A theoretical re-examination of Spencer-Attix cavity theory

The aim of radiation dosimetry is to evaluate, under specific conditions, absorbed dose in a medium of interest using a detection device. In comparison to what is meant to be evaluated, the distinctive composition of the detector causes particle fluence perturbation and shifted absorbed-dose response, both effects depending on beam quality. For electron and megavoltage photon beams, Spencer-Attix cavity theory further adapted by Nahum remains the accepted standard method used to convert absorbed dose in a wall-less detector to absorbed dose in the medium of interest. For several decades, the approach has been widely used in protocols to generate data for ionization chamber dosimetry. As a considerable effort was made towards accurate Monte Carlo methods, computation techniques are nowadays available to determine absorbed dose accurately in complex geometries, including radiation detectors. In the development of nonstandard beam protocols, direct Monte Carlo dose calculations using realistic models are being suggested and used to generate data for ionization chamber dosimetry. This indicates that for a general dosimetric context, including nonstandard beams, a more general cavity theory in agreement with what is currently being done could be adopted. Not only this could be of interest in the dosimetry standards community, but also for educational purposes. This paper re-examines Spencer-Attix theory from first principles, using a new general cavity theory rigorously derived from radiation transport equations. The approach is based on the same schematization as for Spencer-Attix's (i.e. groups of slow and fast electrons) and yields a general expression of absorbed dose for suitably implemented Monte Carlo methods. The Spencer-Attix-Nahum formulation is shown to be a special case of the presented model, outlining specific issues of the standard method. By providing an expression of absorbed dose which reflects the gold standard calculation method (i.e. Monte Carlo), the proposed theory could be adopted by the radiation dosimetry community.