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arxiv: 2510.21645 · v3 · submitted 2025-10-24 · ✦ hep-ph · nucl-th

Coherent elastic scattering of low energy photons by neutrons

P.O. Kazinski , A.A. Sokolov This is my paper

Pith reviewed 2026-05-18 04:23 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords coherent Compton scatteringneutron gasphoton polarization operatorplasmon-polaritonstachyonic instabilityspontaneous magnetizationsusceptibility tensorferromagnetism
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The pith

The photon polarization operator develops pole singularities identified as plasmon-polariton modes in neutron scattering, some tachyonic and unstable.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines coherent Compton scattering of low-energy photons from neutrons whose initial states are given by general density matrices. The coherent contribution to the probability of recording a scattered photon serves as a hologram of the neutron one-particle density matrix. Derivation of the susceptibility tensor leads to an explicit photon polarization operator that exhibits pole singularities in the short-wavelength approximation. These poles are identified with plasmons, yielding eight independent plasmon-polariton modes for a neutron gas and a single-neutron wave packet, several of which are tachyonic and unstable. The instability implies spontaneous magnetic-field generation, with estimates given for the onset of ferromagnetism in the gas.

Core claim

The explicit expression for the photon polarization operator in the presence of free neutrons is derived. It possesses pole singularities in the short wavelength approximation. These singularities are identified with plasmons and the respective plasmon-polaritons are described. There are eight independent plasmon-polariton modes in a neutron gas and on a single neutron wave packet. Some of these modes are tachyonic and unstable, manifesting a spontaneous generation of the magnetic field. Estimates are found for the neutron-gas parameters at which ferromagnetism appears. In the infrared limit the neutron wave packet behaves in coherent Compton scattering as a point particle with dynamical mag

What carries the argument

The photon polarization operator, whose pole singularities in the short-wavelength approximation are identified with plasmons and plasmon-polaritons as additional degrees of freedom.

Load-bearing premise

The short wavelength approximation suffices to equate the polarization-operator poles directly with plasmons and plasmon-polaritons treated as additional degrees of freedom.

What would settle it

Measurement of spontaneous magnetic-field generation inside a neutron gas held at the densities estimated in the paper; its presence or confirmed absence would confirm or refute the tachyonic instability.

Figures

Figures reproduced from arXiv: 2510.21645 by A.A. Sokolov, P.O. Kazinski.

Figure 1
Figure 1. Figure 1: The parameters κ ′ and κ ′′ multiplied by 1013/Nh as functions of the direction of emission of the scattered photon (n ′ x, n′ y) for coherent elastic scattering of polarized photons by polarized neutrons with ξh = (0, 0, 1). The parameters κ ′ and κ ′′ are defined in (74) and determine the evolution of the Stokes vector of scattered photons. The states of photons and neutrons are taken in the form (80) wi… view at source ↗
Figure 2
Figure 2. Figure 2: The parameters κ ′ and κ ′′ multiplied by 1023/Nh as functions of the direction of emission of the scattered photon (n ′ x, n′ y) for coherent elastic scattering of polarized photons by unpolarized neutrons. The parameters κ ′ and κ ′′ are defined in (74) and determine the evolution of the Stokes vector of scattered photons. The states of photons and neutrons are taken in the form (80) with the parameters … view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: the dispersion laws of plasmon-polariton modes on a single unpolarized neutron in its rest frame. The parameter (113) is µ˜ 2 = 0.08. Such a value of this parameter is taken to show the main peculiarities of the dispersion laws. The instability of the transverse mode at |kz| < 2˜µ is clearly seen. Right panel: the same as on the left panel but for a single polarized neutron with ξ = 0.95 and k … view at source ↗
read the original abstract

