Specific heat and thermodynamic critical field for the molecular metallic hydrogen

In the framework of Eliashberg approach, the free energy difference between the superconducting and normal state for the molecular metallic hydrogen was calculated. The pressure values p1=347GPa and p2=428GPa were taken into consideration. It has been shown that the specific heat's jump at the critical temperature and the thermodynamic critical field near zero Kelvin grow with the pressure: [ΔC(TC)]p2/[ΔC(TC)]p1≃2.33[ΔC(TC)]p2/[ΔC(TC)]p1≃2.33 and [HC(0)]p2/[HC(0)]p1≃1.74[HC(0)]p2/[HC(0)]p1≃1.74. The ratio r1≡ΔC(TC)/CN(TC)r1≡ΔC(TC)/CN(TC) increases from 1.91 to 2.39 with p  ; whereas r2≡TCCN(TC)/HC2(0) decreases from 0.152 to 0.140. The last results prove the fact that the r1 and r2 values significantly differ from the predictions based on the BCS model.