Consider the scattering of a particle by an impenetrable sphere

(a) Derive an expression for the s-wave (l = 0) phase shift. (You nee not know the detailed properties of the spherical Bessel functions to be able to do this simple problem!)

(b) What is the total cross section ? [? = f] (d?/d?) d?] in the extreme low-energy limit k ? 0? Compare your answer with the geometric cross section ?a2. You may assume without proof:

Transcribed Image Text:

/a'x fa*x*V{r)V(r%$in'k ix - x1 k?/x-x1? 77