Accurate determination of dose-point-kernel functions close to the origin using Monte Carlo simulations

Dose-point-kernel (DPK) functions are used extensively for the dosimetry of gamma and beta emitters in many physical problems. These functions are usually obtained from Monte Carlo simulations where the energy deposited in concentric spherical shells around a point source is tallied. The energy scored in a spherical shell divided by the shell mass is taken as the dose at some effective radius R(eff) of the shell. The effective radius R(eff), defined as the distance of a hypothetical zero-thickness scoring region from the source, can be evaluated in different ways for a finite thickness scoring region. For a shell thickness that is very small compared to the distance from the origin, this exact evaluation method becomes unimportant and the arithmetic mean is usually an accurate estimator for R(eff). However, accurately determining R(eff) can be problematic for the innermost regions when the radial dose function D(r) varies considerably over the finite spherical shell thickness. In this work, a new method for determining R(eff) is introduced which yields consistent results for any shell thickness, thus improving on previous Monte Carlo calculations for DPKs at or near the origin. Dimensionless DPK functions for monoenergetic electrons were reevaluated using EGSnrc with an emphasis on accuracy and consistency near the origin using our new method for determining R(eff). These improved functions were implemented in a software code to calculate the DPKs for an exhaustive list of 546 beta emitters, thus extending the compilation from previous works.