Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
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 Born-Oppenheimer Approximation near Level Crossing
 

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
Born-Oppenheimer Approximation near Level Crossing
A. Gordon and J. E. Avron
Department of Physics, Technion, 32000 Haifa, Israel
(Received 30 November 1999)
We consider the Born-Oppenheimer 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 Born-Oppenheimer (BO) problem
[1] is concerned with the analysis of Schrödinger-type
operators where the small electron-to-nucleon 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 nucleus-to-electron mass ratio. The identification

  

Source: Avron, Joseph - Physics Department, Technion, Israel Institute of Technology

 

Collections: Physics