On the main term of the asymptotics of the problem of few charged particles in the presence of bound states
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 59-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper, we obtained the results that generalize the BBK-approximation, well known in the physical literature, in a situation where particles in subsystems can approach each other. The results obtained allow one to describe the asymptotics of a few-body Coulomb system ($N=3.4$) in the case when the subsystem is in a state of continuous spectrum, as well as in the case when the subsystem (two or three particles) is in a bound state.
@article{ZNSL_2023_521_a4,
     author = {A. M. Budylin and S. B. Levin},
     title = {On the main term of the asymptotics of the problem of few charged particles in the presence of bound states},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {59--78},
     year = {2023},
     volume = {521},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a4/}
}
TY  - JOUR
AU  - A. M. Budylin
AU  - S. B. Levin
TI  - On the main term of the asymptotics of the problem of few charged particles in the presence of bound states
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 59
EP  - 78
VL  - 521
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a4/
LA  - ru
ID  - ZNSL_2023_521_a4
ER  - 
%0 Journal Article
%A A. M. Budylin
%A S. B. Levin
%T On the main term of the asymptotics of the problem of few charged particles in the presence of bound states
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 59-78
%V 521
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a4/
%G ru
%F ZNSL_2023_521_a4
A. M. Budylin; S. B. Levin. On the main term of the asymptotics of the problem of few charged particles in the presence of bound states. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 53, Tome 521 (2023), pp. 59-78. http://geodesic.mathdoc.fr/item/ZNSL_2023_521_a4/

[1] M. Brauner, J. S. Briggs, H. Klar, J. Phys. B, 22 (1989), 2265–2287 | DOI

[2] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, San Diego, 1963 | MR

[3] L. D. Faddeev, S. P. Merkuriev, Quantum Scattering Theory for Several Particle Systems, Kluwer, Dordrecht, 1993 | MR | Zbl

[4] G. Garibotti, J. E. Miraglia, Phys. Rev. A, 21 (1980), 572 | DOI

[5] 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

[6] V. S. Buslaev, S. B. Levin, Funct. Analys. Appl., 46:2 (2012), 147–151 | DOI | MR | Zbl

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

[8] 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

[9] S. B. Levin, Ya. Yu. Koptelov, “On asymptotics of the scattering problem solution of $n$ like-charged quantum particles”, Few-Body Systems, 55 (2014), 809–812 | DOI

[10] A. M. Budylin, Ya. Yu. Koptelov, S. B. Levin, “O reaktsii razvala v trekhchastichnykh kulonovskikh sistemakh s prilozheniem k opisaniyu protsessov dissotsiativnoi rekombinatsii i perezaryadki v antiprotonnoi fizike”, ZhETF, 160:9 (2021), 372–392 | DOI

[11] D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskii, Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975

[12] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 3, Kvantovaya Mekhanika, Nauka, M., 1989 | MR

[13] Milton Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, USA, 1964 | MR