The Compton process with the initial states of photons and neutrons described by the density matrices of a general form is studied for low energies of photons. The coherent contribution to the inclusive probability to record a photon is investigated in detail. This contribution gives the hologram of the neutron one-particle density matrix. The evolution of the Stokes parameters of scattered photons is described. The susceptibility tensor of a neutron gas and a wave packet of a single neutron is obtained. The explicit expression for the photon polarization operator in the presence of free neutrons is derived. It turns out that this polarization operator possesses pole singularities in the short wavelength approximation. These singularities corresponding to the additional degrees of freedom are identified with plasmons and the respective plasmon-polaritons are described. There are eight independent plasmon-polariton modes in a neutron gas and on a single neutron wave packet. Some plasmon-polariton modes prove to be tachyonic and unstable manifesting a spontaneous generation of the magnetic field. The estimates of the parameters of the neutron gas when it becomes ferromagnetic are found. In the infrared limit, the neutron wave packet behaves in coherent Compton scattering as a point particle with dynamical magnetic moment, the additional degrees of freedom being reduced to the dynamical part of the magnetic moment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper examines coherent elastic Compton scattering of low-energy photons off neutrons whose initial states are described by general density matrices. It derives the coherent contribution to the photon recording probability, which encodes the neutron one-particle density matrix, and obtains the susceptibility tensor for both a neutron gas and a single-neutron wave packet. From this, an explicit expression for the photon polarization operator is constructed. In the short-wavelength approximation this operator develops pole singularities that are identified with eight independent plasmon-polariton modes; several of these modes are reported to be tachyonic, implying an instability that generates a spontaneous magnetic field and drives a ferromagnetic transition in the neutron gas. In the infrared limit the wave packet reduces to a point particle with a dynamical magnetic moment.

Significance. If the mapping of the short-wavelength poles to physical plasmon-polariton degrees of freedom and the subsequent demonstration of tachyonic instabilities are robust, the work would provide a novel mechanism for spontaneous magnetization in a neutron gas, with possible implications for the magnetic properties of neutron matter. The derivation starts from first-principles density-matrix scattering and yields concrete estimates for the density at which the ferromagnetic transition occurs. However, the absence of an explicit verification that the reported poles persist outside the short-wavelength truncation or satisfy causality/unitarity constraints limits the strength of the physical interpretation.

major comments (2)
  1. [derivation of the polarization operator and short-wavelength analysis] The central claim that pole singularities of the photon polarization operator in the short-wavelength approximation correspond to additional physical degrees of freedom (plasmons and plasmon-polaritons) is load-bearing for the instability and ferromagnetism conclusions. No demonstration is given that these poles remain at physical locations or retain their tachyonic character when retardation, gradient corrections to the neutron density matrix, or higher-order terms in the susceptibility are restored; without such a check the identification risks being an artifact of the truncation.
  2. [plasmon-polariton modes and stability analysis] The stability analysis leading to tachyonic modes and spontaneous magnetic-field generation relies on the dispersion relations extracted from the approximated polarization operator. An explicit check against the full (non-approximated) expression or against known causality and unitarity constraints on the photon self-energy in a magnetic-moment medium is missing; this is required to confirm that the reported instabilities are not spurious.
minor comments (2)
  1. The abstract and main text would benefit from a concise statement of the precise short-wavelength limit (e.g., the ordering of k, ω, and neutron momentum scales) together with the explicit form of the polarization operator before the limit is taken.
  2. Notation for the eight independent modes and their dispersion relations should be tabulated or clearly labeled to facilitate comparison with the infrared limit where they reduce to the dynamical magnetic moment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the major comments point by point below, clarifying the scope of our approximations while indicating where revisions will strengthen the presentation.

read point-by-point responses

  1. Referee: [derivation of the polarization operator and short-wavelength analysis] The central claim that pole singularities of the photon polarization operator in the short-wavelength approximation correspond to additional physical degrees of freedom (plasmons and plasmon-polaritons) is load-bearing for the instability and ferromagnetism conclusions. No demonstration is given that these poles remain at physical locations or retain their tachyonic character when retardation, gradient corrections to the neutron density matrix, or higher-order terms in the susceptibility are restored; without such a check the identification risks being an artifact of the truncation.

    Authors: The susceptibility tensor is obtained exactly from the coherent Compton amplitude for low-energy photons interacting with the neutron density matrix. The polarization operator follows directly from this tensor via the standard relation in linear response theory. The short-wavelength approximation is applied only after this derivation to extract the leading dispersion relations for collective modes, following the standard procedure used in plasma and condensed-matter analyses of media with magnetic moments. We agree that an explicit restoration of all higher-order terms would be desirable for full confirmation. In the revised manuscript we will add a dedicated paragraph providing order-of-magnitude estimates of the neglected gradient and retardation corrections, showing that they remain parametrically small in the density and wavelength regime where the tachyonic modes appear. The leading paramagnetic contribution responsible for the instability is unaffected by these corrections at the level considered. revision: partial

  2. Referee: [plasmon-polariton modes and stability analysis] The stability analysis leading to tachyonic modes and spontaneous magnetic-field generation relies on the dispersion relations extracted from the approximated polarization operator. An explicit check against the full (non-approximated) expression or against known causality and unitarity constraints on the photon self-energy in a magnetic-moment medium is missing; this is required to confirm that the reported instabilities are not spurious.

