Status of the CCC method within the frame of the rigorous many-body Coulomb scattering theory
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 281-287.

Voir la notice de l'article provenant de la source Math-Net.Ru

The convergent close-coupling method (CCC), which is now widely used for calculations of charged particles scattering amplitudes, is considered from the viewpoint of the rigorous many-body Coulomb scattering theory. It is shown that the approximate scattering amplitude calculated within the frame of the method does not converge to a solution of the Lippmann–Schwinger equation.
@article{FPM_2002_8_1_a20,
     author = {V. L. Shablov and V. A. Bilyk and Yu. V. Popov},
     title = {Status of the {CCC} method within the frame of the rigorous many-body {Coulomb} scattering theory},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {281--287},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a20/}
}
TY  - JOUR
AU  - V. L. Shablov
AU  - V. A. Bilyk
AU  - Yu. V. Popov
TI  - Status of the CCC method within the frame of the rigorous many-body Coulomb scattering theory
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 281
EP  - 287
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a20/
LA  - ru
ID  - FPM_2002_8_1_a20
ER  - 
%0 Journal Article
%A V. L. Shablov
%A V. A. Bilyk
%A Yu. V. Popov
%T Status of the CCC method within the frame of the rigorous many-body Coulomb scattering theory
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 281-287
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a20/
%G ru
%F FPM_2002_8_1_a20
V. L. Shablov; V. A. Bilyk; Yu. V. Popov. Status of the CCC method within the frame of the rigorous many-body Coulomb scattering theory. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 281-287. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a20/

[1] Bray I., Stelbovics A. T., “Convergent close-coupling calculations of electron-hydrogen scattering”, Phys. Rev. A, 46:11 (1992), 995–7011 | DOI

[2] Bencze G., Chandler C., “Impossibility of distinguishing between identical particles in quantum collision processes”, Phys. Rev. A, 59:4 (1999), 3129–3132 | DOI | MR

[3] Bray I., “Reply to “Possibility of distinguishing between identical particles in quantum collision processes””, Phys. Rev. A, 59:4 (1999), 3133–3135 | DOI

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

[5] Faddeev L. D., Matematicheskie voprosy kvantovoi teorii rasseyaniya dlya sistemy trekh zaryazhennykh chastits, Trudy Mat. in-ta AN SSSR, 69, 1963 | MR | Zbl

[6] Chandler C., “The Coulomb problem. A selective review”, Nucl. Phys. A, 353 (1981), 129–142 | DOI

[7] Shablov V. L., Bilyk V. A., Popov Yu. V., “Metod rezolventnykh integralnykh uravnenii v zadache o rasseyanii trekh chastits s kulonovskim vzaimodeistviem”, Fund. i prikl. mat., 4:4 (1998), 1207–1224 | MR | Zbl

[8] Shablov V. L., Bilyk V. A., Popov Yu. V., “The momentum representation of the two-body Coulomb Green's function in $n$-dimentional space”, International Conference on Coincidence Spectroscopy, Journal de Physique IV France, 9:no. Pr6 (1999), 59–63

[9] Shablov V. L., Bilyk V. A., Popov Yu. V., “The multichannel Coulomb scattering theory and its applications to $(e,2e)$ reactions”, International Conference on Coincidence Spectroscopy, Journal de Physique IV France, 9:no. Pr6 (1999), 65–69

[10] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 3. Teoriya rasseyaniya, Mir, M., 1983 | MR

[11] Nordsieck A., “Reduction of an integral in the theory of Bremsstrahlung”, Phys. Rev., 93:4 (1954), 785–787 | DOI | MR | Zbl

[12] Fedoryuk M. V., Asimptotika: integraly i ryady, Nauka, M., 1987 | MR

[13] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1977 | MR

[14] Popov Yu. V., “Investigation of a three-charged-particle break-up scattering amplitude”, J. Phys. B, 14 (1981), 2449–2457 | DOI

[15] Popov Yu. V., Bang I., Benayoun J. J., “$A(x,x+y)B$ processes with Coulomb interaction in the final state”, J. Phys. B, 14 (1981), 4637–4647 | DOI