Theory of Rotational Excitations in Solid Ortho-Hydrogen

Abstract

A theoretical study is made on the rotational excitations in solid fcc ortho-hydrogen below Tλ. The effective Hamiltonian which is quadratic in the rotational excitation operators of each molecule is set up by the method analogous to the Holstein-Primakoff theory of spin waves. The dispersion relation and the energy spectrum of the rotational excitation mode are obtained by the perturbational calculation. The expectation value of the angular momentum of each molecule generally vanishes in each energy eigenstate and the excited states can approximately be described in terms of quasi-particles for librational excitation which may be called librons. At 0°K libron has a minimum excitation energy of about 10kB and band width of about 5kB. The thermodynamic quantities such as free energy are numerically calculated using the state density, and the phase transition is estimated to be of first order and Tλ ≃ 4.2°K.