The ground-state energy and self-trapping transition in XY8and XY6para-elastic tunnelling systems

Abstract

The ground-state energy and the nature of the transition between the weak-coupling and the self-trapping regime of the truncated para-elastic tunnelling systems XY8 and XY6 are studied by means of a variational calculation. By use of the symmetry of the respective systems, the defect coordinates are eliminated from the Hamiltonian and an equivalent phonon Hamiltonian is obtained which depends parametrically on the symmetry of the defect part of the wavefunction. A variational treatment is then applied to the phonon Hamiltonian. A discontinuous transition is found when only one variational parameter is included in the calculation; this case corresponds to very strong defect-lattice coupling, while the ratio of the rigid-lattice tunnelling matrix element to the small-polaron binding energy remains finite. By introduction of a second variational parameter, thus allowing a finite defect-lattice coupling strength, a lower energy is obtained and the transition becomes either continuous or discontinuous, depending on the magnitude of the phonon overlap integral.