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.

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