Geodesic
Coulomb problem with short-range interaction: Exactly solvable model
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 238-249

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The nonrelativistic Coulomb problem with short-range interaction is considered. The strong potential $V_s(r)$ is modeled by a delta-function interaction on a sphere $r=r_0$. Exact solutions to the Schrödinger equation are obtained for states with arbitrary angular momentum $l$ together with explicit analytic expressions for the scattering lengths, effective ranges, etc. Comparison of the exact solutions with the approximate formulas established earlier [1–4] for arbitrary short-range potential $V_s(r)$ makes it possible to determine the limits of applicability of these approximations. 
@article{TMF_1985_65_2_a7,
     author = {V. D. Mur and V. S. Popov},
     title = {Coulomb problem with short-range interaction: {Exactly} solvable model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {238--249},
     publisher = {mathdoc},
     volume = {65},
     number = {2},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a7/}
}
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V. D. Mur; V. S. Popov. Coulomb problem with short-range interaction: Exactly solvable model. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 238-249. http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a7/