Geodesic
Spurious terms in the three-body problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 253-271 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of hyperharmonics is used to split the central two-body interactions and the Faddeev components of the wave function in a three-body system into physical and spurious terms. The sum of the physical terms of the interactions or of the Faddeev components for all pairs of particles is nonzero, whereas the sums of spurious terms of both the interactions and the Faddeev components over all pairs of particles vanish identically. We establish a criterion for the existence of spurious terms. We show that a sufficient condition for this criterion is equivalent to the conservation law for a certain quantum number. 
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V. V. Pupyshev. Spurious terms in the three-body problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 253-271. http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a4/

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

[2] S. P. Merkurev, L. D. Faddeev, Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR

[3] Gy Bencze, Nucl. Phys. A, 210 (1973), 568 | DOI

[4] E. F. Redish, Nucl. Phys. A, 225 (1974), 16 | DOI

[5] V. I. Kukulin, V. N. Pomerantsev, Ann. Phys., 111 (1978), 333 | DOI | MR

[6] V. I. Kukulin, V. N. Pomerantsev, YaF, 27 (1978), 1668

[7] J. L. Friar, B. F. Gibson, G. L. Payne, Phys. Rev. C, 22 (1980), 284 | DOI | MR

[8] M. Fabre de la Ripelle, S. Y. Larsen, Few-Body Syst., 13 (1992), 199 | DOI

[9] V. V. Pupyshev, EChAYa, 30 (1999), 1562

[10] M. Fabre de la Ripelle, “The hyperspherical expansion method”, Models and Methods in Few-Body Physics, Lect. Notes Phys., 273, eds. L. S. Ferreire, A. C. Fonseca, L. Streit, Springer, Berlin, 1987, 283 | DOI | MR

[11] R. I. Dzhibuti, N. B. Krupennikova, Metod gipersfericheskikh funktsii v kvantovoi mekhanike neskolkikh tel, Metsniereba, Tbilisi, 1984 | MR | Zbl

[12] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavleniya grupp, Nauka, M., 1965 | MR

[13] V. V. Pupyshev, YaF, 62 (1999), 1955

[14] J. Raynal, J. Revai, Nuovo Cimento. A, 68 (1970), 611 | DOI | MR

[15] P. Lankaster, Theory of Matrices, Academic Press, New York–London, 1969 | MR

[16] V. D. Efros, YaF, 15 (1972), 226

[17] Ya. A. Smorodinskii, V. D. Efros, YaF, 17 (1973), 211 | MR

[18] V. V. Pupyshev, TMF, 117 (1996), 501 | DOI | MR

[19] O. F. Nemets, Yu. V. Gofman, Spravochnik po yadernoi fizike, Naukova dumka, Kiev, 1975 | MR | Zbl

[20] B. L. Berman, B. F. Gibson (eds.), The Three-Body Force in the Three-Nucleon System, Lect. Notes Phys., 260, Springer, Berlin, 1986 | DOI

[21] S. Nakaichi-Maeda, E. W. Schmid, Z. Phys. A, 318 (1984), 287 | DOI

[22] E. W. Schmid, S. Nakaichi-Maeda, “Three-body forces in the constituent quark model”, Procced. of the VII International Seminar on Problems in High-Energy Physics, eds. A. I. Titov, E. K. Aksenova, E. V. Ivashkevich, JINR, Dubna, 1984, 429

[23] W. N. Polyzou, W. Glöckle, Few-Body Syst., 9 (1990), 97 | DOI | MR