Casimir Forces Across Magnetic Plasmas at Nuclear Separations

TL;DR

This paper investigates magnetic Casimir forces across a dense electron-positron plasma at nuclear-scale separations, incorporating magnetic permeability and external fields into the Casimir-Lifshitz framework. It decomposes the interaction into zero- and finite-frequency contributions, derives how μ_ep and Langevin-type paramagnetism influence the zero-frequency term, and demonstrates through numerical results that magnetic effects can produce sizable corrections comparable to nuclear energies at separations around a few femtometers. The work builds a Casimir-Yukawa perspective for nuclear interactions, highlighting a potential supplementary role for vacuum fluctuations in screening and meson-like masses, and suggests future studies on plasmon lifetimes, field-dependent permeability, and more complex geometries. Overall, magnetic Casimir physics may contribute non-negligible corrections to nuclear-scale forces and screening phenomena.

Abstract

A theory and numerical findings are presented on the magnetic Casimir interaction that arises from vacuum fluctuations of the quantized field and its effects at the nuclear scale. We investigate how the zero-temperature Casimir effect at nuclear scales can generate the black-body temperatures required to induce a magnetic electron-positron plasma. The magnetic permeability of the plasma and any magnetic fields present influence the screened Casimir-Yukawa potentials between perfect conducting surfaces. We discuss implications for the magnetic Casimir-Yukawa potential, its screening length, and a magnetic permeability-dependent quantity that resembles the meson mass.

Figures (2)

• Figure 1: Zero frequency contribution to interaction free energy from Eq.(\ref{['Eq56']}), considering either $\mu_{ep}=1$ (lower orange curve) or Eq.(\ref{['permeability']}) (upper blue curve). The x-axis is the $L$ distance in femtometers, y-axis is the Casimir interaction free energy in MeV for two perfect conducting plates with an area ($A=\pi R^2$) given in the text and an intermediate plasma density varying with distance via the equilibrium of zero temperature Casimir energy and the black body radiation energy.
• Figure 2: Contributions from zero-frequency term, Eq. (\ref{['Eq56']}) (red), and finite frequency terms, Eq. (\ref{['Eq57']}) (blue), and their sum (dashed black). The x-axis is the $L$ distance in femtometers, y-axis is the Casimir interaction free energy in MeV. In these examples, we consider two perfect conducting plates with an area ($A=\pi R^2$) given in the text and an intermediate plasma density varying with distance via the equilibrium of zero temperature Casimir energy and the black body radiation energy.