Geodesic
On the four-body problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 2, pp. 223-236 
R. I. Jibuti; N. B. Krupennikova; N. I. Shubitidze. On the four-body problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 2, pp. 223-236. http://geodesic.mathdoc.fr/item/TMF_1977_32_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The four-body problem is considered using the hyperspherical basis in the momentum representation. The calculation scheme is suggested for the discrete as well as for the continuous spectrum of the four-body system with two-body potentials of arbitrary form. Recurrence relations for hyperspherical functions in the nine-dimensional space and for the coefficients of the unitary transformation of hyperspherical functions from one set of the Jacobi coordinates to another one are obtained.

[1] O. A. Yakubovskii, YaF, 5 (1967), 1312

[2] L. D. Faddeev, Proc. of the First Intern. Conf. on the Three Body Problem, North. Holland, Amsterdam, 1970, 154

[3] V. F. Kharchenko, V. E. Kuzmichev, YaF, 20 (1974), 334

[4] Y. Avishai, Phys. Rev., C6 (1972), 677

[5] I. M. Narodetskii, O. A. Yakubovskii, YaF, 14 (1971), 315; И. М. Народецкий, ЯФ, 19 (1974), 552

[6] A. M. Badalyan, E. S. Galpern, V. I. Lyakhovitskii, V. V. Pustovalov, Yu. A. Simonov, E. L. Surkov, YaF, 6 (1967), 473; M. Fabre de la Ripelle, Proceedings of the International School on Nuclear Theory Physics, Predeal, 1969

[7] R. M. Mendez-Moreno, Ann. Phys., 88 (1974), 397 | DOI

[8] R. I. Dzhibuti, N. B. Krupennikova, V. Yu. Tomchinskii, YaF, 23 (1976), 539

[9] R. I. Jibuti, N. B. Krupennikova, V. Yu. Tomchinsky, Nucl. Phys., A276 (1977), 421 | DOI

[10] R. I. Dzhibuti, V. Yu. Tomchinskii, N. I. Shubitidze, YaF, 18 (1973), 1164 | MR

[11] J. Raynal, J. Revai, Nuovo Cim., A68 (1970), 612 | DOI | MR

[12] R. I. Dzhibuti, N. I. Shubitidze, YaF, 20 (1974), 666 | MR

[13] H. A. Jahn, Proc. Roy. Soc., 205 (1951), 192 | DOI | Zbl

[14] R. I. Dzhibuti, N. B. Krupennikova, V. Yu. Tomchinskii, Soobsch. AN GSSR, 81 (1976), 69 | MR | Zbl