Geodesic
Analog of the Watson transformation for angular variables and scattering on the potential $a/r^2$
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 223-231 
Yu. N. Demkov; V. N. Ostrovskii. Analog of the Watson transformation for angular variables and scattering on the potential $a/r^2$. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 223-231. http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a6/
@article{TMF_1980_42_2_a6,
     author = {Yu. N. Demkov and V. N. Ostrovskii},
     title = {Analog of~the {Watson} transformation for angular variables and scattering on~the potential $a/r^2$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {223--231},
     year = {1980},
     volume = {42},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a6/}
}
TY  - JOUR
AU  - Yu. N. Demkov
AU  - V. N. Ostrovskii
TI  - Analog of the Watson transformation for angular variables and scattering on the potential $a/r^2$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 223
EP  - 231
VL  - 42
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a6/
LA  - ru
ID  - TMF_1980_42_2_a6
ER  - 
%0 Journal Article
%A Yu. N. Demkov
%A V. N. Ostrovskii
%T Analog of the Watson transformation for angular variables and scattering on the potential $a/r^2$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 223-231
%V 42
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a6/
%G ru
%F TMF_1980_42_2_a6

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

A new representation for the angle-dependent amplitude of scattering on the spherically symmetrical potential is introduced which is complementary to the Watson complex angular momentum representation and includes the integration over the complex scattering angle. The representation proposed is particularly suitable for studying the problems related to the quasiclassical limit. The properties of the representation are illustrated by the example of scattering on the potential proportional to the inverse square of the distance. The role of orbiting and complex paths is discussed and a new closed formula for the amplitude in the eikonal approximation is derived. This formula is obtained also by means of approximate summing up the series over partial waves.

[1] R. Nyuton, Teoriya rasseyaniya voln i chastits, «Mir», 1969 | MR

[2] V. N. Ostrovskii, ZhETF, 73 (1977), 2077 | MR

[3] G. Tiktopulos, Phys. Rev., 138 (1965), B1150

[4] J. N. Das, N. Datta, Canad. J. Phys., 54 (1976), 2346 | DOI

[5] J. C. Chen, J. L. Magee, Proc. Phys. Soc., A270 (1962), 18

[6] G. V. Golubkov, F. I. Dalidchik, G. K. Ivanov, ZhETF, 71 (1976), 1299

[7] B. P. Kaulakis, L. P. Presnyakov, Kratkie soobscheniya po fizike, 1977, no. 5, 3

[8] A. M. Perelomov, V. S. Popov, TMF, 4 (1970), 48

[9] M. J. Englefield, Proc. Phys. Soc., 83 (1964), 519 | DOI

[10] H. Narnhofer, Acta Phys. Austr., 40 (1974), 306 | MR

[11] B. Kayser, Amer. J. Phys., 42 (1974), 960 | DOI

[12] H. J. Korsch, Phys. Rev., A14 (1976), 1645 | DOI

[13] H. J. Korsch, D. Lessing, J. Phys., B9 (1976), 1857

[14] E. Nelson, J. Math. Phys., 5 (1964), 332 | DOI | MR | Zbl

[15] N. Mott, G. Messi, Teoriya atomnykh stolknovenii, «Mir», 1969

[16] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, «Nauka», 1971 | MR

[17] R. J. Gordon, J. Chem. Phys., 63 (1975), 3109 | DOI

[18] G. E. Zahr, W. H. Miller, Mol. Phys., 30 (1975), 951 | DOI | MR

[19] G. N. Vatson, Teoriya besselevykh funktsii, IL, 1949

[20] Yu. N. Demkov, V. N. Ostrovsky, IX International Conference on the Physics of Electronic and Atomic Collisions, Abstracts of Papers, Seattle, 1975, 656

[21] I. I. Goldman, V. D. Krivchenkov, Sbornik zadach po kvantovoi mekhanike, GITTL, 1957