Reassessing the gallium anomaly using self-consistent electron wave functions

The gallium anomaly, a persistent discrepancy exceeding $4σ$ in the $^{71}$Ga neutrino capture rates from $^{51}$Cr and $^{37}$Ar radioactive sources by the GALLEX, SAGE, and recently BEST experiments, has challenged particle physics and nuclear theory for over three decades. We present a new calculation of the neutrino capture cross section, abandoning the conventional leading-order approximation for electronic wave functions by numerically solving the Dirac-Coulomb equation for both bound and continuum electron states. Finally, we reevaluate the gallium anomaly, updating its global significance and presenting the most up-to-date status of its interpretation in terms of sterile neutrinos.

💡 Research Summary

The paper presents a comprehensive re‑evaluation of the neutrino capture cross‑section on 71Ga, which underlies the long‑standing “gallium anomaly” observed in the GALLEX, SAGE, and most recently BEST experiments. The anomaly consists of a measured deficit of electron‑neutrino‑induced inverse beta‑decay (IBD) events relative to theoretical predictions, now exceeding a 4σ discrepancy. Traditional calculations of the capture cross‑section rely on a leading‑order (LO) approximation for the electronic wave functions, essentially treating the electron as a slowly varying plane wave inside the nuclear volume and applying a simple Fermi function to account for Coulomb distortion.

To improve upon this, the authors abandon the LO approximation and solve the Dirac‑Coulomb (Dirac‑Hartree‑Fock‑Slater, DHFS) equations numerically for both bound (especially the 1s shell) and continuum electron states. They employ the RADIAL code, incorporating a realistic nuclear charge distribution (a two‑parameter Fermi model with a measured charge radius R_ch = 4.032 fm for 71Ge) and an electronic potential that includes the nuclear, electron‑cloud, and exchange contributions. The exchange constant C_ex is taken as the average of the Slater (3/2) and Kohn‑Sham (1) values, C_ex = 1.25, with a systematic uncertainty reflecting the spread between these limits.

The bound‑state wave functions g₁ₛ(r) and f₁ₛ(r) are used to compute the electron density at the nucleus, 4π|ψ_be,1s(r₀)|², for two reference radii: r₀ = 0 and r₀ = (5/3)R_ch (the “box” radius). The results agree with previous literature (Behrens, Band, etc.) within 0.2 % and with the fully relativistic GRASP code within 1 %, demonstrating that the chosen potential and exchange treatment are sufficiently accurate.

For the outgoing electron, the authors evaluate the generalized Fermi function
F(E_e,Z,r) =