2021/10/03 by Evgeny Z. Liverts, Liverts, Evgeny Z.
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Atomic and Molecular Physics #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear Theory (nucl-th) #Optics (physics.optics) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.2110.01977
openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The scattering of two and more particles at low energies is described by the so called effective-range expansion. The leading terms of this expansion are the scattering length and effective range. The analytic expressions for both of the aforementioned scattering parameters are presented for the inverse-power potential and the Woods-Saxon potential. A technique for calculating the approximate scattering parameters is proposed. Approximate analytic formulas representing the scattering length and effective range are obtained for the Yukawa potential. The corresponding figures demonstrate a few interesting features of the effective range. All analytic formulas, both exact and approximate, were verified by comparing with the corresponding results obtained by direct numerical calculations. Wolfram Mathematica is heavily used. The presented results can be used with advantage in the fields of nuclear physics, atomic and molecular physics, quantum chemistry and many others.