  The difference in the adiabatic gradient gamma_1 between inverted solar data
and solar models is analyzed. To obtain deeper insight into the issues of
plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted,
that is, the difference due to the change in the equation of state alone. Our
method uses reference models based on two equations of state currently used in
solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL
equation of state (developed at Livermore). Solar oscillation frequencies from
the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days
in operation are used. Our results confirm the existence of a subtle effect of
the excited states in hydrogen that was previously studied only theoretically
(Nayfonov & Dappen 1998). The effect stems from internal partition function of
hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen
effect, it takes place in somewhat deeper layers of the Sun, where more than
90% of hydrogen is ionized, and where the second ionization zone of helium is
located. Therefore, the effect will have to be taken into account in reliable
helioseismic determinations of the astrophysically relevant helium-abundance of
the solar convection zone.
