Recent multidimensional numerical simulations [Pauls et al., 1995] of
the solar wind interaction with the local interstellar medium have pro
duced a self-consistent description of the interstellar neutral hydrog
en at the heliopause. In this report, we develop a simple one-dimensio
nal model of the solar wind interaction with interstellar hydrogen whi
ch is capable of describing the basic features of the interaction alon
g the solar wind stagnation line that were obtained in the numerical s
imulations. It is shown that pickup ions in the subsonic solar wind ca
n stagnate the plasma flow completely at a distance of 40 AU from the
termination shock thus defining the position of the contact discontinu
ity relative to the termination shock. The plasma number density incre
ases considerably but remains finite on the solar wind side of the con
tact discontinuity, for a finite velocity of the neutral hydrogen. For
the interstellar wind, deceleration due to the interaction with solar
hydrogen is found to be important, even though the solar hydrogen den
sity flux is relatively small. The characteristic scale of this intera
ction is defined by the depth of penetration of the solar hydrogen ato
ms into the interstellar wind. We find that for observed solar wind an
d interstellar medium parameters, the deceleration is sufficient to st
agnate the interstellar wind at the contact discontinuity.