Numerical evaluation of Bragg-Gray cavity integrals by modeling the mass electronic stopping power as a Gaussian function

Abstract

In radiation dosimetry, measuring the dose in a medium can be done by introducing a radiation-sensitive device into a medium composed of a material different from that of the device. Cavity theory is the formalism that relates the absorbed dose in this radiation-sensitive device to the absorbed dose in the surrounding medium. The presence of cavity integrals in this formalism requires evaluation to determine the cavity factor, which is the ratio of the absorbed dose in the medium to the absorbed dose in the detector. In this paper, an evaluation of the cavity integrals in a Bragg-Gray cavity was performed using four different computational methods. The simulation of the cavity was conducted using the Particle and Heavy Ion Transport Code System (PHITS). The stopping power values were obtained from a table provided by NIST on their website. The resulting Gaussian function from the stopping power values was evaluated using MatLab, in which all the numerical methods tested yielded a result of <1% error from the simulated dose of the medium to the detector ratio of PHITS. This proposes a method for calculating the cavity factor without the need of high computational power or Monte Carlo simulations.