High energy scattering off of an attractive potential can be handled by the WKB approximation.

tex2html_wrap128 goes to tex2html_wrap129 in the limit of large r. tex2html_wrap130 .

apply WKB to U(r)= tex2html_wrap131 for the S-wave

Then tex2html_wrap132 tex2html_wrap133 This means tex2html_wrap134 In the limit of high energy, tex2html_wrap135 for V tex2html_wrap136 0, you get tex2html_wrap137 tex2html_wrap138 0 = a phase advance.

time delay is tex2html_wrap139 where v is the velocity.

Also works for repulsive potentials as long as the energy is sufficiently large.

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