We present a theoretical model for investigating the magnetically tuned Feshbach resonance (MTFR) of alkali metal atoms using the separable potential method (SPM). We discuss the relationship and difference between the SPM and the asymptotic bound state model. To demonstrate the validity of the SPM, we use it to calculate the weakly bound state energy and magnetically tuned scattering length for the 6Li–40K, 7Li2, and 6Li2 systems with narrow and broad Feshbach resonances. The results of the SPM calculations are in good agreement with those of coupled channel calculations and with experimental measurements for all three systems. The SPM, by simplifying the calculation of the two-body MTFR, is expected to simplify numerical computations for three-atom collisions in a magnetic field and the Feshbach-optimized photoassociation process.
We study Clary's theory for an electron in the field of a dipolar molecule. We find for a molecule of rotor constant
B and dipole moment $\ensuremath{\mu}$ that Clary's ``rotationally adiabatic'' molecular potential
ϵad(r) behaves like $\ensuremath{-}64{r}^{4}∕3{\ensuremath{\mu}}^{4}$ near
r=0 and like $\ensuremath{-}{\ensuremath{\mu}}^{2}∕6B{r}^{4}$ at infinity. We show, using general results about the spectrum of the Schr\"odinger Hamiltonian, that the salient features of the electron bound states spectrum, i.e., the existence of only a few weakly bound states, are a consequence of these asymptotic formulas. We argue that the long-range
(1∕r4) part of the interaction may be interpreted as resulting from the angle-averaged molecular dipole potential at some rotation temperature. Our results should be contrasted with those of Camblong et al. Phys. Rev. Lett. 87, 220402 (2001), who claim that these features arise from the renormalization of the static point dipole interaction.