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Coherent elastic scattering of low energy photons by neutrons

P. O. Kazinski, A. A. Sokolov

TL;DR

The paper develops a density-matrix framework for the coherent, low-energy scattering of photons by neutrons, establishing a holographic interpretation of the neutron state through the photon output. A macroscopic dielectric susceptibility tensor is derived for neutron wave packets and gases, enabling a medium-like treatment of coherent scattering and linking the hologram to the neutron's one-particle density matrix. The off-shell photon polarization operator is computed, revealing eight plasmon-polariton modes in neutron media, including tachyonic branches that signal a ferromagnetic instability at sufficiently high density and low temperature; in the infrared limit the neutron acts as a neutral particle with a dynamical magnetic moment, governed by effective Maxwell equations. The results provide a predictive framework for experimental probes of neutron quantum states via coherent light scattering and bear relevance for ultracold neutrons and astrophysical neutron systems, including potential ferromagnetic transitions in dense neutron matter. Overall, the study bridges quantum-state holography with macroscopic electromagnetic responses in neutron-rich media.

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.

Coherent elastic scattering of low energy photons by neutrons

TL;DR

The paper develops a density-matrix framework for the coherent, low-energy scattering of photons by neutrons, establishing a holographic interpretation of the neutron state through the photon output. A macroscopic dielectric susceptibility tensor is derived for neutron wave packets and gases, enabling a medium-like treatment of coherent scattering and linking the hologram to the neutron's one-particle density matrix. The off-shell photon polarization operator is computed, revealing eight plasmon-polariton modes in neutron media, including tachyonic branches that signal a ferromagnetic instability at sufficiently high density and low temperature; in the infrared limit the neutron acts as a neutral particle with a dynamical magnetic moment, governed by effective Maxwell equations. The results provide a predictive framework for experimental probes of neutron quantum states via coherent light scattering and bear relevance for ultracold neutrons and astrophysical neutron systems, including potential ferromagnetic transitions in dense neutron matter. Overall, the study bridges quantum-state holography with macroscopic electromagnetic responses in neutron-rich media.

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.
Paper Structure (15 sections, 162 equations, 3 figures)

This paper contains 15 sections, 162 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model and notation
  3. Inclusive probability
  4. Density matrix of scattered photons
  5. Evolution of the Stokes parameters
  6. Gaussian wave packets
  7. Dielectric susceptibility of a neutron wave packet
  8. Dielectric susceptibility on the mass-shell
  9. Off-shell polarization operator
  10. Polarization operator in the infrared limit
  11. Conclusion
  12. Acknowledgments.
  13. Tensors $M_{\mu\nu}$ and $N_{a\mu\nu}$
  14. Contractions of the tensors $M_{\mu\nu}$ and $N_{a\mu\nu}$ with the tensors $G_3^{\mu\nu}$ and $Z_3^{i\mu\nu}$
  15. Tensors $G_3^{\mu\nu}$ and $Z_3^{i\mu\nu}$ in the small recoil limit

Figures (3)

  • Figure 1: The parameters $\varkappa'$ and $\varkappa"$ multiplied by $10^{13}/N_h$ 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 $\boldsymbol\xi_h=(0,0,1)$. The parameters $\varkappa'$ and $\varkappa"$ are defined in \ref{['de_xi']} and determine the evolution of the Stokes vector of scattered photons. The states of photons and neutrons are taken in the form \ref{['Gaussian_states']} with the parameters $\mathbf{k}_0=(0,0,100)$ keV, $\sigma_{ph}=5$ keV, $\mathbf{g}_{ph}-\mathbf{g}_h=(0,0.2,0)$ keV${}^{-1}$, $\mathbf{p}_0=0$ keV, $\sigma_h=5$ keV.
  • Figure 2: The parameters $\varkappa'$ and $\varkappa"$ multiplied by $10^{23}/N_h$ 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 $\varkappa'$ and $\varkappa"$ are defined in \ref{['de_xi']} and determine the evolution of the Stokes vector of scattered photons. The states of photons and neutrons are taken in the form \ref{['Gaussian_states']} with the parameters $\mathbf{k}_0=(0,0,100)$ keV, $\sigma_{ph}=5$ keV, $\mathbf{g}_{ph}-\mathbf{g}_h=(0,0.2,0)$ keV${}^{-1}$, $\mathbf{p}_0=(10,0,0)$ keV, $\sigma_h=5$ keV.
  • Figure 3: Left panel: the dispersion laws of plasmon-polariton modes on a single unpolarized neutron in its rest frame. The parameter \ref{['mus']} is $\tilde{\mu}^2=0.08$. Such a value of this parameter is taken to show the main peculiarities of the dispersion laws. The instability of the transverse mode at $|k_z|<2\tilde{\mu}$ is clearly seen. Right panel: the same as on the left panel but for a single polarized neutron with $\xi=0.95$ and $\mathbf{k}\parallel\mathbf{s}_h$. It is clear that the transverse modes possess instabilities. The estimates for the points where the group velocity is infinity are given in \ref{['sing_points']}. It is also seen that the two transverse modes are tachyonic even at large momenta. The transverse mode, which dispersion curve is slightly above the free dispersion law, is tachyonic for any value of the momentum.