Classical analysis gives the differential scattering cross section for a
repulsive 
Coulomb potential to be
where 
is the distance of closest
possible approach of an alpha particle of charge ze=2e, mass M and
traveling at velocity v toward a heavy nucleus of charge Ze. Note
that, unlike the case of scattering from hard spherical reflectors,
the cross section depends on both the velocity of the incoming
particles and the scattering angle. Using the same approach as in
(3.5), answer the following two questions:
A beam of 
-particles, of kinetic energy 5 MeV and intensity
particle/sec, is incident normally on a silver foil of
thickness 
cm. (The density, atomic weight and
atomic number of silver are 10.5 g/cm
, 107.87 and 47
respectively.) An 
particle counter of area 1 cm
is
placed on the opposite side of the foil from the incoming beam at a
distance of 50 cm at an angle of 
from the incoming flux (+
direction). How many counts should we expect per hour if the
detector registers all particles passing through it? How many counts
will there be per hour for back-scattering events 
away from
the direction of incoming flux?