An analysis of the effects of level crossing and anticrossing in the resonant scattering of thermal phonons

An analysis is given of the changes that occur in the thermal conductivity of a solid containing resonant phonon scattering centres when there are crossings or anticrossings of levels involved in the scattering. At a level crossing, the changes are due to interference between the scattering processes involving the two levels. At a level anticrossing, the two levels repel because of the coupling between them and the changes in conductivity are due to the effects of state mixing as well as to interference. The effects of both types of crossing are discussed in the two limiting cases of weak and strong resonant scattering in comparison with the other scattering rates present. Observation of these effects can in principle provide rather accurate spectroscopic information about the positions of energy levels. In addition, information should be obtainable on the eigenstates and on the lifetimes of the levels involved.