Efimov effect in the distorted cluster state representation

Abstract

The Efimov effect for a three-body system was studied previously in an adiabatic representation, where the distance between two ``heavy'' particles was represented by x, and the third ``light'' particle was described by coordinate y relative to the center of mass of the heavy ones. When x is held fixed, an exact solution for the light particle can be obtained if the interaction is assumed to be of separable form. The resulting adiabatic potential between the heavy particles shows the critical $\ensuremath{-}{1/x}^{2}$ behavior that leads to an infinite number of bound states. However, subsequently the leading nonadiabatic effect was shown to generate an undesirable correction of $1/x$ type, the pseudo-Coulomb disease (PCD). To remedy the PCD, the Efimov effect is reexamined in the adiabatic state representation, but with the new Jacobi coordinates (r,R), where r describes the distance between one of the heavy particles and the light one and R is the position of the other heavy particle with respect to the center of mass of the subsystem of light-heavy particles. It is then shown that the adiabatic potential in this distorted cluster state representation behaves as $\ensuremath{-}{1/R}^{2}$ at large R if the pair described by r has a zero-energy bound state. Moreover, in this case the leading nonadiabatic correction term does not manifest the PCD, thus explicitly showing that the PCD is due to the ``wrong'' choice of coordinates (x,y). Alternatively, a particle boost factor is introduced to eliminate the PCD in the treatment with the original (x,y) coordinates. This is shown to be equivalent to the change in coordinates, described above. Such a factor is usually associated with high energy collisions, but for the first time shown here to play also an important role in near zero-energy situations.