A model of dense-plasma atomic structure for equation-of-state calculations

A model of dense plasmas relying on the superconfiguration approximation is presented. In each superconfiguration the nucleus is totally screened by the electrons in a Wigner–Seitz sphere (ion–sphere model). Superconfigurations of the same charge are grouped into ions. It is shown that boundary values of the wavefunctions play a crucial role in the form of the Virial theorem from which the pressure formula is derived. Finally, a condition is presented and discussed which makes the ion–sphere model variational when bound electrons are treated quantum mechanically and free electrons quasiclassically.

[1]  J. Pain,et al.  Quantum mechanical model for the study of pressure ionization in the superconfiguration approach , 2006 .

[2]  J. Pain,et al.  Self-consistent approach for the thermodynamics of ions in dense plasmas in the superconfiguration approximation , 2003 .

[3]  J. Pain,et al.  New approach to dense plasma thermodynamics in the superconfiguration approximation , 2002 .

[4]  F. Perrot,et al.  Virial theorem and pressure calculations in the GGA , 2001 .

[5]  Thomas Blenski,et al.  A superconfiguration code based on the local density approximation , 2000 .

[6]  M. Klapisch,et al.  The effect of configuration interaction on relativistic transition arrays , 2000 .

[7]  T. Lehecka,et al.  EFFECT OF CONFIGURATION INTERACTION ON SHIFT WIDTHS AND INTENSITY REDISTRIBUTION OF TRANSITION ARRAYS , 1999 .

[8]  C. Blancard,et al.  Statistical mechanics of highly charged ion plasmas in local thermodynamic equilibrium , 1997 .

[9]  A. Grimaldi,et al.  HARTREE-FOCK STATISTICAL APPROACH TO ATOMS AND PHOTOABSORPTION IN PLASMAS , 1997 .

[10]  Ishikawa,et al.  Pressure ionization in the spherical ion-cell model of dense plasmas and a pressure formula in the relativistic Pauli approximation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  A. Bar-Shalom,et al.  Configuration interaction in LTE spectra of heavy elements , 1992 .

[12]  Bloom,et al.  Computation of spectral arrays in hot plasmas using the Lanczos algorithm. , 1991, Physical Review A. Atomic, Molecular, and Optical Physics.

[13]  Goldstein,et al.  Super-transition-arrays: A model for the spectral analysis of hot, dense plasma. , 1989, Physical review. A, General physics.

[14]  Goldberg,et al.  Intermediate-coupling calculation of atomic spectra from hot plasma. , 1986, Physical review. A, General physics.

[15]  Ichimaru,et al.  Free energies of electron-screened ion plasmas in the hypernetted-chain approximation. , 1986, Physical review. A, General physics.

[16]  F. Rogers.  Equation of state of dense, partially degenerate, reacting plasmas , 1981 .

[17]  F. Perrot.  Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations , 1979 .

[18]  W. Kohn,et al.  CONTINUITY BETWEEN BOUND AND UNBOUND STATES IN A FERMI GAS , 1965 .

[19]  N. Metropolis,et al.  Equations of State of Elements Based on the Generalized Fermi-Thomas Theory , 1949 .

[20]  L. H. Thomas.  The calculation of atomic fields , 1927, Mathematical Proceedings of the Cambridge Philosophical Society.

[21]  F. Gilleron,et al.  Stable method for the calculation of partition functions in the superconfiguration approach. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Perrot.  Ion-ion interaction and equation of state of a dense plasma: Application to beryllium. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  R. More.  Pressure Ionization, Resonances, and the Continuity of Bound and Free States , 1985 .

[24]  B. Rozsnyai.  Relativistic Hartree-Fock-Slater Calculations for Arbitrary Temperature and Matter Density , 1972 .

[25]  E. Fermi.  Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente , 1928 .