Multiplescatter

Multiplescatter, often written as multiple scattering, is the cumulative deflection of a charged particle as it traverses matter due to successive Coulomb interactions with nuclei (and, to a lesser extent, with electrons). Each interaction perturbs the particle’s direction by a small angle; the random sequence of these deflections leads to an overall angular distribution and a net lateral displacement of the particle’s path. In many practical situations the angular distribution near small deflections is well described by a Gaussian, with larger-angle tails described by more complete theories such as Molière theory.

A commonly used estimate for the infrared of the effect is the root-mean-square (RMS) scattering angle, theta0, given approximately by theta0 ≈ (13.6 MeV)/(β p) z sqrt(x/X0) [1 + 0.038 ln(x/X0)], where p is momentum, β = v/c, z is the charge number of the incident particle, x is the material thickness, and X0 is the radiation length of the material. The effect strengthens with higher material thickness and higher Z materials, and weakens for higher-energy particles.

In detector design and analysis, multiple scattering sets a limit on track angular and vertex resolution and must be accounted for in track fitting and momentum estimation, especially in non-magnetic or partial-field environments. It also influences imaging and dosimetry in medical physics, proton therapy, and radiography, where accurate modeling of scatter improves image quality and dose calculations.

Limitations include that the simple Gaussian approximation breaks down for very thin materials or large-angle scatter; more complete descriptions (such as Molière theory) provide better accuracy in those regimes.