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Some Comments on the Jin-Martin Lower Bound

Simon, Barry (1970) Some Comments on the Jin-Martin Lower Bound. Physical Review D, 1 (4). pp. 1240-1241. ISSN 2470-0010.

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We present an extremely simple derivation of the Jin-Martin bound in a slightly weakened form. Explicitly, let f^(AB→AB)(s) be the spin-averaged forward-scattering amplitude for the process AB→AB [normalized by σ_(tot) = 4π(Im f(s))/k√s]. Then we prove that there is a constant C and a sequence s_n→∞ such that either f^(AB→AB)(s_n) > Cs_n^(−2) (all n) or f^(A¯B→A¯B)(s_n)) > Cs_n^(−2) (all n). We also clarify the connection between allowable asymptotic behavior and the sign of the scattering length found by Jin and Martin.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 1970 American Physical Society. (Received 6 October 1969) Research partially sponsored by the U. S. Air Force Once of Scientific Research, under Contract No. AF49(638)1545.
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Air Force Office of Scientific Research (AFOSR)AF49(638)1545
Issue or Number:4
Record Number:CaltechAUTHORS:20180417-154003485
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85925
Deposited By: George Porter
Deposited On:18 Apr 2018 23:15
Last Modified:03 Oct 2019 19:37

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