Analytical results for the Morse potential in s-wave ultracold   scattering: three dimensional vs. one dimensional problem
  Taking advantage of the known analytic expression of the eigenfunctions and eigenenergies of the Morse Hamiltonian, explicit expressions are found for the scattering length $a$ and the effective range $r_e$ which determine the s-wave scattering of ultracold atoms. The effects on $a$ and $r_e$ of considering the radial coordinate in the interval $[0,\infty)$ or in the extended region $(-\infty, \infty)$ are studied in detail. 
Asaf Paris-Mandoki, Roc\'io J\'auregui
quant-ph physics.atom-ph