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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $k\to\infty$. 
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     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},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_26_1_a4/}
}
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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/

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