Solar Neutrinos from theHe3(p, e+ν)He4Reaction

An upper limit to the cross section for the reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}(p, e^{+}\nu ){}_{}{}^4{}_{}{}^{}\mathrm{He}$ is calculated by comparing its matrix element with the matrix element of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}(n, \gamma ){}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction, for which an experimental upper limit of 100 μb has been obtained. Expressing the cross section in the form ${\sigma }_{\beta }=\left(\frac{S}{E_p}\right)\exp (-2\mathrm{}\pi \eta )$, where $E_p$ is the center-of-momentum proton energy and $\eta =2\mathrm{}\times 3\frac{{\mathrm{Me}}^2}{4{\hslash }^2{k}_p}$ with $k_p$ the relative proton wave number, we get a value for the constant $S$ of $S\cong 3.7\times {10}^{-20\mathrm{}}$ keV b, as against the older value of 6.3×${10}^{-18\mathrm{}}$ keV b. This result indicates that the ${}_{}{}^3{}_{}{}^{}\mathrm{He}(p, e^{+}\nu ){}_{}{}^4{}_{}{}^{}\mathrm{He}$ reaction is a negligible source of solar neutrinos compared to the ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ decay.