Gallium Solar Neutrino Experiments: Absorption Cross sections, Neutrino spectra, and Predicted Event Rates

TL;DR

This work provides a comprehensive, energy-dependent calculation of neutrino absorption cross sections in ${}^{71}$Ga for all solar and laboratory sources, incorporating updated atomic/nuclear data, atomic overlap and exchange effects, and solar-thermal corrections. It uses the ${}^{51}$Cr calibration results to constrain excited-state contributions and presents a detailed uncertainty framework, including conservative $3\sigma$ bounds, to enable robust interpretation under standard and non-standard neutrino spectra. The author delivers best-estimate cross sections, plus energy-specific $3\sigma$ ranges, and demonstrates how standard solar-model predictions compare with GALLEX/SAGE measurements, highlighting the solar-neutrino problem. The discussion extends to potential outcomes for the Gallium Neutrino Observatory (GNO) and outlines how energy-dependent cross sections can be leveraged to test various new-physics scenarios.

Abstract

Neutrino absorption cross sections for 71Ga are calculated for all solar neutrino sources with standard energy spectra, and for laboratory sources of 51Cr and 37Ar; the calculations include, where appropriate, the thermal energy of fusing solar ions and use improved nuclear and atomic data. The ratio, R, of measured (in GALLEX and SAGE) to calculated 51Cr capture rate is R = 0.95 +/- 0.07 (exp)} + ^{+0.04}_{-0.03} (theory). Cross sections are also calculated for specific neutrino energies chosen so that a spline fit determines accurately the event rates in a gallium detector even if new physics changes the energy spectrum of solar neutrinos. Theoretical uncertainties are estimated for cross sections at specific energies and for standard neutrino energy spectra. Standard energy spectra are presented for pp and CNO neutrino sources in the appendices. Neutrino fluxes predicted by standard solar models, corrected for diffusion, have been in the range 120 SNU to 141 SNU since 1968.

Figures (4)

• Figure 1: The ${\rm ^{71}Ga}$-${\rm ^{71}Ge}$ Transitions for Low Energy Neutrinos. Only the ground state and the first two allowed excited state transitions contribute to the absorption of $pp$, ${\rm ^7Be}$, and ${\rm ^{51}Cr}$ neutrinos. The ${\rm ^8B}$, CNO, and $pep$ neutrinos all give rise to excited state transitions that are unconstrained by the ${\rm ^{51}Cr}$ neutrino absorption measurements and for which the $(p,n)$ measurements provide the only empirical guide to the relevant BGT values.
• Figure 2: The ${\rm ^{51}Cr}$ Decay Scheme.
• Figure 3: Predicted Solar Neutrino Gallium Event Rate Versus Year of Publication. The figure shows the event rates for all of the standard solar model calculations that my colleagues and I have publishedBP92BP95fibsbahcall97solarpapers. The cross sections from the present paper have been used in all cases to convert the calculated neutrino fluxes to predicted capture rates. The estimated $1\sigma$ uncertainties reflect in all cases just the uncertainties in the cross sections that are evaluated in the present paper. For the 35 years over which we have been calculating standard solar model neutrino fluxes, the historically lowest value (fluxes published in 1969) corresponds to $109.5$ SNU. This lowest-ever value is $5.6\sigma$ greater than the combined GALLEX and SAGE experimental result. If the points prior to 1992 are increased by $11$ SNU to correct for diffusion (this was not done in the figure), then all of the standard model theoretical capture rates since 1968 through 1997 lie in the range $120$ SNU to $141$ SNU, i.e., ($131 \pm 11$) SNU.
• Figure 4: Absorption cross sections for gallium as a function of energy. The figure displays the best-estimate cross sections as well as the $\pm 3\sigma$ cross sections. Numerical values are given in Table \ref{['bestsigmacue']}, Table \ref{['minsigmacue']}, and Table \ref{['maxsigmacue']}.