    Authors: The full polarization operator satisfies the Ward identity k_μ Π^{μν} = 0 by construction from the gauge-invariant Compton vertex. The eight modes are obtained by solving the resulting dispersion equation in the short-wavelength limit. The imaginary part of the susceptibility is positive and consistent with the optical theorem applied to the underlying Compton process, thereby satisfying the basic causality requirement. Unitarity of the low-energy scattering amplitude is preserved. In the revision we will insert an explicit verification of these properties together with a qualitative argument that the tachyonic character of the modes survives small corrections because it is driven by the sign of the magnetic susceptibility. A complete numerical solution of the exact dispersion relation lies outside the present analytic scope but will be noted as a natural extension. revision: partial

Circularity Check

0 steps flagged

No circularity: polarization operator and plasmon modes derived from explicit scattering calculation

full rationale

The paper begins with the Compton process for photons and neutrons described by general density matrices, computes the coherent contribution to the inclusive photon recording probability, obtains the susceptibility tensor, and derives an explicit expression for the photon polarization operator. Pole singularities are reported as a computed feature that appears when the short-wavelength approximation is applied to this operator. The identification of these singularities with plasmons, the enumeration of eight independent plasmon-polariton modes, and the observation of tachyonic instabilities are interpretive steps performed after the poles have been obtained mathematically; they do not redefine the input operator or presuppose the result. No self-citations are shown to be load-bearing for the central claims, no parameters are fitted to a data subset and then relabeled as predictions, and the infrared-limit reduction to a point-particle magnetic moment is presented as a limiting case of the same derived expressions. The derivation chain therefore remains independent of the target conclusions and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claims rest on the validity of the low-energy Compton regime, the short-wavelength approximation for identifying singularities, and the physical interpretation of poles as plasmons without additional external constraints.

axioms (2)
  • domain assumption Low-energy limit of Compton scattering on neutrons is sufficient to capture coherent contributions and collective modes
    Invoked throughout the study of the Compton process and derivation of the susceptibility tensor.
  • ad hoc to paper Pole singularities in the polarization operator correspond to physical plasmon degrees of freedom
    Used to identify the additional modes and analyze their stability.
invented entities (1)
  • Plasmon-polariton modes in neutron gas and wave packet no independent evidence
    purpose: To account for the pole singularities and collective excitations in the photon polarization operator
    Introduced via identification of singularities; no independent experimental signature provided in the abstract.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    hep-th 2026-04 unverdicted novelty 7.0

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Works this paper leans on

70 extracted references · 70 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Gabor, Microscopy by reconstructed wavefronts, Proc

    D. Gabor, Microscopy by reconstructed wavefronts, Proc. Roy. Soc. London A197, 454 (1949)

    work page 1949

  2. [2]

    L.Cser,B.Farago,G.Krexner,I.Sharkov,Gy.Török,Atomicresolutionneutronholography(principles and realization), Physica B350, 113 (2004)

    work page 2004

  3. [3]

    P. W. Hawkes, J. C. H. Spence (Eds.),Springer Handbook of Microscopy(Springer, Cham, 2019)

    work page 2019

  4. [4]

    Winkler, J

    F. Winkler, J. Barthel, R. E. Dunin-Borkowski, K. Müller-Caspary, Direct measurement of electrostatic potentials at the atomic scale: A conceptual comparison between electron holography and scanning transmission electron microscopy, Ultramicroscopy210, 112926 (2020)

    work page 2020

  5. [5]

    Harada, Interference and interferometry in electron holography, Microscopy70, 3 (2021)

    K. Harada, Interference and interferometry in electron holography, Microscopy70, 3 (2021)

    work page 2021

  6. [6]

    Inoue, K

    T. Inoue, K. Nagao, A. Matsunaka, T. Kokubu, K. Nishio, T. Kubota, Y. Awatsuji, Motion-picture recording of light pulses with ultrashort time difference by polarization camera, IEEE Photonics Tech- nology Letters34, 931 (2022)

    work page 2022

  7. [7]

    Daimon, T

    H. Daimon, T. Matsushita, F. Matsui, K. Hayashi, Y. Wakabayashi, Recent advances in atomic reso- lution three-dimensional holography, Advances in Physics: X9, 2350161 (2024)

    work page 2024

  8. [8]

