We investigate the possibility to characterize the differences between
interior models of Jupiter and Saturn with the help of seismological
criteria. For both planets we consider two groups of models : first, m
odels based on different descriptions of the hydrogen equation of stat
e (plasma phase transition (PPT) or interpolated EOS) and second, mode
ls with different descriptions of the energy transport mechanism (full
y convective models and radiative-convective models). The acoustic mod
es eigenfrequency patterns of both planets are calculated for the diff
erent models for degrees up to 30 (Jupiter) or 15 (Saturn), and for fr
equencies up to the tropospheric cutoff frequency. The different treat
ments of the hydrogen pressure ionization lead to substantial differen
ces in the oscillation frequencies, up to 120 mu Hz for Jupiter and 40
mu Hz for Saturn. These variations come partly from the fact that the
location of the rock/ice core depends strongly on the equation of sta
te in the fluid envelope. The differences between the oscillation freq
uencies corresponding respectively to fully and non fully adiabatic mo
dels vary from 0 to 80 mu Hz for Jupiter and to 40 mu Hz for Saturn. T
his stems from the fact that the location of the PPT in the planetary
interior and the core size depend strongly on the characteristics of t
he models. The amplitudes of the calculated variations suggest that fu
ture seismological observations should provide stringent tests to disc
riminate between various planetary interior models. Jupiter or Saturn
may in fact be used as natural high-pressure laboratories to character
ize the very nature of hydrogen pressure-metallization.