On the scattering power of radiotherapy protons

Area of Science:

• Physics
• Radiation Transport
• Medical Physics

Background:

• Accurate scattering power (T) calculations are crucial for charged particle transport simulations.
• Existing formulas often neglect the competition between Gaussian core and single scattering tail, impacting Gaussian width.
• The single scattering correction (SSC) introduces nonlocal dependencies for T(x).

Purpose of the Study:

• To demonstrate that accurate scattering power (T) formulas require accounting for single scattering corrections (SSC).
• To establish that SSC necessitates nonlocal T(x) formulas dependent on prior scattering history.
• To derive an improved differential Molière formula, T(dM), and assess its applicability.

Main Methods:

• Numerical differentiation of Molière/Fano/Hanson (theta2) to determine SSC.
• Simplification of T(IC) for protons, introducing a material-dependent 'scattering length' X(s).
• Development of T(dM) using a nonlocal correction factor fdM based on the Øverås approximation.

Main Results:

• The improved scattering power formula is T(dM) = fdM(pv,p1v1) x (E(s)/pv)^2 / X(s).
• The nonlocal correction factor fdM is material-independent and easily computable.
• T(dM) generalizes readily to mixed material slabs.

Conclusions:

• The necessity of accurate T formulas depends on the specific application, with significant impact in materials like lead.
• Accurate T is vital for precise beam spreading calculations and sensitive to downstream beam characteristics.
• Implementing accurate scattering power calculations is important for general-purpose Monte Carlo codes to ensure reliable results across diverse problems.