    P. O. Kazinski, G. Yu. Lazarenko, Transition radiation from a Dirac-particle wave packet traversing a mirror, Phys. Rev. A103, 012216 (2021)

    work page 2021

  9. [9]

    P. O. Kazinski, T. V. Solovyev, Coherent radiation of photons by particle wave packets, Eur. Phys. J. C82, 790 (2022)

    work page 2022

  10. [10]

    P. O. Kazinski, T. V. Solovyev, Susceptibility of a single photon wave packet, Phys. Rev. D108, 016004 (2023)

    work page 2023

  11. [11]

    P. O. Kazinski, D. I. Rubtsova, A. A. Sokolov, Inclusive probability to record an electron in elastic electromagnetic scattering by a spin one-half hadron wave packet, Phys. Rev. D108, 096011 (2023). 24

    work page 2023

  12. [12]

    P. O. Kazinski, V. A. Ryakin, P. S. Shevchenko, Radiation from Dirac fermions caused by a projective measurement, Phys. Rev. D110, 116011 (2024)

    work page 2024

  13. [13]

    I. M. Akimov, P. O. Kazinski, A. A. Sokolov, Plasmon-polariton modes on a single electron wave packet, Phys. Rev. D111, 036028 (2025)

    work page 2025

  14. [14]

    V. A. Bednyakov, D. V. Naumov, Concept of coherence in neutrino and antineutrino scattering off nuclei, Phys. Part. Nucl.52, 39 (2021)

    work page 2021

  15. [15]

    P. O. Kazinski, Coherent effects in scattering of particle wave packets, in Proceedings of Efim Fradkin Centennial Conference, Moscow, Russia (Lebedev Physical Insitute, Moscow, 2024). https://esf.lpi.ru/proceedings/qft/Kazinski.pdf

    work page 2024

  16. [16]

    M. D. Schwartz,Quantum Field Theory and the Standard Model(Cambridge University Press, Cam- bridge, 2014)

    work page 2014

  17. [17]

    Weinberg,The Quantum Theory of FieldsVol

    S. Weinberg,The Quantum Theory of FieldsVol. 1:Foundations(Cambridge University Press, Cam- bridge, 1996)

    work page 1996

  18. [18]

    Marcuse, Emission of radiation from a modulated electron beam, J

    D. Marcuse, Emission of radiation from a modulated electron beam, J. Appl. Phys.42, 2255 (1971)

    work page 1971

  19. [19]

    Peatross, C

    J. Peatross, C. Müller, K. Z. Hatsagortsyan, C. H. Keitel, Photoemission of a single-electron wave packet in a strong laser field, Phys. Rev. Lett.100, 153601 (2008)

    work page 2008

  20. [20]

    J. P. Corson, J. Peatross, C. Müller, K. Z. Hatsagortsyan, Scattering of intense laser radiation by a single-electron wave packet, Phys. Rev. A84, 053831 (2011)

    work page 2011

  21. [21]

    J. P. Corson, J. Peatross, Quantum-electrodynamic treatment of photoemission by a single-electron wave packet, Phys. Rev. A84, 053832 (2011)

    work page 2011

  22. [22]

    M. Ware, E. Cunningham, C. Coburn, J. Peatross, Measured photoemission from electron wave packets in a strong laser field, Opt. Lett.41, 689 (2016)

    work page 2016

  23. [23]

    Y. Pan, A. Gover, Spontaneous and stimulated radiative emission of modulated free electron quantum wavepackets – semiclassical analysis, J. Phys. Commun.2, 115026 (2018)

    work page 2018

  24. [24]

    Remezet al., Observing the quantum wave nature of free electrons through spontaneous emission, Phys

    R. Remezet al., Observing the quantum wave nature of free electrons through spontaneous emission, Phys. Rev. Lett.123, 060401 (2019)

    work page 2019

  25. [25]

    O. Kfir, V. DiGiulio, F. J. G. de Abajo, C. Ropers, Optical coherence transfer mediated by free electrons, Sci. Adv.7, eabf6380 (2021)

    work page 2021

  26. [26]

    L. J. Wonget al., Control of quantum electrodynamical processes by shaping electron wavepackets, Nat. Commun.12, 1700 (2021)

    work page 2021

  27. [27]

    Ligez, R

    R. Ligez, R. B. MacKenzie, V. Massart, M. B. Paranjape, U. A. Yajnik, What is the gravitational field of a mass in a spatially nonlocal quantum superposition?, Phys. Rev. Lett.130, 101502 (2023)

    work page 2023

  28. [28]

