Module straggling 

Electronic energy-loss straggling.

Bohr (1948), Mat. Fys. Medd. Dan. Vid. Selsk. 18 (8): for a thick-target free-electron estimate the variance of the energy loss per unit areal density is

Ω_B² = 4π z² Z2 (e²/(4π ε0))² (J² m² per target atom),

independent of energy in the non-relativistic regime. A relativistic factor (1 − β²/2) / (1 − β²) (Bethe and Livingston 1937; Fano 1963) is included in StragglingModel::BohrRelativistic.

Not implemented

The Chu and Yang-O’Connor-Wang corrections, which reduce Bohr’s value at intermediate energies, are published as Hartree-Fock-Slater tables and as fits to data (declined, see docs/stopping-models.md), and the Lindhard- Scharff low-velocity correction was not verified against the original. They are omitted. Bohr is therefore an upper-end estimate below about 1 MeV/u; see docs/stopping-models.md.

Enums

StragglingModel

Straggling model choice.

Functions

variance_per_atom

Energy-loss variance per target atom of element target_z, J² m².

variance_per_atom_material

Bragg-additive variance per average atom of a material, J² m² (Σ_j x_j Ω_j²).