Geodesic
Bound states near the limit of the lower continuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 2, pp. 204-216 
V. D. Mur; V. S. Popov. Bound states near the limit of the lower continuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 27 (1976) no. 2, pp. 204-216. http://geodesic.mathdoc.fr/item/TMF_1976_27_2_a8/
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     title = {Bound states near the limit of the lower continuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {204--216},
     year = {1976},
     volume = {27},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_27_2_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The effective range approximation is generalized to the case of the Dirac equation. Formulas are obtained that express the parameters in the expansion of the $S$ matrix as $\varepsilon\to -mc^2$ in terms of the wave function of the level at the critical point. These formulas are used to investigate the entry of levels of the discrete spectrum into the lower continuum. The critical charge of the nucleus for muons is calculated (the case $R\gg\hbar/mc$).

[1] V. S. Popov, YaF, 12 (1970), 429

[2] Ya. B. Zeldovich, V. S. Popov, UFN, 105 (1971), 403 | DOI | MR

[3] S. Brodsky, Commun. Atomic Molec. Phys., 4 (1973), 109

[4] L. B. Okun', Commun. Nucl. Part. Phys., 6 (1974), 25

[5] J. Rafelski, B. Müller, W. Greiner, Nucl. Phys., B68 (1974), 585 | DOI

[6] A. B. Migdal, ZhETF, 61 (1971), 2209

[7] A. B. Migdal, Phys. Lett., 52B (1974), 264 | DOI

[8] V. D. Mur, V. S. Popov, TMF, 27 (1976), 81

[9] V. S. Popov, V. D. Mur, YaF, 18 (1973), 684

[10] A. B. Migdal, A. M. Perelomov, V. S. Popov, YaF, 14 (1971), 874

[11] W. Pieper, W. Greiner, Z. Phys., 218 (1969), 327 | DOI

[12] W. Magnus, F. Oberhettinger, R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer-Verlag, Berlin, 1966 | MR

[13] Ya. A. Smorodinskii, DAN SSSR, 60 (1948), 217

[14] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, «Nauka», 1974 | MR