    Klein, Low-energy theorems for renormalizable field theories, Phys

    A. Klein, Low-energy theorems for renormalizable field theories, Phys. Rev.99, 998 (1955)

    work page 1955

  29. [29]

    A. M. Baldin, Polarizability of nucleons, Nucl. Phys.18, 310 (1960)

    work page 1960

  30. [30]

    Two-photon

    V. A. Petrun’kin, “Two-photon” interactions of elementary particles at small energies, Proc. P. N. Lebedev Phys. Inst.41, 165 (1968) [in Russian]

    work page 1968

  31. [31]

    P. S. Baranov, L. V. Fil’kov, Compton scattering on the proton at low and medium energies, Fiz. Elem. Chastits At. Yadra7, 108 (1976) [Sov. J. Part. Nucl.7, 42 (1976)]

    work page 1976

  32. [32]

    Schwinger, Brownian motion of a quantum oscillator, J

    J. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys.2, 407 (1961)

    work page 1961

  33. [33]

    L. V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz.47, 1515 (1964) [Sov. Phys. JETP20, 1018 (1965)]. 25

    work page 1964

  34. [34]

    K. Chou, Z. Su, B. Hao, L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rep. 118, 1 (1985)

    work page 1985

  35. [35]

    E. S. Fradkin, D. M. Gitman, Sh. M. Shvartsman,Quantum Electrodynamics with Unstable Vacuum (Springer, Berlin, 1991)

    work page 1991

  36. [36]

    B. S. DeWitt,The Global Approach to Quantum Field Theory, Vol. 1,2 (Clarendon Press, Oxford, 2003)

    work page 2003

  37. [37]

    E. A. Calzetta, B. L. Hu,Nonequilibrium Quantum Field Theory(Cambridge University Press, New York, 2008)

    work page 2008

  38. [38]

    V. K. Ignatovich, Ultracold neutrons – discovery and research, Phys. Usp.39, 283 (1996)

    work page 1996

  39. [39]

    A. P. Serebrov, Supersource of ultracold neutrons at the WWRM reactor and the program of funda- mental research in physics, Crystallography Reports56, 1230 (2011)

    work page 2011

  40. [40]

    Yu. N. Pokotilovski, Experiments with ultracold neutrons – first 50 years, arXiv:1805.05292

    work page internal anchor Pith review Pith/arXiv arXiv

  41. [41]

    Lauss, B

    B. Lauss, B. Blau, UCN, the ultracold neutron source – neutrons for particle physics, SciPost Phys. Proc.5, 004 (2021)

    work page 2021

  42. [42]

    A. E. Delsante, N. E. Frankel, Relativistic paramagnetism: Quantum statistics, Phys. Rev. D20, 1795 (1979)

    work page 1979

  43. [43]

    J. D. Anand, P. Bhattacharjee, S. N. Biswas, M. Hasan, Paramagnetism of hot magnetic neutron gas, Phys. Rev. D23,316(1981)

    work page 1981

  44. [44]

    A. I. Akhiezer, N. V. Laskin, S. V. Peletminski˘i, Spontaneous magnetization in a dense neutron gas and a dense plasma of particles and antiparticles: magnetohydrodynamic waves in dense neutron matter, Zh. Eksp. Teor. Fiz.109, 1981 (1996) [JETP82, 1066 (1996)]

    work page 1981

  45. [45]

    R. E. Prange, Dispersion relations for Compton scattering, Phys. Rev.110, 240 (1958)

    work page 1958

  46. [46]

    A. C. Hearn, E. Leader, Fixed-angle dispersion relations for nucleon Compton scattering. I, Phys. Rev. 126, 789 (1962)

    work page 1962

  47. [47]

    W. A. Bardeen, W.-K. Tung, Invariant amplitudes for photon processes, Phys. Rev.173, 1423 (1968)

    work page 1968

  48. [48]

    F. E. Low, Scattering of light of very low frequency by systems of spin1 2, Phys. Rev. D96, 1428 (1954)

    work page 1954

  49. [49]

    Gell-Mann, M

    M. Gell-Mann, M. L. Goldberger, Scattering of low-energy photons by particles of spin1 2, Phys. Rev. D96, 1433 (1954)

    work page 1954

  50. [50]

    Weinberg, Dynamics and algebraic symmetries, inLectures on Elementary Particles and Quantum field Theory – 1970 Brandeis Summer Institute in Theoretical Physics, Vol

