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Published February 15, 1970 | Published
Journal Article Open

Some Comments on the Jin-Martin Lower Bound

Abstract

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.

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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Created:
August 19, 2023
Modified:
October 18, 2023