Finite-range model potentials for resonant interactions

Abstract

We show that it is possible to model two-body resonant interactions at low energy with a class of finite-range potentials based on the methods of Jost and Kohn. These potentials are expressed in terms of the effective range $r_0$ and the $s$-wave scattering length $a_s$. We derive continuum solutions of these potentials. By writing $V_{\pm }(r)=V_0(r)+V_{\pm }^{\epsilon }(r)$, where the sign +(-) refers to positive(negative) scattering length, $V_0(r)$ is of the form of Pöschl-Teller potential and $V_{\pm }^{\epsilon }$ is expressed as a power series of the small parameter $\epsilon =(\sqrt{1-2r_0/a_s}{)}^{-1}-1$ when $a_s$ is large, we derive Green function of $V_0(r)$. Using the Green function, solutions of $V_{\pm }(r)$ for $|a_s|>>r_0$ can be obtained numerically by treating $V_{\pm }^{\epsilon }(r)$as a perturbation. We describe the threshold behavior of scattering phase shift for $V_0(r)$. This study may be important for developing a better understanding of physics of strongly interacting ultracold atomic gases with tunable interactions.

15 pages, 2 figures, title changed, new references added. Accepted in Int. J. Mod. Phys. B

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances
• Effective-range approximations for resonant scattering of cold atoms
• A simple model for interactions and corrections to the Gross-Pitaevskii Equation
• A model study on atom-atom interactions with large scattering length in quasi-two dimensional traps

Cited by in corpus (4)

• A model study on a pair of trapped particles interacting with an arbitrary effective range
• Modeling atom-atom interactions at low energy by Jost-Kohn potentials
• Number-phase uncertainty and quantum dynamics of bosons and fermions interacting with a finite range and large scattering length in a double-well potential
• A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential