Module forward_scatter 

Neutrons scattered once in a slab sample that leave through its back face.

A neutron of energy E enters a slab of optical depth D(E) at normal incidence. It scatters elastically at depth fraction s with probability D_s·e^(−D(E)·s)·ds, D_s the elastic optical depth, isotropically in the centre-of-mass frame of a nucleus of mass ratio A. At centre-of-mass cosine c it leaves with energy E' along lab cosine μ,

E' = E·(A² + 2Ac + 1)/(A + 1)²,   μ = (1 + Ac)/√(A² + 2Ac + 1),

and crosses the rest of the slab with transmission e^(−D(E')·(1 − s)/μ). The share of incident neutrons that scatter once and leave through the back face, c > c₀ = max(−1/A, −1), is D_s·G(E):

G(E) = ½ ∫ g(D(E), D(E')/μ) dc  over c₀ < c < 1,
g(a, b) = ∫₀¹ e^(−a·s − b·(1 − s)) ds = (e^(−b) − e^(−a))/(a − b).

On a grid, D(E') is linear in E' between grid energies and equal to the value at the lowest grid energy below it.

Structs

ForwardYield

G on a grid, with its slopes in the optical depths.

Enums

ForwardYieldError

Why forward_yield refuses its inputs.

Functions

forward_yield

ForwardYield at grid energies energies_ev, descending, with optical depths depth and mass ratio awr.

lowest_exit_ratio

The lowest E'/E of a neutron scattered once that leaves through the back face of a slab of nuclei of mass ratio awr, at c = c₀: (A − 1)/(A + 1) for A above 1, ((1 − A)/(1 + A))² otherwise.

slab_escape

g(a, b), ∂g/∂a and ∂g/∂b for optical depths a, b of 0 or more.