ANALYTIC SOLUTION OF THE GENERALIZED KUMMER EXPONENTIAL MODEL

A new two-state exactly solvable Kummer model embracing three non-adia batic parameters is presented. Application of phase-integral technique s gives a simple interpretation of the semi-classical scattering colli sion matrix, which is derived using both strong and weak coupling asym ptotics of the generalized Kummer functions. On this basis simple anal ytic formulae are obtained for both elastic and inelastic transition p robabilities which incorporate the effects of the classical turning po int. The generalized Kummer model formula is shown to reduce correctly in certain limiting cases to yield other well known potential problem s, which include the Rosen-Zener, Demkov, parabolic model formulae, sy mmetric resonance and also a two-parameter exponential limiting model of our three-parameter model.