    S. Weinberg, Dynamics and algebraic symmetries, inLectures on Elementary Particles and Quantum field Theory – 1970 Brandeis Summer Institute in Theoretical Physics, Vol. 1 edited by S. Deser, M. Grisaru, H. Pendelton (MIT Press, Cambridge, 1970)

    work page 1970

  51. [51]

    V. B. Berestetskii, E. M. Lifshitz, L. P. Pitaevskii,Quantum Electrodynamics(Butterworth- Heinemann, Oxford, 1982)

    work page 1982

  52. [52]

    V. N. Baier, V. M. Katkov, V. M. Strakhovenko,Electromagnetic Processes at High Energies in Ori- ented Single Crystals(World Scientific, Singapore, 1998)

    work page 1998

  53. [53]

    M. E. Peskin, D. V. Schroeder,An Introduction to Quantum Field Theory(Addison-Wesley, Reading, 1995)

    work page 1995

  54. [54]

    I. S. Gradshteyn, I. M. Ryzhik,Table of Integrals, Series, and Products(Acad. Press, Boston, 1994)

    work page 1994

  55. [55]

    L. D. Landau, E. M. Lifshitz,Electrodynamics of Continuous Media(Pergamon, Oxford, 1984)

    work page 1984

  56. [56]

    Gavassino, M

    L. Gavassino, M. M. Disconzi, J. Noronha, Dispersion relations alone cannot guarantee causality, Phys. Rev. Lett.132, 162301 (2024). 26

    work page 2024

  57. [57]

    R. E. Hoult, P. Kovtun, Causality and classical dispersion relations, Phys. Rev. D109, 046018 (2024)

    work page 2024

  58. [58]

    D.-L. Wang, S. Pu, Stability and causality criteria in linear mode analysis: Stability means causality, Phys. Rev. D109, L031504 (2024)

    work page 2024

  59. [59]

    Haensel, A

    P. Haensel, A. Y. Potekhin, D. G. Yakovlev,Neutron Stars 1:Equation of State and Structure(Spinger, New York, 2007)

    work page 2007

  60. [60]

    L. D. Landau, E. M. Lifshitz,The Classical Theory of Fields(Pergamon, Oxford, 1962)

    work page 1962

  61. [61]

    L. D. Landau, E. M. Lifshitz,Statistical Physics. Part 2(Pergamon, Oxford, 1980)

    work page 1980

  62. [62]

    V. L. Ginzburg, On the magnetic fields of collapsing masses and the nature of superstars, Dokl. Akad. Nauk SSSR156, 43 (1964) [Sov. Phys. Dokl.9, 329 (1964)]

    work page 1964

  63. [63]

    V. A. Urpin, S. A. Levshakov, D. G. Yakovlev, Generation of neutron star magnetic fields by thermo- magnetic effects, Mon. Not. R. astr. Soc.219, 703 (1986)

    work page 1986

  64. [64]

    Thompson, R

    C. Thompson, R. C. Duncan, Neutron star dynamos and the origins of pulsar magnetism, Astrophys. J.408, 194 (1993)

    work page 1993

  65. [65]

    Price, S

    D. Price, S. Rosswog, Producing ultra-strong magnetic fields in neutron star mergers, Science312, 719 (2006)

    work page 2006

  66. [66]

    A. Yu. Potekhin, The physics of neutron stars, Phys. Usp.53, 1235 (2010)

    work page 2010

  67. [67]

    J. Dong, W. Zuo, J. Gu, Magnetization of neutron star matter, Phys. Rev. D87, 103010 (2013)

    work page 2013

  68. [68]

    Igoshev, P

    A. Igoshev, P. Barrère, R. Raynaud, J. Guilet, T. Wood, R. Hollerbach, A connection between proto- neutron-star Tayler-Spruit dynamos and low-field magnetars, Nature Astronomy9, 541 (2025)

    work page 2025

  69. [69]

    Hendersonet al., The Spallation Neutron Source accelerator system design, Nucl

    S. Hendersonet al., The Spallation Neutron Source accelerator system design, Nucl. Instrum. Methods A763, 610 (2014)

    work page 2014

  70. [70]

    I. S. Anderson, C. Andreani, J. M. Carpenter, G. Festa, G. Gorini, C.-K. Loong, R. Senesi, Research opportunities with compact accelerator-driven neutron sources, Phys. Rep.654, 1 (2016). 27

    work page 2016