Ionization potential depression and ionization balance in dense carbon plasma under solar and stellar interior conditions

Abstract

Recent quantitative experiments on the ionization potential depression (IPD) in dense plasma show that the observational results are difficult to explain with the widely used analytical models for plasma screening. Here, we investigate the effect of plasma screening on the IPD and ionization balance of dense carbon plasma under solar and stellar interior conditions using our developed consistent nonanalytical model. The screening potential can be primarily attributed to the free electrons in the plasma and is determined by the microspace distribution of these free electrons. The ionization balance is determined by solving the Saha equation, including the effect of IPD. The predicted IPD and average ionization degree are larger than those obtained using the Stewart–Pyatt model for mass densities that are greater than 3.0 g cm−3. Under solar interior conditions, our results are in better agreement with the Ecker–Kröll model at electron temperatures and densities lower than 250 eV and 2.1 × 1023 cm−3 and in the best agreement with the ion-sphere model at 303 eV and 4.3 × 1023 cm−3. Finally, our results are compared with those obtained via a recent experiment on a CH-mixture plasma that has been compressed six times. The predicted average ionization degree of C in a CH mixture agrees better with the experiment than the Stewart–Pyatt and Thomas–Fermi models when the screening from free electrons contributed by hydrogen atoms is included. Our results provide useful information concerning the ionization balance and can be applied to investigate the opacity and equations of state for dense plasma under the solar and stellar interior conditions.

Structural modifications of two-electron systems under isotropic harmonic confinement

“…The H − ion is of particular interest which shows that even under very feeble harmonic confine- ment, where the one-electron level has hardly been modified, the two-electron ground state moves above continuum and becomes quasi-bound. Variation of the ionization potential of quantum chemical systems has been studied by researchers in various confining environments, e.g., impenetrable spherical cavity [43,44], dense plasma environment [45], fullerene cage [46], in astrophysical context [47], etc. Both one-electron and two-electron energies are altered in presence of external environment and the ionization potential, calculated as the difference between these energy values, reflects the combined effect of these changes.…”

The Strong Enhancement of Electron-Impact Ionization Processes in Dense Plasma by Transient Spatial Localization

“…For an isolated ion of nuclear number Z with N electrons ( refers to an atom), the atomic properties and wave functions are determined by solving the Dirac equation using a consistent field method [ 60 , 61 ]. In dense plasma, which is characterized by electron temperature T and density , both the bound and continuum electrons of the ion feel a plasma screening potential that originates from the interaction with surrounding electrons and ions in the plasma [ 62 , 63 , 64 , 65 , 66 ]: where defines the radius of the ion sphere. The free-electron density distribution follows Fermi–Dirac statistics, which are obtained from the ionization equilibrium equation of the plasma.…”

Multi-Configuration Calculation of Ionization Potential Depression

“…In practice, R ∞ ≈ 10 R ws , but we always check that the results are not affected if we take a higher value (in the limit of the numerical capabilities of the code, of course). The mono-electronic energies k , solutions of Schrödinger Equation (6), are dependent on the assumption that the potential V scf is zero outside the sphere, which is not the case, and must be shifted from the quantity…”

“…Let us consider an isolated (unscreened) ion of average ionization Z * . The energy of the mono-electronic Kohn-Sham orbital is k + V scf (R ∞ ) associated to the wave function ψ k of state k, and solution of Equation (6). The mono-electronic potential entering the definition of the Hamiltonian H is…”

“…Their experimental and theoretical studies have aroused the interest of scientists for many years, either for accurate determination [1] or looking for regularities along isoelectronic sequences [2], etc. Ionization potential depression (IPD) or continuum lowering in dense plasmas has been the subject of many investigations over the past years [3][4][5][6]. This many-body effect significantly alters the ionization balance and the corresponding charge state distribution, which have a strong influence on thermodynamic [7], transport [8][9][10] and radiative properties of the system [11,12].…”