Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Birrell, Jeremiah; Formanek, Martin; Steinmetz, Andrew; Yang, Cheng Tao; Rafelski, Johann

doi:10.1007/s10773-024-05695-8

Int J Theor Phys

2024

DOI: 10.1007/s10773-024-05695-8

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Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Jeremiah Birrell,

Martin Formanek,

Andrew Steinmetz

et al.

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Self-consistent Strong Screening Applied to Thermonuclear Reactions

Grayson,

Yang,

Formanek

et al. 2024

ApJ

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Self-consistent strong plasma screening around light nuclei is implemented in the Big Bang nucleosynthesis (BBN) epoch to determine the short-range screening potential, e ϕ(r)/T ≥ 1, relevant for thermonuclear reactions. We numerically solve the nonlinear Poisson–Boltzmann equation incorporating Fermi–Dirac statistics, adopting a generalized screening mass to find the electric potential in the cosmic BBN electron–positron plasma for finite-sized α particles (4He++) as an example. Although the plasma follows Boltzmann statistics at large distances, Fermi–Dirac statistics is necessary when work performed by ions on electrons is comparable to their rest-mass energy. While self-consistent strong screening effects are generally minor owing to the high BBN temperatures, they can enhance the fusion rates of high-Z (Z > 2) elements while leaving fusion rates of lower-Z (Z ≤ 2) elements relatively unaffected. Our results also reveal a pronounced spatial dependence of the self-consistent strong screening potential near the nuclear surface. These findings about the electron–positron plasma’s role refine BBN theory predictions and offer broader applications for studying weakly coupled plasmas in diverse cosmic and laboratory settings.

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Self-consistent Strong Screening Applied to Thermonuclear Reactions

Grayson,

Yang,

Formanek

et al. 2024

ApJ

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show abstract

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Fermi-Dirac Integrals in Degenerate Regimes: Novel Asymptotic Expansion

Cited by 1 publication

References 33 publications

Self-consistent Strong Screening Applied to Thermonuclear Reactions

Self-consistent Strong Screening Applied to Thermonuclear Reactions

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