  The current literature is rather vague regarding how to calculate the exact
numerical value of the resonant ion scattering cross-section that should be
used for a specific bandpass of finite width. Such a value was needed in order
to calculate the ion and mass densities in the shock fronts of hot, close
binary star systems. This was done based on a modeling of ultraviolet wind-line
profiles, using IUE spectra. Therefore, a numerical integration has been
carried out, in wavelength-space, of the exact expression for the cross-section
over two band-passes of astrophysical interest. The exact expression employed
was that derived from a solution of the Abraham-Lorentz equation. The numerical
results depend on the resonant wavelength, which is taken to be at the center
of the bandpass. Most texts on the subject derive an expression for the
scattering cross-section in frequency-space, based on the assumption that the
radiation reaction term in the Abraham-Lorentz equation may be approximated by
a resistive term. The integral of this cross-section over the entire spectrum
is independent of the resonant frequency, except for the transition
probability. This has limited practical use when dealing with fluxes measured
in a bandpass of finite width expressed in wavelength units and scattering is
the only mechanism for producing the observed fluxes. Such is the case when
dealing with the low densities encountered in stellar winds and shock fronts.
  Integrated cross-sections that depend on the resonant wavelength are used to
determine the number and mass densities of C IV and N V ions in the shock
fronts found in some hot, eclipsing binary star systems, for which several IUE
spectra have been obtained over a Keplerian orbital period. This then leans to
a determination of the mass density and total mass in the shock once the volume
of the shock is determined.
