Regarding neutron-nucleus interaction, so far we dealt with elastic collision for isotropic and anisotropic scatterings. In this problem, we want to find E’/E for an inelastic scattering in which the...

Regarding neutron-nucleus interaction, so far we dealt with elastic collision for isotropic and anisotropic scatterings. In this problem, we want to find
E’/E
for an inelastic scattering in which the target nucleus absorbs an amount of energy
. Use the energy equation, which now accounts for
 and the velocity diagram of Problem 12 to show that:

Problem 12

The collision in Problems 8 and 9 is described from the point of view of a stationary observer, referred to as the laboratory (LAB) system. Now, consider a case were the observer is instead located at the center of momentum of the neutron and nucleus, referred to as the center of momentum (COM) system. In this case the total momentum before and after the collision is zero. Show that the velocity of the center of momentum (which for non-relativistic events is the same as the center of mass) for the stationary nucleus is given by
V_COM

=
V_n,LAB
/(A
+ 1) where
V_n,LAB

is the neutron velocity in the LAB system before collision. Also show that
V_n,COM

=
A
V_n,LAB
/(A
+ 1) and
V_N,COM

= –
V_n,LAB
/(A
+ 1) where
V_N,COM

is the velocity of the nucleus before the collision in the COM system.

Problems 8

Collision between neutrons and nucleus of the moderator results in slowing down the newly born fast neutrons. Such a collision is depicted in the figure. The striking fast neutron has an initial energy
E_n

and an initial momentum
p_n
. The target nucleus is initially at rest. Considering an elastic scattering, following the collision, the scattered neutron has an energy of
E'
_n

and momentum of
p'
_n

while the recoiling nucleus has an energy of
E'
_N

and momentum of
p'
_N
. Use the conservation of momentum and energy to drive a relation for energy of the scattered neutron in terms of the initial neutron energy and mass number of the target nucleus. [Hint: Find the momentum of the recoiling nucleus in terms of the momentum of the initial and the scattered neutron. Substitute for momentum terms
(p
²
= 2mE) and for the recoiling energy from the energy balance].

Problems 9

The energy of the scattered neutron following an elastic scattering between the neutron and the target atom is given as (note that the molecular mass of the nucleus,
M
divided by the mass of neutron,
m
is
M/m
=
A):

Find the minimum energy of the scattered neutron following a collision with the atom of C-12. The striking neutron has an initial energy of 5 MeV.