Geodesic
Some aspects of the scattering problem for the system of three charged particles
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 65-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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The influence aspects of the spectral vicinity accumulation point of pair subsystem bound energies on the Hamiltonian continuous spectrum eigenfunctions structure of three charged particles system is discussed. The cumulative contribution of pair highly excited states is separated in the coordinate asymptotics of these functions. 
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A. M. Budylin; Ya. U. Koptelov; S. B. Levin. Some aspects of the scattering problem for the system of three charged particles. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 47, Tome 461 (2017), pp. 65-94. http://geodesic.mathdoc.fr/item/ZNSL_2017_461_a3/

[1] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “O difraktsionnom kharaktere rasseyaniya v kvantovoi sisteme trekh odnomernykh chastits”, Probl. Mat. Fiz., 9, Leningrad. Univ., 1979, 14–30

[2] V. S. Buslaev, S. P. Merkurev, S. P. Salikov, “Opisanie parnykh potentsialov, dlya kotorykh rasseyanie v sisteme trekh odnomernykh chastits svobodno ot difraktsionnykh effektov”, Zap. nauchn. semin. LOMI, 84, 1979, 16–22 | MR | Zbl

[3] V. S. Buslaev, S. B. Levin, “Asymptotic Behavior of the Eigenfunctions of the Many-particle Shrödinger Operator. I. One-dimentional Particles”, Amer. Math. Soc. Transl., 225 (2008), 55–71 | MR | Zbl

[4] V. S. Buslaev, S. B. Levin, “Asimptoticheskoe povedenie sobstvennykh funktsii trekhchastichnogo operatora Shredingera. II Odnomernye zaryazhennye chastitsy”, Algebra i analiz, 22:3 (2010), 60–79 | MR | Zbl

[5] V. S. Buslaev, S. B. Levin, “Sistema trekh trekhmernykh zaryazhennykh kvantovykh chastits: asimptoticheskoe povedenie sobstvennykh funktsii nepreryvnogo spektra na beskonechnosti”, Funk. analiz prilozh., 46:2 (2012), 83–88 | DOI | MR | Zbl

[6] Ya. Yu. Koptelov, S. B. Levin, “Ob asimptotike zadachi rasseyaniya neskolkikh zaryazhennykh kvantovykh chastits s ottalkivatelnymi parnymi potentsialami”, Yadernaya fizika, 77:4 (2014), 557–565 | DOI

[7] A. M. Budylin, Ya. Yu. Koptelov, S. B. Levin, “On continuous spectrum eigenfunctions asymptotics of three three-dimensional unlike-charged quantum particles scattering problem”, Days on Diffraction, Proceedings of the International Conference, 2016, 89–94

[8] S. B. Levin, “Ob asimptoticheskom povedenii sobstvennykh funktsii nepreryvnogo spektra na beskonechnosti dlya sistemy trekh trekhmernykh odnoimenno zaryazhennykh kvantovykh chastits”, Zap. Nauchn. Sem. POMI, 451, 2016, 79–115 | MR

[9] E. O. Alt, A. M. Mukhamedzhanov, “Asymptotic solution of the Schroedinger equation for three charged particles”, JETP Lett., 56:9 (1992), 435–438 | MR

[10] E. O. Alt, A. M. Mukhamedzhanov, “Asymptotic solution of the Schroedinger equation for three charged particles”, Phys. Rev. A, 47:3 (1993), 2004–2022 | DOI | MR

[11] M. Brauner, J. S. Briggs, H. Klar, “Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons”, J. Phys. B, 22 (1989), 2265–2287 | DOI

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

[13] G. Garibotti, J. E. Miraglia, “Ionization and electron capture to the continuum in the $H+$-hydrogen-atom collision”, Phys. Rev. A, 21 (1980), 572–580 | DOI

[14] A. L. Godunov, Sh. D. Kunikeev, V. N. Mileev, V. S. Senashenko, Proc. 13th Int. Conf. on Physics of electronic and atomic collisions, Abstracts (Berlin), ed. J. Eichler, Noth-Holland, Amsterdam, 1983, 380 pp.

[15] L. D. Faddeev, Mathematical aspects of the three-body problem of the quantum scattering theory, Daniel Davey and Co., Inc., Jerusalem, 1965 | MR

[16] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Moskva, 1963 | MR

[17] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 3, Kvantovaya Mekhanika, Nauka, Moskva, 1989

[18] N. Mak-Lakhlan, Teoriya i prilozheniya funktsii Mate, IL, M., 1953

[19] F. Tricomi, “Sul comportamento asintotico dei polinomi di Laguerre”, Ann. Mat. Pura Appl., 28:4 (1949), 263–289 | DOI | MR | Zbl

[20] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Moskva, 1959 | MR