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
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.
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