Neutron Moderation Simulator

Moderator Material

Source & Beam

Neutron energy 2000 keV

Moderator density 1.0×

Neutron population 18

Live Readout

Mean fast energy

— eV

Thermalized

Total collisions

Observed N (avg)

—

ξ (log decrement)

1.000

Theoretical N

—

How it works

A fast neutron born in fission (~2 MeV) loses energy through elastic scattering off moderator nuclei. For a neutron (mass 1) striking a nucleus of mass number A, if the scattering is isotropic in the centre-of-mass frame the outgoing energy depends on the CM scattering angle θ_c:

E' / E = (A² + 2A·cosθc + 1) / (A + 1)²

Averaging −ln(E'/E) over all angles gives the average logarithmic energy decrement ξ, a constant for each material that does not depend on the neutron's current energy:

ξ = 1 + (A−1)²/(2A) · ln[(A−1)/(A+1)]     (ξ = 1 exactly when A = 1)

Because ξ is constant per collision, the number of collisions N needed to slow a neutron from source energy E₀ down to thermal energy E_th ≈ 0.025 eV follows directly:

N = ln(E₀ / E_th) / ξ

Hydrogen (A=1) — a head-on hit can strip almost all the neutron's energy in one collision (ξ=1); only ~18 collisions thermalize a 2 MeV neutron. This is why ordinary (light) water is such an effective moderator.
Deuterium (A=2) — heavy water; a good compromise between energy loss per hit and low neutron absorption.
Carbon (A=12) — graphite; each collision removes far less energy (~114 collisions needed), but graphite absorbs almost no neutrons, so it was used in the earliest reactors.
Lead (A=207) — essentially reflects neutrons with negligible energy loss (~2,150 collisions needed); shown here for contrast, not as a real moderator.

Each bright particle is a neutron; every flash where it meets a lattice nucleus is a real elastic collision sampled from the formula above with a random CM angle. Particles fade from hot orange to cool blue as they slow, and turn into a slow random walk once thermalized — exactly how a real neutron diffuses through a moderator before being absorbed or causing the next fission.

Moderator nuclei Fast neutron Thermalized neutron

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