  The Very Local Interstellar Medium (VLISM) neutral hydrogen and proton
densities are still not precisely known even after three decades of deep space
research and the existence of the EUV and other diagnostic data obtained by
Pioneer 10/11, Voyager 1/2 and other spacecraft. The EUV data interpretation,
in particular, has suffered because of inadequate neutral hydrogen-plasma
models, difficulty of calculating the multiply scattered Lyman alpha glow and
calibration uncertainties. Recently, all these difficulties have been
significantly reduced. In the present work we have used the latest state of the
art supersonic VLISM neutral hydrogen-plasma and Monte Carlo radiative transfer
model, incorporating neutral density, temperature, and velocity variations,
actual solar line shape, realistic redistribution function, Doppler and
aberration effects. This work presents the methodology of the radiative
transfer code and the first results of the comparison of the model predictions
with the Pioneer 10 data. Monte Carlo radiative transfer calculations were
carried out for five neutral hydrogen- plasma models and compared with Pioneer
data. The first results are quite encouraging. We found that the VLISM
ionization ratio is between 0.2 and 0.5 and that the VLISM neutral hydrogen
density is less than 0.25 cm^{-3}. The present calculation suggests that the
Pioneer 10 photometer derived intensities (Rayleighs) need to be increased by a
factor of 2. If this model- derived calibration is used then the difference
between Pioneer 10 and Voyager 2 intensity values is reduced to about 2.2. The
model, neutral hydrogen density = 0.15 cm${-3} and proton density = 0.07
cm^{-3}, is found to best fit the Pioneer 10 data.
