Screening corrections to electron capture rates and resulting constraints on primordial magnetic fields

Abstract

We explore screening effects arising from a relativistic magnetized plasma with applications to Big Bang nucleosynthesis (BBN). The screening potential which depends on the thermodynamics of charged particles in the plasma is altered by the magnetic field. We focus on the impact of screening on the electron capture interaction. Taking into account the correction in BBN arising from a homogeneous primordial magnetic field (PMF), we constrain the epoch at which the PMF was generated and its strength during BBN. Considering such screening corrections to the electron capture rates and using up-to-date observations of primordial elemental abundances, we also discuss the possibility of solving the problem of under-estimation of the deuterium abundance. We find for certain values of the PMF strength predicted D and 4 He abundances are both consistent with the observational constraints.

Nuclear Reaction Screening, Weak Interactions, and r-Process Nucleosynthesis in High Magnetic Fields

“…In addition to the inclusion of magnetized plasma effects on screening of the Coulomb potential and modifications to the electron-positron chemical potential, effects on weak interaction rates have also been examined. Weak interactions can be altered by changes to the electron Fermi-Dirac distribution function and the electron energy spectrum in weak decays (Luo et al 2020;Grasso & Rubinstein 2001;Fassio-Canuto 1969). In addition, the shifts to the electron-positron chemical potentials in the thermal plasma are also modified.…”

“…The corresponding shift in the lepton energy spectra can have dramatic effects on the weak interaction rates in a magnetized plasma. With the inclusion of density distributions modified by the existence of Landau levels, the approximate weak interaction rates can be rewritten with the momentum component parallel to the magnetic field vector and the discrete transverse momentum components (Luo et al 2020;Grasso & Rubinstein 2001;Fassio-Canuto 1969):…”

“…• Relativistic screening including effects on the TF length from an external magnetic field on the Fermi gas (Luo et al 2020). (Models D logB and DF logB .…”

“…Coulomb screening reduces their Coulomb barrier because the effective charge between two particles is reduced. The commonly-used "extended" (Jancovici 1977;Itoh et al 1977) screening and recent evaluations of screening from relativistic effects have been explored (Famiano et al 2016;Luo et al 2020). In evaluating the screening effect, even a small shift in the potential energy can result in significant changes in the classical turning points of the WKB approximation, resulting in an increase in the reaction rate.…”

Distribution function of nuclei from $e^\pm$ scattering in the presence of a strong primordial magnetic field

“…A possible source of deviation of particle distributions from MB is the existence of a primordial magnetic field (PMF). A strong magnetic field changes weak [15][16][17] and nuclear [18] reaction rates, as well as thermodynamic properties of the e ± s [18,19] through Landau discretization of the particle momenta. In addition, the PMF energy enhances the cosmic expansion rate [20], and mainly through this effect the PMF is constrained to be B 0 < 1.5µG at present or B < 2.0 × 10 11 G at T 9 ≡ T /(10 9 K) = 1 [18,21].…”