Abstract
Numerical results for the Nikitin exponential model at non-zero impact parameters are presented. It is confirmed that in order to derive the correct strong-coupling approximation of the transition probability, one need only include the leading terms of the asymptotic expansions of the confluent hypergeometric functions. Development beyond leading order is inappropriate to the particular model, because by construction the non-analytic wavefunction is discontinuous in its second-order derivative at the turning point, which follows from the cusp-like discontinuity in the first-order derivative of at least the off-diagonal Hamiltonian potential matrix elements. It is therefore concluded that the Stueckelberg phase-integral derivations of Crothers are essential if transition probabilities and cross sections are not to be underestimated at large impact parameters, due to neglecting the bending of the double Stokes line.
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