Nonadiabatic corrections to the adiabatic Efimov potential
Yukap Hahn1 - B.G. Giraud2
1 Department of Physics, University of Connecticut, Storrs, CT 06269, USA
2 Service de Physique Theorique, DSM, CE Saclay, F-91191 Gif/Yvette France
Received: 22 August 1997 / Revised version: 3 November 1997 Communicated by P. Schuck
Abstract
Our discussion of the Efimov effect in an adiabatic representation
is completed here by examining the contribution of all the nonadiabatic
corrections. In a previous article by Fonseca et al, the lowest order
adiabatic potential was derived in a model three-body problem, which showed the
critical -1/x2 behavior for large x, where x is the relative distance
of two heavy particles. Such a potential can support an infinite number of bound
states, the Efimov effect. Subsequently, however, we showed that the leading
nonadiabatic correction term < Kx >, where Kx is the heavy particle relative
kinetic energy operator, exhibited an unusually strong 1/x repulsion, thus
nullifying the adiabatic attraction at large values of x. This pseudo-Coulomb disease
(PCD) was speculated to be the consequence of a particular choice of the Jacobi
coordinates, freezing both heavy particles. It is shown here that at large x, the
remaining higher-order correction 
cancels the PCD of < Kx
>, thus restoring the adiabatic potential and the Efimov effect. Furthermore, the
nonadiabatic correction is shown to be at most of order 1/x3. This completes the
discussion of the Efimov effect in the adiabatic representation. Alternatively, a
simple analysis based on the static picture is presented, for comparison with the
adiabatic procedure. The non-static correction is of order -1/x2; this suggests
that the adiabatic picture may be preferred in obtaining the Efimov potential.
PACS
24.10.-i Nuclear-reaction models and methods -
21.10.Re Collective levels -
34.10.+x General theories and models of atomic and molecular collisions and
interactions
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