Modified energy-deposition model, for the computation of the stopping-power ratio for small cavity sizes

Abstract

This paper presents a modification to the Spencer-Attix theory, which allows application of the theory to larger cavity sizes. The modified theory is in better agreement with the actual process of energy deposition by delta rays. In the first part of the paper it is recalled how the Spencer-Attix theory can be derived from basic principles, which allows a physical interpretation of the theory in terms of a function describing the space and direction average of the deposited energy. A realistic model for the computation of this function is described and the resulting expression for the stopping-power ratio is calculated. For the comparison between the Spencer-Attix theory and this modified expression a correction factor to the "Bragg-Gray inhomogeneous term" has been defined. This factor has been computed as a function of cavity size for different source energies and mean excitation energies; thus, general properties of this factor have been elucidated. The computations have been extended to include the density effect. It has been shown that the computation of the inhomogeneous term can be performed for any expression describing the energy loss per unit distance of the electrons as a function of their energy. Thus an expression has been calculated which is in agreement with a quadratic range-energy relationship. In conclusion, the concrete procedure for computing the stopping-power ratio is reviewed.