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Non-Relativistic Dispersion Relations for a Two Channel Scattering Process

Published online by Cambridge University Press:  24 October 2008

J. Underhill
J. Underhill
Affiliation:
Department of Mathematics University of Glasgow
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Extract

In (l) Khuri has proved the validity of a dispersion relation for non-relativistic potential scattering. More precisely, he has shown that if the potential V(r) is central and satisfies: then the scattering amplitude f(k, τ) = M(E, τ) (where E = k2 is the energy) satisfies the following dispersion relation for fixed momentum transfer τ ≤ 2α: In (2), Rj(τ) is the (real) residue of the scattering amplitude at the bound state Ej and is the Fourier transform of the potential .

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 363 - 376
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Khuri, N. NPhys. Rev. 107 (1957), 1148.CrossRefGoogle Scholar
(2)Jost, R. and Pais, A.Phys. Rev. 82 (1951), 840.CrossRefGoogle Scholar
(3)Underhill, J. Thesis, University of London, 1960 (unpublished).Google Scholar
(4)Caratheodory, C.Theory of functions, vol. 2 (Chelsea; New York, 1954).Google Scholar