https://doi.org/10.1140/epjd/e2010-10498-x
Error cancellation in the semiclassical calculation of the scattering length
1
School of Computing Science, University of Glasgow, Glasgow, G12 8QQ, UK
2
Mediterranean Institute of Fundamental Physics, Via Appia Nuova 31, 00040 Marino, Rome, Italy
Corresponding author: a mjj@dcs.gla.ac.uk
Received:
9
September
2010
Revised:
26
November
2010
Published online:
14
January
2011
We investigate the effects of two approximations concerning
long range dispersion forces that are made in the
derivation of the semiclassical formula
for the scattering length of a pair of neutral atoms. We demonstrate
numerically, using a published model interaction potential for a pair of Cs
atoms in the 
molecular state,
that the subsequent long range errors tend to
cancel and we show, from an approximate analytical relationship,
that the first order errors do indeed largely cancel.
We suggest a hybrid method that combines quantum mechanical
and semiclassical calculations. We explore its use
in finding the scattering lengths of 7Li atoms and
133Cs atoms interacting via the X
and a
molecular potentials and we use it
to demonstrate that the semiclassical formula fails
for cold collisions of
H atoms in the X
molecular state
because of the long range errors rather than because of inadequacies in
describing the motion over the potential well semiclassically.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011
