Improved effective-range expansions for small and large values of scattering length

Abstract

The textbook effective-range expansion of scattering theory is useful in the analysis of low-energy scattering phenomenology when the scattering length |a| is much larger than the range R of the scattering potential: |a| ≫ R. Nevertheless, the same has been used for systems where the scattering length is much smaller than the range of the potential. We suggest and numerically study an effective-range expansion for |a| ≪ R as well as improved twoparameter effective-range expansions for the cases |a| > R and |a| < R. The improved effective-range expansions for |a| > R and |a| < R reduce to the expansions for |a| R ≫ 1 and |a| R ≪ 1, respectively, in appropriate limits.