Abstract
We derive an optimal condition for the finiteness of total cross-sections in potential scattering at any given energy, and by copying Froissart’s trick for elementary particles, explicit bounds on amplitudes and cross-sections in the spherically symmetric case. We also study the coupling constant dependence of the cross-sections for potentials of a given sign by using analyticity properties with respect to this coupling constant. This paper contains several new unpublished results.
Lectures given at the XX. Internationale Universitätswochen für Kernphysik, Schladming, Austria, February 17–26, 1981.
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References
W.O. Amrein and D.C. Pearson, J. Phys. A12 (1979) 1469
W. O. Amrein, D. C. Pearson and K. B. Sinha, Scattering Theory in Quantum Mechanics, Reading, Benjamin (1977).
This paper contains references to previous work.
V. Enss and B. Simon, Phys. Rev. Letters 44 (1980) 319 and 764
V. Enss and B. Simon, to appear in Comm. Math. Phys.
V. Enss and B. Simon, preprint to appear in Classical, Semi-Classical and Quantum Mechanical Problems in Mathematics, Chemistry and Physics, editors K. Gustafson and W. P. Reinhardt, Plenum (1980/81).
J.M. Combes and M. Guez, private communication, to be published.
M. Froissart, Phys. Rev. 123 (1961) 1053
A. Martin, Nuovo Cimento 42 (1966) 930.
A. Martin, Lectures at the University of Washington, Seattle (1964), unpublished.
See also A. Martin, Nuovo Cimento 23 (1962) 641
A. Martin, Nuovo Cimento 31 (1964) 1229.
K. Chadan and A. Martin, appendix of Comm. Math. Phys. 70 (1979) 1.
A. Martin, Comm. Math. Phys. 69 (1979) 89;
Notice that in the present lectures we give an improved version in which the total cross-section is bounded by I3/2 for large I, Instead of I2
A. Martin, Comm. Math. Phys. 73(1980) 79.
J.A. Shohat and J.D. Tamarkin, “The Problem of Moments”, American Mathematical Society, New York (1943).
See for instance, A. Martin, Nuovo Cimento 39 (1965) 704
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Martin, A. (1981). Finiteness of Total Cross-Sections. In: Mitter, H., Pittner, L. (eds) New Developments in Mathematical Physics. Acta Physica Austriaca, vol 23/1981. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8642-8_7
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DOI: https://doi.org/10.1007/978-3-7091-8642-8_7
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