Distribution of deviation angles: Cylindrical scattering of thermal neutrons

n = 1 – δ

δ = ρλ²ε / 2π

(Where:

ρ = nuclei / volume

λ = wavelength

ε = mean coherent scattering length)

If,

α = angle of incidence

Radius of wire = R

Snell’s law:

cos α = Z / R = z (deviated beam position)

z = n cos β

ν = 2(α – β)

Now,

α is proportional to z

ν is proportional to n, α

With a series of layers of wires, angular distribution of the beam = I(ν)

For R >> ε,

sin (ν/2) = (1 – z²)^1/2 . z / (1 – δ) – z . {1 – z² / (1 – δ)²}^1/2

For small δ and ν,

ν = 2zδ / (1 – z²)^1/2

Thus,

z = ν / (4δ² + ν²)^1/2