  In particle therapy, knowledge of the stopping-power ratios (STPRs) of the
ion beam for air and water is necessary for accurate ionization chamber
dosimetry. Earlier work has investigated the STPRs for pristine carbon ion
beams, but here we expand the calculations to a range of ions (1 <= z <= 18) as
well as spread out Bragg peaks (SOBPs) and provide a theoretical in-depth study
with a special focus on the parameter regime relevant for particle therapy. The
Monte Carlo transport code SHIELD-HIT is used to calculate complete
particle-fluence spectra which are required for determining STPRs according to
the recommendations of the International Atomic Energy Agency (IAEA).
  We confirm that the STPR depends primarily on the current energy of the ions
rather than on their charge z or absolute position in the medium. However,
STPRs for different sets of stopping-power data for water and air recommended
by the International Commission on Radiation Units & Measurements (ICRU) are
compared, including also the recently revised data for water, yielding
deviations up to 2% in the plateau region. In comparison, the influence of the
secondary particle spectra on the STPR is about two orders of magnitude smaller
in the whole region up till the practical range. The gained insights enable us
to propose an analytic approximation for the STPR for both pristine and SOBPs
as a function of penetration depth, which parametrically depend only on the
initial energy and the residual range of the ion, respectively.
