Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities

Contributions to Plasma Physics

2019

Self Cite

The Mott effect describes the dissolution of bound states in a dense partially ionized plasma. It occurs when the ionization potential depression, owing to effects of correlation and degeneracy, compensates the binding energy of the bound state. At high densities and moderate temperatures, the Pauli blocking becomes important and influences significantly the degree of ionization in the region of degenerate plasmas. A quantum statistical approach is used where the total density is decomposed in an uncorrelated, “free” part and correlations, as a consequence of the cluster decomposition of the self‐energy. The contribution of correlations to the total density is given by bound states and continuum correlations. Exact solutions for a separable potential are compared to perturbation theory and numerical solutions of the in‐medium Schrödinger equation. The in‐medium scattering phase shifts are evaluated, and the role of continuum correlations is discussed. The Pauli blocking of bound states and the density of states are considered for warm dense matter conditions.

V_{{normalC}^{6 +}, e}^{normalscr} (boldq)

and introduce the quasi‐particle shifts Δ( k ),

\begin{array}{l} ([], E_{e} ((), p) + Δ_{e} ((), p) + E_{{normalC}^{6 +}} ((), k) + Δ_{{normalC}^{6 +}} ((), k)) ψ_{n}^{5 +} ((),, p, k) \\ + ([], 1 - f_{e} ((), p)) \sum_{q} V_{C^{6 +}, normale}^{scr} ((), q) ψ_{n}^{5 +} ((),, boldp + boldq, boldk - boldq) = E_{n}^{5 +} ψ_{n}^{5 +} ((),, p, k) . \end{array}

…”

Section: Pauli Blocking and Perturbation Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The ion densities are

n_{normali} = \frac{1}{Λ^{3}} σ_{normali} (T) e^{{β μ}_{i}}, Λ = {([], 2 π β ℏ^{2} false/ M)}^{1 / 2}

(ion mass M ) with the generalized Beth‐Uhlenbeck formula for the intrinsic partition function, see ref. ,

σ_{normali} (T) = \underset{γ}{false\sum} [{false\sum}_{ν}^{bound} (e^{β E_{i, γ, ν}} - 1) + \frac{β}{π} \int_{0}^{\infty} d {italicEe}^{- β italicE} \{δ_{i, γ} (E) - \frac{1}{2} \sin [2 δ_{i, γ} (E)]\}] .

…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Pauli blocking in degenerate plasmas and the separable potential approach

Contributions to Plasma Physics

2019

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Equation of state of hydrogen, helium, and solar plasmas

Ébeling

Reinholz

Contributions to Plasma Physics

2021

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The equation of state (EOS) for plasmas of the two lightest elements H and He, and mixtures as typical for the plasmas in the sun are calculated. The contributions of deep bound states are included by using inverted fugacity expansions. The inversion of fugacities to densities is reduced to solvable algebraic problems and expressed by rational polynomials. The calculation of relative pressures is carried out separately for low and high densities. Near the crossing point, in between, the separate solutions are connected to each other by smooth concatenation. Applications to hydrogen–helium plasmas in the sun including estimates for the isentropic EOS are discussed.

Thermodynamic and transport properties of plasmas: Low‐density benchmarks

2023

Contrib. Plasma Phys

Physical properties of plasmas, such as equations of state (EoS) and transport coefficients, are expressed in terms of correlation functions, which can be calculated using various approaches (analytical theory and numerical simulations). The method of Green's functions provides benchmark values for these properties in the low‐density limit. For the EoS and electrical conductivity, expansions with respect to density (virial expansions) are considered. The comparison of analytical results with numerical simulations is used to verify theory, to prove the accuracy of simulations, and establish interpolation formulas.