Precision Measurement of the Recoil Energy Spectrum from the Decay ofHe6

Abstract

The energy spectrum of recoil ions from the ${\beta }^{-}$ decay of ${\mathrm{He}}^6$ was observed repeatedly under a variety of operating conditions with a spectrometer which uses a tandem arrangement of magnetic and electrostatic analysis. Analyzed ions were detected with an electron multiplier. A composite spectrum is formed from the several observations, random errors are assigned on the basis of the observed fluctuations, and four parameters are adjusted to give the best fit of theory to experiment. These parameters are the maximum ${\beta }^{-}$ energy $W_0$, an electron-neutrino correlation coefficient $\alpha$, a normalization constant, and a detector parameter. The analysis gives $\alpha =-0.3343\mathrm{}\pm 0.0030$, where the uncertainty represents a careful evaluation of both random and systematic effects. The conclusion is reached, with "68% posterior probability," that the limit to the tensor interaction is $\frac{({\left|C_T\right|}^2+{\left|{C_T}^{\prime }\right|}^2)}{({\left|C_A\right|}^2+{\left|{C_A}^{\prime }\right|}^2)}\le 0.4\%$. If one assumes that there is no tensor interaction but that higher order terms may be present, then one can conclude from a plane-wave ($Z=0\mathrm{}$) approximation for the ${\mathrm{He}}^6$ decay that $b=-(0.5\mathrm{}\pm 1.3){\mathrm{}\left(2M\right)\mathrm{}}^{-1\mathrm{}}$, where $b$ is a second-order term defined in Gell-Mann's paper on weak magnetism, and $M$ is the ratio of nucleon-to-electron mass.