 
Summary: VOLUME 85, NUMBER 1 P H Y S I C A L R E V I E W L E T T E R S 3 JULY 2000
BornOppenheimer Approximation near Level Crossing
A. Gordon and J. E. Avron
Department of Physics, Technion, 32000 Haifa, Israel
(Received 30 November 1999)
We consider the BornOppenheimer problem near conical intersection in two dimensions. For energies
close to the crossing energy we describe the wave function near an isotropic crossing and show that it is
related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the
Airy function is to a classical turning point. As an application we calculate the anomalous Zeeman shift
of vibrational levels near a crossing.
PACS numbers: 31.15.Gy, 33.20.t, 33.55.Be
Introduction.The BornOppenheimer (BO) problem
[1] is concerned with the analysis of Schrödingertype
operators where the small electrontonucleon mass ratio
plays the role of the semiclassical parameter [29]. The
theory identifies distinct energy scales: the electronic scale
which, in atomic units, is of order 1 and the scale of nu
clear vibrations which is of order 1 M 1 2
in these units.
M is the nucleustoelectron mass ratio. The identification
