Summary
The study of the energy dependence of scattering and reaction cross sections near thresholds is performed by a method which has its basis in the construction of the effective potentials in every single channel. The formalism employed presents some advantage with respect to other kind of approaches in that it gives a simple physical description of the anomaly (cusp or rounded step) which appears in the scattering cross section at the opening up of a new channel. Furthermore, with this method it is effectively possible to give an explanation why the energy derivative of the scattering cross section is infinite when the threshold is approached from below. The effect is found to be purely quantum mechanical.
Riassunto
Questo lavoro presenta un nuovo metodo per lo studio delle anomalie che appaiono nelle sezioni d’urto di scattering e di reazione alla soglia per la produzione di un nuovo canale. Con tale metodo è possibile effettivamente dare una spiegazione del perchè la derivata rispetto all’energia della sezione d’urto di scattering è infinita quando la soglia è raggiunta come processo limite per energie minori dell’energia di soglia. L’effetto è puramente quanto-meccanico.
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References
E. P. Wigner:Phys. Rev.,73, 1002 (1948).
A. I. Baz:Journ. Exp. Theor. Phys.,6, 709 (1958).
G. Breit:Phys. Rev.,107, 1612 (1957).
R. G. Newton:Ann. Phys.,4, 29 (1958) andPhys. Rev. (in press).
R. K. Adair:Phys. Rev.,111, 632 (1958).
L. Fonda andR. G. Newton:Ann. Phys. (in press).
L. Fonda andR. G. Newton: AKproduction near the Σ threshold, Washington Meeting of the Amer. Phys. Soc., April 1959 (to be published).
P. A. M. Dirac:Quantum Mechanics, 1st ed. (Oxford, 1930), p. 193.
M. Cini andS. Fubini:Nuovo Cimento,2, 75 (1955).
H. Feshbach:Ann. Phys.,5, 357 (1958).
The simplest justification to the rule (4.2) one could find in the literature, is that given byNewton (see ref.(4)). As a matter of fact, other people seem not to realize that the reason, just like that stated here, why (4.2) should be valid is extremely simple.
G. Breit andE. P. Wigner:Phys. Rev.,49, 519, 642 (1936).
R. G. Newton:Phys. Rev.,101, 1588 (1956).
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Work supported by the National Science Foundation.
On leave of absence from Trieste University on a Fulbright traveling grant.
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Fonda, L. Effective potential approach to the threshold behaviour of cross sections. Nuovo Cim 13, 956–968 (1959). https://doi.org/10.1007/BF02724823
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DOI: https://doi.org/10.1007/BF02724823