1.1

Using Eq. (1.38) calculate the approximate total cross sections for Rutherford scattering of a 10 MeV ?-particle from a lead nucleus for impact parameters b less than 10 ^?12, 10 ^?10 and 10 ^?8 cm. How well do these agree with the values of ?b ²?

1.2

Prove that Eq. (1.55) follows from the relations in Eqs. (1.53) and (1.54).

1.3

Sketch cos ? _Lab as a function of cos ? _CM for the nonrelativistic elastic scattering of particles of unequal mass, for the cases when ?=0.05 and ?=20 in Eqs. (1.52) and (1.53).

1.4

What would be the approximate counting rate observed in the Rutherford scattering of 10 MeV ?-particles off lead foil at an angle of ?= ?/2 in the laboratory? Assume an incident flux of 10 ⁶ ?-particles per second on the foil, a foil 0.1 cm thick, and a detector of transverse area 1 cm 1 cm placed 100 cm from the interaction point, and density of lead of 11.3 g/cm ³. What would be the counting rate at ?=5 ? By about how much would your answers change if the above angles were specified for the center-of-mass be quantitative, but use approximations where necessary. (Why don t you have to know the area of the foil?)

1.5

Sketch the cross section in the laboratory frame as a function of cos ? _Lab for the...