Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Reflection Approximation in Photoassociation Spectroscopy



C Boisseau, E Audouard, J Vigue, Paul S. Julienne


We construct an analytical wavefunction in the phase-amplitude formalism to describe collisions between two neutral atoms. This wavefunction is valid from intermediate to asymptotic internuclear distance over a large energy range near zero energy; and is especially suitable for cold and ultracold collisions. We have used this analytic wavefunction with the reflection approximation formula for calculating Franck-Condon factors for photoassociative spectroscopy. Numerical tests show very satisfactory agreement between the resulting analytic formula and the fully quantum numerical results in most cases investigated. Finally, we show in a model case that our analytical wavefunction enables us to relate the scattering length directly to a preasymptotic node in the ground state wavefunction, which in principle could be measured by photoassociative spectroscopy.
Physical Review A (Atomic, Molecular and Optical Physics)


analytic wavefunction, cold atom collisions, Franck-Condon factors, photoassociation spectroscopy, reflection approximation


Boisseau, C. , Audouard, E. , Vigue, J. and Julienne, P. (2000), Reflection Approximation in Photoassociation Spectroscopy, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed July 17, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 31, 2000, Updated October 12, 2021