Back to Search
Start Over
Low-energy scattering parameters: A theoretical derivation of the effective range and scattering length for arbitrary angular momentum
- Source :
- American Journal of Physics 91, 90 (2023)
- Publication Year :
- 2023
-
Abstract
- The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the effective range for any angular momentum, as long as the Wigner threshold law holds. Using that formalism, we obtain a set of useful formulas for the angular-momentum scattering parameters of four different model potentials: hard-sphere, soft-sphere, spherical well, and well-barrier potentials. The behavior of the scattering parameters close to Feshbach resonances is also analyzed. Our derivations can be useful as hands-on activities for learning scattering theory.<br />Comment: Main document with two supplementary materials
- Subjects :
- Quantum Physics
Condensed Matter - Quantum Gases
Subjects
Details
- Database :
- arXiv
- Journal :
- American Journal of Physics 91, 90 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2302.08331
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1119/5.0079744