On small angle multiple coulomb scattering of protons in the gaussian approximation

Area of Science:

• Physics
• Particle Physics
• Medical Physics

Background:

• Small-angle multiple Coulomb scattering is crucial for understanding particle interactions in materials.
• Existing formulas like Highland's have limitations in accounting for energy loss and precision with certain materials.

Purpose of the Study:

• To develop a more accurate Gaussian approximation for proton scattering angles.
• To create an equation that integrates energy loss in scattering media.
• To improve upon existing formulas for specific material types and scatterer thicknesses.

Main Methods:

• Analysis of experimental literature data on proton scattering.
• Development of a new equation based on the Gaussian approximation.
• Comparison of the new formula with Highland's existing approximation.

Main Results:

• A novel, integrable equation for scattering angle in the Gaussian approximation was derived.
• The new approximation shows improved precision over Highland's formula for thin and thick scatterers of low atomic number elements.
• The derived equation successfully incorporates energy loss within the scattering medium.

Conclusions:

• The developed equation offers a more precise and versatile tool for calculating proton scattering angles.
• This new formula can provide rapid solutions for scattering problems in fields like proton therapy and radiography.
• The findings enhance the predictive capabilities for proton transport in various applications.