Use the result of Problem 21to find the average fractional energy loss in an elastic scattering collision. The average fractional energy loss is defined as / E . Problem 21 In Problem 13 it is shown...

Use the result of Problem 21to find the average fractional energy loss in an elastic scattering collision. The average fractional energy loss is defined as
/E.

Problem 21

In Problem 13 it is shown that there is a one-to-one relation between the change in neutron energy and the change in the scattering angle. Thus, it can be concluded that
p(E
E’)dE’ = –p(Ω
 Ω’)dΩ’ where
p
is probability and the minus sign reflects the fact that the larger the scattering angle, the lower the energy of the scattered neutron. We represent
p(Ω
 Ω’) = 4

_s
(Ω
Ω’)/

_s

where


_s
(Ω
 Ω’) is the differential scattering cross section and ɭ_Ω’

_s
(Ω
 Ω’)dΩ’ =


_s
. Use this information and find
p(E
E’) for an elastic scattering and isotropic in the COM where


_s
(Ω
 Ω’)=


_s
/4.

Problem 13

Use the diagram showing neutron velocity before and after a collision to conclude that:

where
a
= [(A
– 1)/(A
+ 1)]²
is known as the
collision parameter. Use this relation to:

a) find the angle corresponding to the minimum energy of the emerging neutron (
E′_min
  )

b) find
E′
_min
, the minimum energy of the emerging neutron