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Taking advantage of the known analytic expression of the eigenfunctions andeigenenergies of the Morse Hamiltonian, explicit expressions are found for thescattering length $a$ and the effective range $r_e$ which determine the s-wavescattering of ultracold atoms. The effects on $a$ and $r_e$ of considering theradial coordinate in the interval $[0,\infty)$ or in the extended region$(-\infty, \infty)$ are studied in detail.

Analytical results for the Morse potential in s-wave ultracold scattering: three dimensional vs. one dimensional problem