On the low energy behavior of Regge poles

Hiscox, Aaron Joseph, Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 2010. On the low energy behavior of Regge poles. Journal of Mathematical Physics 51 (10) , 102104. 10.1063/1.3496811

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Abstract

We investigate the behavior of Regge poles in the low energy limit. With the use of small argument asymptotics of the spherical Hankel functions, we show that for a finite square well potential, the associated Regge poles tend to the spectral points of the limiting self-adjoint problem. This is generalized to a compactly supported potential by applying a resolvent argument to the difference of the nonzero and zero energy wavefunctions. Furthermore, by an integral equation method we prove analogous results for a potential such that |(1+r)U(r)| is integrable. This confirms the experimental results which show that Regge poles formed during low energy electron elastic scattering become stable bound states.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	bound states; Hankel transforms; integral equations; molecule-electron collisions; Regge poles; wave functions
Additional Information:	13 pp.
Publisher:	American Institute of Physics
ISSN:	0022-2488
Last Modified:	19 Oct 2022 08:39
URI:	https://orca.cardiff.ac.uk/id/eprint/18608

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