Fig. 1. Principal Hugoniot of Cu as P vs η (“Compression”): our new analytic model (solid line) vs the experimental data from Refs. 3, 21, and 51, and the theoretical calculations in Refs. 52 and 53 using the average-atom approximation implemented with three quantum-statistical models, specifically Thomas–Fermi, Thomas–Fermi with quantum and exchange corrections, and Hartree–Fock–Slater.

Fig. 2. Principal Hugoniot of Ag as P vs η (“Compression”): our new analytic model (solid line) vs the experimental data from Ref. 3 and the theoretical calculations in Ref. 54 using the relativistic Green’s function quantum average atom code Tartarus.

Fig. 3. Principal Hugoniot of Ir as P vs η (“Compression”): our new analytic model (solid line) vs the experimental data from Ref. 55 (“Shock Wave Database”) and our own theoretical calculations, similar to those in Ref. 56 for Pt, using the Thomas–Fermi model with corrections (“Thomas–Fermi Corr.”).

Fig. 4. Principal Hugoniot of Pt as P vs η (“Compression”): our new analytic model (solid line) vs the experimental data from Refs. 57 and 58 and the theoretical calculations in Ref. 56 using the Thomas–Fermi model with corrections (“Thomas–Fermi Corr.”).

Fig. 5. Comparison between N in (11), n in (12), and n≡Up**/c/a, where Up** is the solution of (3), all three being functions of Z.

Fig. 6. Y defined in (23) as a function of Z.

Fig. 7. Grüneisen gamma for Cu along its principal Hugoniot vs η (“Compression”): our new analytic model (solid line) vs the theoretical results of Ref. 64, the results of Refs. 3 and 65 using some functional forms of γ(ρ) applied to the corresponding experimental data, and the theoretical model of Ref. 66.