Distribution of radial dose in water at nanometer scale for ions of the same linear energy transfer: benefits of the concept of annular dose

Annular-dose AD is a new conception , based on the radial dose distribution, RDD, introduced by the present work. AD is the integrated dose for many shells around the ions and it is defined as the dose deposited in the shell volume perpendicular to the ion path of width (r = 0.1 -> R-min), length equal 271 and thickness equal unity (1 nm). Thus, it integrates and maps the deposited dose due to ion in any medium at nanometer scale better than the ordinary radial dose. Katz and Awad radial dose formulae plus Butts-Katz and Tabata electron range-energy relations are composing three different approaches. These approaches were used for studying the AD for 30 ions forming 4 different equal LET groups and have energy at Bragg peak region from 1.5 to 24 MeV n(-1). The annular dose, AD as a function of the shell width for the ions under investigation showed that dose distributions around the ions of same LET are not the same and a clear peak at certain shell width called the ion's maximum annular dose width, r(MADW) was determined for the first time. The r(MADW) is the position where the maximum reachable dose is delivered by secondary electrons around the ion. The ion's r(MADW) showed an increasing function with Z*beta within the same LET group. Interestingly, it was found that r(MADW) behaves as an increasing monotonic function of the relative ion velocity, beta using the three approaches considered in this work.