  Purpose: To present a closed formalism calculating charged particle radiation
damage induced in DNA. The formalism is valid for all types of charged
particles and due to its closed nature is suited to provide fast conversion of
dose to DNA-damage. Methods: The induction of double strand breaks in
DNA--strings residing in irradiated cells is quantified using a single particle
model. This leads to a proposal to use the cumulative Cauchy distribution to
express the mix of high and low LET type damage probability generated by a
single particle. A microscopic phenomenological Monte Carlo code is used to fit
the parameters of the model as a function of kinetic energy related to the
damage to a DNA molecule embedded in a cell. The model is applied for four
particles: electrons, protons, alpha--particles, and carbon ions. A geometric
interpretation of this observation using the impact ionization mean free path
as a quantifier, allows extension of the model to very low energies. Results:
The mathematical expression describes the model adequately using a chi--square
test ($\chi^2/NDF < 1$). This applies to all particle types with an almost
perfect fit for protons, while the other particles seem to result in some
discrepancies at very low energies. The implementation calculating a strict
version of the RBE based on complex damage alone is corroborated by
experimental data from the measured RBE. The geometric interpretation generates
a unique dimensionless parameter $k$ for each type of charged particle. In
addition, it predicts a distribution of DNA damage which is different from the
current models.
