  By reevaluating a 13-month stretch of Ulysses SWICS H pickup ion measurements
near 5 AU close to the ecliptic right after the previous solar minimum, this
paper presents a determination of the neutral interstellar H density at the
solar wind termination shock and implications for the density and ionization
degree of hydrogen in the LIC. The density of neutral interstellar hydrogen at
the termination shock was determined from the local pickup ion production rate
as obtained close to the cut-off in the distribution function at aphelion of
Ulysses. As shown in an analytical treatment for the upwind axis and through
kinetic modeling of the pickup ion production rate at the observer location,
with variations in the ionization rate, radiation pressure, and the modeling of
the particle behavior, this analysis turns out to be very robust against
uncertainties in these parameters and the modeling. Analysis using current
heliospheric parameters yields the H density at the termination shock equal to
$0.087\pm0.022$ cm$^{-3}$, including observational and modeling uncertainties.
