Improvement of the equivalent sphere model for better estimates of skin or eye dose in space radiation environments

It is often useful to get a quick estimate of the dose or dose equivalent of an organ, such as blood-forming organs, the eye or the skin, in a radiation field. Sometimes an equivalent sphere is used to represent the organ for this purpose. For space radiation environments, recently it has been shown that the equivalent sphere model does not work for the eye or the skin in solar particle event environments. In this study, we improve the representation of the eye and the skin using a two-component equivalent sphere model. Motivated by the two-peak structure of the body organ shielding distribution for the eye and the skin, we use an equivalent sphere with two radius parameters, for example a partial spherical shell of a smaller thickness over a proper fraction of the full solid angle combined with a concentric partial spherical shell of a larger thickness over the rest of the full solid angle, to represent the eye or the skin. We find that using an equivalent sphere with two radius parameters instead of one drastically improves the accuracy of the estimates of dose and dose equivalent in space radiation environments. For example, in solar particle event environments the average error in the estimate of the skin dose equivalent using an equivalent sphere with two radius parameters is about 8%, while the average error of the conventional equivalent sphere model using one radius parameter is around 100%.