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Fermion scattering in a Bose-Einstein condensate

César E. Echevarría*, José F. Nieves†, and Francisco Orbe‡

Sarira Sahu§

  • *Contact author: cesar.echevarria@upr.edu
  • †Contact author: nieves@ltp.uprrp.edu
  • ‡Contact author: francisco.orbe@upr.edu
  • §Contact author: sarira@nucleares.unam.mx
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Phys. Rev. D 114, 075007 – Published 7 October, 2026

DOI: https://doi.org/10.1103/3lmw-djxy

Abstract

In a recent work, we considered the propagation of fermions in the background of a scalar Bose-Einstein (BE) condensate. Using some illustrative Yukawa-type coupling models between the fermions and the scalar fields, we determined the dispersion relations of the fermions and the scalar modes in various models. To complement that work, here we consider the corresponding fermion spinors and propagators, which are required for the calculation of rates of processes involving the fermions, as well as the thermal, and/or higher order, corrections to such rates. We obtain and present here concise formulas which are useful for those applications. As an application and for illustrative purposes we consider the scattering rate for a generic fermion (which we denote by χ) with the fermion modes (f) in the BE condensate, using commonly used models for the fχ interactions. Due to the fact that the fermion modes dispersion relations are helicity dependent, the kinematics have some unique and nonstandard features. For example, at a particular value of the momentum one of the fermion modes has zero group velocity, which leads to effects of the type of the Van Hove singularity in the density of states of some condensed matter systems. The results of the framework presented here, besides their merit in their own right, can be useful in specific contexts and applications, such as cosmic-ray electron cooling through dark matter-electron scattering, and similar ones involving neutrino and/or electron propagation in a dark matter background.

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Phys. Rev. D 114, 075007– Published 7 October, 2026
  • Received 8 April 2026
  • Accepted 27 August 2026
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