 
Summary: BornOppenheimer wave function near level crossing
J. E. Avron and A. Gordon
Department of Physics, Technion, 32000 Haifa, Israel
Received 18 June 2000; published 3 November 2000
The standard BornOppenheimer 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 secondorder 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 1/6
, where is the
electron to nuclear mass ratio.
PACS number s : 31.15.Gy, 33.55.Be, 33.20. t
I. INTRODUCTION
In 1927, in a landmark paper, Born and Oppenheimer 1
paved the way toward applying quantum mechanics to mo
lecular spectra. In their paper they introduced an approxima
tion that greatly simplified the treatment of quantum
mechanical spectral problems in which the particles can be
divided into heavy and light. Molecules are an example since
the nuclei are much heavier than the electrons. We shall
