Study on Several Pade Approximants for Fully Ionized Hydrogen Plasmas

Based on the current proposed three type Pade approximations of fully ionized hydrogen plasmas. Using Fortran program, we calculated the Helmholtz free energy of hydrogen plasmas and made a comparison of these Helmholtz free energy. It is concluded that the dimensionless parameter f(ee)(c) of W. Stolzmann's theoretical analysis presents unphysical tendency within Gamma(e)>15 and r(s)<4, and f(ie)(c) gives an unreasonable result within 8.0<Gamma(e)<9.1 and 7.0<r(s)<8.0 at low temperature T=5000K, but this range of the odd variation and the values of Gamma(e) (r(s)) will change with the increase of temperature, when the temperature reaches super-high temperature (T>10(7)K), f(ie)(c) almost is applicable to all range of the values of Gamma(e) and r(s), f(ee)(c) is applicable to the values of 0<Gamma(e)<0.3 and r(s)>0. In addition, the dimensionless parameter f(ii)(c) of Gilles Chabrier's article and W. Stolzmann's article have a good consistency. Finally, we presented a interpolational formula for hydrogen plasmas, making up for those small odd variation. It demonstrates that the interpolation formula for hydrogen plasmas has a practical application.