Nonadiabatic corrections to the adiabatic Efimov potential

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 < K(x)G(Sigma)K(x) > 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(3) 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 nonstatic correction is of order -1/x(2); this suggests that the adiabatic picture may be preferred in obtaining the Efimov potential.