13.12. Consider the spherically symmetric potential energy 2u V(r)/h = yo(r - a). where y is a constant and 8(r - a) is a Dirac delta function that vanishes ev- erywhere except on the spherical surface specified by r = a. (a) Show that the S-wave phase shift &, for scattering from this potential satisfies the equation tan ka tan (ka + 80) = 1 + (y/k ) tan ka (b) Evaluate the phase shift in the low-energy limit and show that the total cross section for S-wave scattering is o = 4wal ya + ya