Configuration mixing in particle decay and reaction

Background: Decay constants of unstable nuclei and particles are quantum constants. Recent controversy on the existence (versus non-existence) of variability in the observation of decay rate can be settled by considering mixing in decay configuration. Purpose: Variability in decay rate was investigated based on the available information of beta decay rate data, solar neutrino flux, and energy distribution. Method: Full systematic analysis of the oscillatory behavior was carried out. Based on the zero threshold energy for neutrino absorption in beta emitters, a model for configuration mixing between two distinct beta disintegration modes $\beta^\nu$-disintegration (electron from neutrino interaction) and the $\beta^-$-disintegration (electron from natural decay) was proposed. Results: The phenomenon of variability in beta decay rate was related to the possible exothermic neutrino absorption by unstable nuclei which, in principle, should include the whole range of flux energies involving flux with energy below the $^{71}$Ga threshold at 0.23 MeV. These two disintegration modes occur independently and model for their apparent mixing rate was proposed. Conclusions: The configuration mixing between the two modes causes depletion of radioactive nuclei which is subject to change with seasonal solar neutrino variability. Ability to detect this variability was found to be dependent on the Q-value of the $\beta^\nu$ disintegration and detection instrument setup. Value of neutrino cross section weighted by the ratio between $\beta^\nu$ and $\beta^-$ detection efficiencies was found to be in the range $10^{-44}$ to $10^{-36}$ cm$^{2}$. For experiments that uses the end point to determine the neutrino mass, interference due to mixing should be taken into account.