Efimov Effect Revisited with Inclusion of Distortions

An elementary proof of the 3-body Efimov effect is provided in the case of a separable 2-body potential which binds at zero energy a light particle to a heavy one. The proof proceeds by two steps, namely {\it i)} a projection of the Hamiltonian in a subspace and the observation that the projected Hamiltonian generates an arbitrarily large number of bound states, and {\it ii)} a use of the Hylleraas-Undheim theorem to recover the unprojected Hamiltonian. The definition of the projectors we use can include mean field distortions.Comment: 17 pages, TeX Email contact= [email protected]

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 , 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 $1/x^3$. 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 non-static correction is of order $-1/x^2$; this suggests that the adiabatic picture may be preferred in obtaining the Efimov potential

Nonlocality of the optical potential and the adiabatic approximation

The nonlocality property of the elastic channel optical potential is studied using a schematic coupled-channel system. It is explicitly shown that, consistent with the usual adiabatic approximation, the nonlocality is reduced as the scattering energy approaches the elastic threshold. The residual nonlocality found in the data may be partly due to the artificial truncation of the channels, and strong indications are found that a more complete treatment which includes a large number of channels would lead to better locality of the optical potential at low energy. For optical potentials corresponding to the inelastic channels, we find that the adiabaticity and the consequent locality is not well satisfied