**1**, 383-390

## Nonadiabatic corrections to the adiabatic Efimov potential

**Yukap Hahn ^{1} - B.G. Giraud^{2}**

^{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/*x ^{2}* 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 <

*K*

_{x}>, where

*K*

_{x}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 <

*K*

_{x}>, thus restoring the adiabatic potential and the Efimov effect. Furthermore, the nonadiabatic correction is shown to be at most of order 1/

*x*. 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/

^{3}*x*; this suggests that the adiabatic picture may be preferred in obtaining the Efimov potential.

^{2}**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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