Geodesic
Amplitude of scattering at high energies on a singular potential of power type
Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 1, pp. 48-60 
V. A. Gribov. Amplitude of scattering at high energies on a singular potential of power type. Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 1, pp. 48-60. http://geodesic.mathdoc.fr/item/TMF_1976_26_1_a4/
@article{TMF_1976_26_1_a4,
     author = {V. A. Gribov},
     title = {Amplitude of scattering at high energies on a~singular potential of power type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {48--60},
     year = {1976},
     volume = {26},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_26_1_a4/}
}
TY  - JOUR
AU  - V. A. Gribov
TI  - Amplitude of scattering at high energies on a singular potential of power type
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1976
SP  - 48
EP  - 60
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1976_26_1_a4/
LA  - ru
ID  - TMF_1976_26_1_a4
ER  - 
%0 Journal Article
%A V. A. Gribov
%T Amplitude of scattering at high energies on a singular potential of power type
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1976
%P 48-60
%V 26
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1976_26_1_a4/
%G ru
%F TMF_1976_26_1_a4

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

The well-known approximate expressions for the phase shifts $\delta(\lambda,k)$ for the potential $V(r)=g^2r^{-n}$ $(g>0, n>2)$ at high energies are improved by adding to the approximation of small $\lambda$ a certain polynomial in $\lambda$ with subsequent “joining” to the approximation of large $\lambda$. Approximate expressions are obtained for the scattering amplitude $f(\theta, k)$ and the differential cross section $d\sigma/d\theta$ as $k\to\infty$ for different values of $theta$. It is shown that the power potentials are weakly singular in the sense that their singular core, which determines the partial waves with small $\lambda$ and the scattering through large angles, does not influence the total cross section as $k\to\infty$.

[1] R. F. Sawyer, Phys. Rev., 134B (1964), 448 | DOI | MR

[2] V. Sh. Gogokhiya, A. T. Filippov, TMF, 21 (1974), 37 | Zbl

[3] W. M. Frank, D. J. Land, R. M. Spector, Rev. Mod. Phys., 46 (1971), 36 | DOI | MR

[4] A. A. Logunov, A. N. Tavkhelidze, Nuovo Cim., 29 (1963), 380 | DOI | MR

[5] H. H. Aly, H. J. W. Müller, J. Math. Phys., 8 (1967), 367 | DOI

[6] L. Bertocchi, S. Fubini, G. Furlan, Nuovo Cim., 35 (1965), 633 | DOI | MR

[7] R. J. Jabbur, Phys. Rev., 138B (1965), 1525 | DOI | MR

[8] A. Paliov, S. Rosendorff, J. Math. Phys., 8 (1967), 1829 | DOI

[9] F. Kalodzhero, Metod fazovykh funktsii v teorii potentsialnogo rasseyaniya, «Mir», 1972

[10] T. Dolinszky, Nuovo Cim., 22A (1974), 578 | DOI

[11] E. Yanke, F. Emde, F. Lesh, Spetsialnye funktsii, «Nauka», 1968

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

[13] R. M. Spector, J. Math. Phys., 10 (1969), 503 | DOI

[14] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatgiz, 1963