130_notes.dvi

δ 0 (k) =−kr 0

dσ

dΩ

=

1

k^2

∣

∣

∣eiδℓ(k)sin(δℓ(k))P 0 (cosθ)

∣

∣

∣

2

dσ

dΩ

=

1

k^2

∣∣

e−ikr^0 sin(kr 0 )

∣∣ 2

dσ

dΩ

=

sin^2 (kr 0 )

k^2

For very low energy,kr 0 <<1 and
dσ
dΩ

≈

(kr 0 )^2

k^2

=r^20

The total cross section is thenσ= 4πr^20 which is 4 times the area of the hard sphere.

30.3 Homework Problems

1. Photons from the 3p → 1 stransition are observed coming from the sun. Quantitatively
   compare the natural line width to the widths from Doppler broadening and collision broadening
   expected for radiation from the sun’s surface.

30.4 Sample Test Problems

1. Calculate the differential cross section,ddσΩ, for high energy scattering of particles of momentum
   p, from a spherical shell delta function

V(r) =λδ(r−r 0 )

Assume that the potential is weak so that perturbation theory can be used. Be sure to write

your answer in terms of the scattering angles.

2. Assume that a heavy nucleus attractsK 0 mesons with a weak Yakawa potentialV(r) =Vr^0 e−αr.
   Calculate the differential cross section,dσdΩ, for scattering high energyK 0 mesons (massmK)
   from that nucleus. Give your answer in terms of the scattering angleθ.