quadrupole interaction between ortho-hydrogen molecules. The double time Green's function technique is adopted to investigate the ground state configuration, low lying excitations and the tempera­ ture dependence of long range order in a self-consistent way. The inelastic scattering cross section of neutron by solid hydrogen due to the excitation of libration waves is also calculated. It has been known that normal hydrogen undergoes a phase transitiOn ac­ companied by a J.-shaped anomaly in specific heat at about 1.5° K. This transition is believed to be related closely to the removal of the three-fold degeneracy in rotational states of ortho-molecules and many experimental evidences to support this supposition have been accumulated. The observations of the specific heat anomaly, l) of a line shape change in nuclear magnetic resonance 2 ) and of the dependence of transition temperature on ortho-molecule concentrations 3 ) are such examples. Furthermore the fact that the interaction responsible for the removal of the degeneracy mentioned above mainly comes from the quadrupole-quadrupole interaction between ortho-molecules has been proved by the theoretical analysis of the anomalous specific heae) and by the experiment on pressure dependence of transition temperature. 5 ) Theoretical investigations of this phase transition are already abundant. Among them, Tomita 6 ) laid emphasis on the cooperative nature in the transition and tried a theory of order-disorder transition with the Weiss and Bethe ap­ proximations. At that time, however, the molecular interaCtion responsible for the transition was not yet clear, and hence microscopic theories of the ordered phase and of phase transition which take account of the correct interactions have appeared comparatively recently. Many attempts have been made to find the ordered orientation of molecules in solid ortho-hydrogen with the lowest energy. Nagai and Nakamura 7 ) have obtained the lowest energy state of the quadupole moment array in fcc lattice by generalizing Luttinger and Tisza's method. 8 ) On the other hand, for the hcp structure Danielian, 9 ) Kitaigorodskii and Mirskaya/ 0 ) and Felsteiner 11 ) have proposed different orderd configurations of ortho-hydrogen molecules with the lowest classical quadrupole energy. All these authors have ignored the quantum effect which is not necessarily small