Geodesic
Effective-radius approximation in the~problem of two-dimensional scattering by a~central short-range potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 315-337

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We study the role of weakly bound and near-threshold resonance states of a quantum particle in its two-dimensional elastic low-energy scattering. The energies of such states are determined in the effective-radius approximation using the roots of transcendental equations. The same approximation is used to analyze scattering. We obtain and study the explicit low-energy asymptotic forms of all partial phases and cross sections. These asymptotic forms contain energies of weakly bound or near-threshold resonance states.
Keywords: two-dimensional scattering, short-range potential, weakly bound resonance state, near-threshold resonance state. 
@article{TMF_2015_182_2_a7,
     author = {V. V. Pupyshev},
     title = {Effective-radius approximation in the~problem of two-dimensional scattering by a~central short-range potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {315--337},
     publisher = {mathdoc},
     volume = {182},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a7/}
}
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V. V. Pupyshev. Effective-radius approximation in the~problem of two-dimensional scattering by a~central short-range potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 315-337. http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a7/