Diffusionsquerschnitt

Diffusionsquerschnitt, in englischsprachigen Texten often called diffusion or transport cross-section, is a cross-section that characterizes how scattering processes influence diffusive transport of particles, such as neutrons, electrons, or photons, in a medium. It focuses on the portion of scattering events that effectively alter the particle’s direction and momentum, thereby driving diffusion rather than simply counting all interactions.

In kinetic and transport theory, the diffusion cross-section is closely related to the transport cross-section. For a differential scattering cross-section dσ/dΩ, the transport cross-section is defined as σ_tr = ∫ (1 − cos θ) (dσ/dΩ) dΩ, where θ is the scattering angle. The macroscopic transport cross-section is Σ_tr = N σ_tr, with N the number density of scattering centers. The diffusion coefficient D is linked to σ_tr (or Σ_tr) through relations such as D ≈ (1/3) v l_tr = v / (3 n σ_tr) for isotropic scattering, where v is particle speed, l_tr = 1/(n σ_tr) is the transport mean free path, and n is the scatterer density.

The term is commonly used in neutron diffusion theory, radiative transport, and charged-particle diffusion in plasmas or semiconductors. It is energy-dependent and sensitive to the anisotropy of scattering: highly forward-peaked scattering can yield a small σ_tr despite a large total cross-section. While sometimes used interchangeably with the transport cross-section, the diffusion cross-section emphasizes the role of scattering in producing diffusive, rather than ballistic, transport.