[Submitted on 17 Oct 2025]
Born series for s-wave scattering length and some exact results
In these notes the Born series for the -wave scattering is calculated for a class of central potentials up to sixth order in a dimensionless coupling strength . Examples of exponentially decaying potentials as well truncated potentials involving a single length-scale are considered. In certain favorable cases the exact result for the -dependent -wave scattering length can be given in terms of special functions. The poles of at increasing positive values of correspond to the thresholds, where -wave bound-states occur successively. A scattering problem, where is solvable in terms of elementary functions, is also presented.
- Comments:
- 14 pages, 12 figures
- Subjects:
- Nuclear Theory (nucl-th); Quantum Physics (quant-ph)
- arXiv:
- 2510.16212 [pdf]