  We provide a quantitative description of a method to measure neutron-induced
fission cross sections in ratio to elastic hydrogen scattering in a
white-source neutron beam with the fission Time Projection Chamber. This
detector has measured precision fission cross section ratios using actinide
references such as $^{235}$U(n,f) and $^{238}$U(n,f). However, by employing a
more precise reference such as the H(n,el) cross section there is the potential
to further reduce the evaluation uncertainties of the measured cross sections.
In principle the fissionTPC could provide a unique measurement by
simultaneously measuring both fission fragments and proton recoils over a large
solid angle. We investigate one method with a hydrogenous gas target and with
the neutron energy determined by the proton recoil kinematics. This method
enables the measurement to be performed in a white-source neutron beam and with
the current configuration of the fissionTPC. We show that while such a
measurement is feasible in the energy range of 0.5 MeV to $\sim$10 MeV,
uncertainties on the proton detection efficiency and the neutron energy
resolution do not allow us to preform a fission ratio measurement to the
desired precision. Utilizing either a direct measurement of the neutron
time-of-flight for the recoil proton or a mono-energetic neutron source or some
combination of both would provide a path to a sub-percent precision
measurement.
