Casimir forces across magnetic plasmas at nuclear separations
S. K. Panja · L. Inacio · S. Pal · M. Boström
Abstract and summary · read the original at the source
In one page
Two mirrors a few hundred nanometres apart feel the Casimir force, and everyone measures it there. Suman Panja, Luiza Inacio, Subhojit Pal and Mathias Boström, working at the ENSEMBLE3 centre in Warsaw and in Palermo, ask what the same vacuum force does at separations a hundred million times smaller — the femtometre gap between two protons. Their chain of reasoning is direct. At that spacing the zero-point energy in the gap, set equal to the black-body energy it could support, corresponds to a temperature near a trillion kelvin, hot enough to fill the gap with a plasma of electrons and positrons. That plasma then screens the vacuum force, and the screened form is the same expression nuclear physics writes as the Yukawa potential. This paper adds the piece its predecessors left out: the plasma’s magnetic permeability, and any magnetic field present. Both change the screening length, and the energies that come out land in the range of measured nuclear binding energies.
Why it matters hereChapter 2 says the vacuum is a real medium with real forces, and this paper follows that force down to nuclear separations and finds it is not negligible there — with the plasma it generates screening it into the shape of the strong-force potential. That makes it a chapter 12 paper too: if vacuum structure contributes to the environment a nucleus sits in, then the environment is something an experiment can change, which is the whole premise of the lattice work.
What it claims
01Nuclear separations are hot. Setting the zero-temperature Casimir energy between two perfectly conducting plates of proton-radius area equal to the black-body energy of the gap gives a temperature that falls as the reciprocal of the separation, with a numerical factor of forty-eight to the one-quarter. At one femtometre that is about 8.7 times ten to the eleventh kelvin, and it drops to about 2.9 times ten to the eleventh at three femtometres — well past the threshold for populating the gap with electrons and positrons.Section 2.1, equations 2 to 6; Table 2
Published and peer-reviewed02That temperature fixes a plasma density with an explicit distance dependence. Integrating the Fermi distribution in the ultrarelativistic limit gives a combined electron and positron number density of about 0.020 divided by the cube of the separation — roughly two times ten to the forty-third per cubic metre at one femtometre — and with it a plasma frequency near 2.5 times ten to the twenty-third radians per second and a magnetic permeability of order a few hundred.Section 2.1, equations 7 to 12; Table 1 and Table 2
Published and peer-reviewed03The Casimir force is of nuclear size at nuclear size. Equating the Casimir energy between two protons with their Coulomb energy gives a cubic equation whose solution by Cardano’s method returns an equilibrium separation of 2.6 femtometres. The authors read that as evidence the Casimir force is relevant at nuclear scale distances, and it agrees with an earlier estimate by Fleming using the proximity force theorem, which found Casimir and electrostatic interactions similar in magnitude there.Section 2.2, equations 13 to 16
Published and peer-reviewed04Screened by that plasma, the vacuum interaction takes the shape nuclear physics already uses. As Ninham and colleagues showed, the explicit form of the Casimir interaction with a plasma in the gap is the same as the Klein-Gordon-Yukawa potential. The contribution of this paper is to carry the magnetic permeability and the applied magnetic field through the Lifshitz reflection coefficients, so that both the transverse-magnetic and the transverse-electric modes respond, and to show how that modifies the potential and its screening length.Section 3, equations 22 and 23; Section 6, Conclusions
Published and peer-reviewed05The energies land in the right range. The interaction free energies the model returns are of the same order as the experimentally measured nuclear interaction energies that vary with the environment — the authors cite roughly 1.1 MeV for deuterium up to 8.8 MeV for nickel-62. It is that environment dependence, already established by measurement, that the vacuum contribution is being offered to help explain.Section 6, Conclusions
Published and peer-reviewed06The paper’s own forward marker is a quantity that behaves like a meson mass. Setting the exponent of the screened Casimir free energy equal to the exponent of the Yukawa potential gives an expression for the mediating mass in terms of permeability and plasma density; between one and three femtometres it runs from 329 down to 13 MeV with magnetic effects left out, and from 6242 down to 84 MeV with spin permeability included, bracketing the known 135 MeV. The authors call these simple estimates and are explicit that they do not propose replacing established nuclear theory — their claim is that Casimir physics may play a small complementary role. The next steps they name are two-sphere geometry, relativistic spin-dependent Casimir-Lifshitz interactions, and the lifetimes of electron-positron plasmons.Section 5, Discussions, equations 58 to 60
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Read it · abstract
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.
The way in
https://doi.org/10.1016/j.aop.2025.170191Published in Annals of Physics (2025) by Elsevier; the licences Elsevier declares for the record are text-and-data-mining and user licences, not an open licence. The preprint is on arXiv as 2505.07860, version 1 posted 8 May 2025, under the arXiv.org perpetual non-exclusive licence, which grants arXiv distribution and no redistribution right — checked on the arXiv record for this paper on 2026-09-08, where no Creative Commons statement appears, and the preprint text carries none. So this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source; the claims are read against the preprint, whose numbering is used for the locators. Panja, Inacio and Boström are at the ENSEMBLE3 Centre of Excellence in Warsaw, Pal at the Università degli Studi di Palermo, and Boström also at the Centre of New Technologies, University of Warsaw. The work extends a line running from Ninham and Daicic in 1998 through Ninham and Boström in 2003 and Ninham and colleagues in 2014 and 2022.
How to cite it
S. K. Panja, L. Inacio, S. Pal, M. Boström (2025) Casimir forces across magnetic plasmas at nuclear separations. doi:10.1016/j.aop.2025.170191
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