Librational motion in the α phase of solid nitrogen. I. Basic theory and results

Abstract

Librational motion in the α phase of solid nitrogen is studied on the basis of a model that ignores the translational motion of the molecular centres of mass. A general expansion in spherical harmonics is written down for an arbitrary two-body intermolecular potential, and methods are presented for obtaining the expansion coefficients for a particular potential model. The crystal Hamiltonian is written down and the mean-field approximation is briefly discussed. The eigenstates of the mean-field Hamiltonian are shown to correspond formally to the eigenstatesof the two-dimensional isotropic harmonic oscillator, and this correspondence is exploited to define boson creation and annihilation operators for excitations of a single molecule. The full crystal Hamiltonian is expressed in terms of these operators and the bilinear terms are diagonalized by an RPA treatment which is an extension of one given by Raich and Etters. Numerical results for the libron frequencies at the Γ and R points in the Brillouin zone are presented for the potential models proposed by Kohin and by Raich and Mills, the calculations having been performed with the intermolecular potential including terms as far as l = 6. The temperature dependence of the nuclear quadrupole resonance (NQR) frequency calculated with the Raich–Mills potential is shown to be in very good agreement with the measurements of Brookeman, McEnnan, and Scott. Finally the orientational probability density is presented as a function of temperature.