J. E. Avron and A. Gordon
The Born Oppenheimer wave function near level crossing
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ABSTRACT. The standard Born Oppenheimer theory does not give an accurate
description of the wave function near points of level crossing. We
give such a description near an isotropic conic crossing, for
energies close to the crossing energy. This leads to the study of
two coupled second order ordinary differential equations whose
solution is described in terms of the generalized hypergeometric
functions of the kind 0F3(;a,b,c;z). We find that, at low
angular momenta, the mixing due to crossing is surprisingly large,
scaling like \mu^(1/6), where \mu is the electron to nuclear
mass ratio.