Geodesic
Coulomb problem with short-range interaction: Exactly solvable model
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 238-249 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
     year = {1985},
     volume = {65},
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     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/

[1] Kudryavtsev A. E., Popov V. S., Pisma v ZhETF, 29:5 (1979), 311–316

[2] Popov V. S., Kudryavtsev A. E., Mur V. D., ZhETF, 77:5(11) (1979), 1727–1750

[3] Popov V. S., Kudryavtsev A. E., Lisin V. I., Mur V. D., ZhETF, 80:4 (1981), 1271–1287 | MR

[4] Mur V. D., Kudryavtsev A. E., Popov V. S., Preprint ITEF-1980, ITEF, M., 1980; ЯФ, 37:6 (1983), 1417–1428 | MR

[5] Kudryavtsev A. E., Markushin V. E., Shapiro I. S., ZhETF, 74:2 (1978), 432–444

[6] Shapiro I. S., Phys. Rep., 35:2 (1978), 129–185 | DOI

[7] Kudryavtsev A. E., Lisin V. I., Popov V. S., Pisma v ZhETF, 34:5 (1981), 292–296 | MR

[8] Kudryavtsev A. E., Mur V. D., Popov V. S., Pisma v ZhETF, 37:8 (1983), 412–414; Phys. Lett., B95:1 (1980), 137

[9] Badalyan A. M., Kok L. P., Polikarpov M. I., Simonov Yu. A., Phys. Rep., 82:2 (1982), 31–177 | DOI | MR

[10] Popov V. S., Kudryavtsev A. E., Lisin V. I., Mur V. D., Pisma v ZhETF, 36:6 (1982), 207–210 | MR

[11] Zeldovich Ya. B., FTT, 1:11 (1959), 1637–1641

[12] Karnakov B. M., Mur V. D., Popov V. S., DAN SSSR, 279:2 (1984), 345–349

[13] Bethe H. A., Phys. Rev., 76:1 (1949), 38–50 | DOI | Zbl

[14] Trueman T. L., Nucl. Phys., 26:1 (1961), 57–67 | DOI | MR

[15] Lambert E., Helv. Phys. Acta, 42:4 (1969), 667–677

[16] Kirzhnits D. A., ZhETF, 49:5(11) (1965), 1544–1555 | Zbl

[17] Kirzhnits D. A., Penkov F. I., ZhETF, 82:3 (1982), 657–669 | MR

[18] Andreev S. P., Karnakov B. M., Mur V. D., Pisma v ZhETF, 37:3 (1983), 155–157 | MR

[19] Andreev S. P., Karnakov B. M., Mur V. D., TMF, 64:2 (1985), 287–298

[20] Kok L. P., De Maag J. W., Brower H. H., van Haeringen H., Phys. Rev., C26:6 (1982), 2381–2396 | MR

[21] Blinder S. M., Phys. Rev., A18:3 (1978), 853–861 | DOI | MR

[22] Jost R., Pais A., Phys. Rev., 82:6 (1951), 840–851 | DOI | MR | Zbl

[23] Baz A. I., Zeldovich Ya. B., Perelomov A. M., Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, Nauka, M., 1971 | Zbl

[24] Yanke E., Emde F., Lesh F., Spetsialnye funktsii, Nauka, M., 1977

[25] Mur V. D., Popov V. S., TMF, 27:2 (1976), 204–216

[26] Schwinger J., Phys. Rev., 78:2 (1950), 135–139 | DOI | MR | Zbl

[27] Brayan R. A., Phillips R. J. N., Nucl. Phys., B5:2 (1968), 201–219 | DOI

[28] Yamaguchi Y., Phys. Rev., 95:6 (1954), 1628–1643 | DOI | Zbl

[29] Van Haeringen H., Kok L. P., Phys. Lett., A82:7 (1981), 317–320 | MR

[30] Abramovitts M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979, 354–359. | MR