  An analytical inactivation cross section formula based on the analytical
formula for calculating the radial dose distribution of Awad et al. (Awad et
al., 2018) was proposed. The formula is a multi-hit model based on the track
structure theory of Katz that was not updated since Katz and co-workers in
1970s-1980s. The formula was solved numerically to calculation the inactivation
cross section, sigma and action cross section for double strand break, sigma
DSB for the two strains of the vegetative E. coli cells (BS-1 and B/r)
bombarded with heavy ions of O, Ne, Ar, Kr, Xe, Au, Pb and U of energy between
1.1 to 19.4 MeV/n. The response of the cell and hence the corresponding
inactivation cross section is affected by m, the number of targets that must be
inactivated per cell; D0, the characteristic x or gamma-ray dose; a0, the
target radius and Rmax, the maximum range travelled by the liberated delta-ray
in the medium. The variations in the inactivation cross section in terms of
these parameters were studied. The model predicts the available measured
inactivation cross sections data for E. coli cells (BS-1 and B/r),sigma as well
as the double strand break, sigma DSB ones with good accuracy. It was found
that as the ion charge increases as the inactivation probability increases and
the corresponding inactivation cross section of the ion increases.
