Journal of Mathematical Physics

Short-Range Interactions and Analyticity in Momentum Transfer

J. D. Finley

Published Nov 1, 1969• 1 citation

Abstract

We investigate possible characterizations of ``short-range'' interactions by means of conditions on the total transition probability ∥Tψ∥2. We desire to require that the total transition probability decrease exponentially as the displacement of the wavepacket ψ increases. It is shown that this can only be done for certain types of sequences of wavepackets, and a criterion is developed for selecting these ``proper'' wavepackets. We then show for all such interactions that what is essentially the square of the scattering amplitude is analytic, in the cosine of the scattering angle, in an ellipse which always includes the physical region. We then compare these results with the Schrödinger potential theory and thereby relate the type of the exponential decrease of a potential to the type of the exponential decrease of the corresponding transition probability. Finally, our results are compared with similar results previously obtained by others working on this problem.

DOI: 10.1063/1.1664801

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