Nonadiabatic corrections to the adiabatic Efimov potential

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 , 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 , 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.