Asymptotic Behavior of Schrödinger Scattering Amplitudes

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Abstract
The behavior of the S‐wave scattering amplitude for large k is studied for potentials which vanish at infinity faster than any exponential, but are not cut off. The asymptotic behavior is very sensitive to the shape of the potential tail. If the potential decreases very rapidly, the growth of the Jost function resembles that with a cut‐off potential. If V(r) decreases only slightly more rapidly than an exponential, then f(k) exhibits a very rapid growth in the vicinity of the positive imaginary axis. In this case also the zeros of f(k) become very dense and are concentrated near the positive imaginary axis.

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