Curve-crossing and the WKB approximation

The transition probabilities and phase changes associated with passage through a potential curve crossing are derived in the form of connection formulae between WKB solutions on either side of the crossing point. The formulae are expressed in terms of three integrals v and ε± which may be evaluated for arbitrary potential curves and interaction function without knowledge of the associated wavefunctions. The theory, which is fully developed in the chemical energy region (< 100 ev), is applied to a model for the covalent-ionic crossing responsible for inelastic scattering of alkali atoms from neutral targets and its extension to the higher energy region for this model indicated.