Neutron Moderation

Neutron Moderation

Fission of U-235 releases fast neutrons with energies around 2 MeV. However, U-235 fissions most efficiently with thermal neutrons at around 0.025 eV (room temperature). A moderator slows neutrons down through elastic collisions.

Average Logarithmic Energy Decrement

Each collision reduces a neutron's energy. The average logarithmic energy loss per collision is:

$\xi = 1 + \frac{(A-1)^2}{2A} \ln\!\left(\frac{A-1}{A+1}\right)$

For hydrogen ($A = 1$): $\xi = 1$ (special case, largest possible energy loss per collision).

Number of Collisions to Thermalise

Starting from $E_0 = 2 \times 10^6$ eV (fast neutron), reaching $E_f = 0.025$ eV (thermal):

$n = \frac{\ln(E_0/E_f)}{\xi}$

Hydrogen requires only ~18 collisions; graphite requires ~115.

Average Energy After One Collision

For a neutron of energy $E$ colliding with a nucleus of mass $A$ (in neutron mass units):

$E_{\text{avg}} = E \cdot \frac{A^2 + 1}{(A + 1)^2}$

Your Task

All constants must be defined inside each function. Use import math for math.log.

• log_energy_decrement(A) — returns $\xi$ for mass number $A$ (return 1.0 for $A = 1$)
• collisions_to_thermalize(A, E0_eV=2e6, Ef_eV=0.025) — number of collisions needed
• energy_after_collision(E, A) — average energy after one elastic collision