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

goes to in the limit of large r. .

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

Then This means In the limit of high energy, for V 0, you get 0 = a phase advance.

time delay is where v is the velocity.

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

source psfile jl@crush.caltech.edu index WKB