Question

Neutron interactions

[5 marks] Calcu late the m aximum energy transfer of a 2 MeV neutron via an elastic scatterin g collision with 1 H and 12 C nucle i, respectively.

[5 marks] Calculate the number of collisions to slow the 2 MeV neutron down to the thermal energy (0.025 eV) with the 1 H and 12 C moderators, respectively .

[4 marks] Discuss the efficiency of the processes that slow down the neutron using the results obtained in (b).

Answer 1

with an elastic collision

₁ and ₂ are the velocities before collision and  '₁ and '₂ are velocities after collision

'₁ = (m₁ - m₂)/(m₁ + m₂) ₁ + 2m₂/(m₁ + m₂) ₂ and

'₂ = -(m₁ - m₂)/(m₁ + m₂) ₂ + 2m₁/(m₁ + m₂) ₁  

m₁ and m₂ are mass of the two objects

   a. in case of collision between neutron and H-1 nucleus , we can ignore the small mass difference between the proton and neutron and consider as m₁ = m₂

The H-1 nucleus is at rest i.e. ₂ =0 from the above eq. of collision

'₁ =0 and '₂ = ₁

entire energy of the neutron is transfered to the H-1 nucleus and the incoming neutron comes to rest.

max. energy transfer = 2Mev

with C-12 nucleus m₂ = 12 m₁ and ₂ =0

'₂ = 2/13 ₁

C-12 energy = 1/2* m₂'₂² =  1/2 *12 m₁ *(2₁/13)² =

= 48/169 * 1/2*m₁₁²

= 48/169* 2 Mev = 0.568 Mev

with H-1 nucleus the neutron is thermalised to 0.025 ev just in one collision

with C-12 nucleus in each collision 48/169 of the neutron energy is transferred

after each collision energy of the neutron = 121/169

final energy E_f = 0.025 ev = E_i * (121/169)ⁿ  

n is the number of collisions required to thermalise the neutrons

2.0E+6*(121/169)ⁿ   = 0.025

n= 54.47

With C-12 it takes typically 55 collisions to thermalise 2.0 Mev neutrons.

H-1 is a very efficient moderator to themalise the neutrons and C-12 is very poor moderator compared to H-1. To thermalise the neutrons it takes much larger volume of C-12 compared to H-1