Recoil Energy in Electron Capture Beta Decay and the Search for Sterile Neutrinos

The left-handed electron neutrino generated in nuclear beta decays may be mixed with a hypothetical right-handed sterile neutrino with a mass much greater than the masses of the mass states of the active (electron, muon, and tau) neutrinos. In electron capture beta decay, the emitted neutrino may sometimes collapse into a sterile neutrino, reducing the recoil energy of the daughter atom. In this paper, we consider the electron capture beta decay of a 7Be atom from the point of view of the possible detection of sterile neutrinos. We study theoretically the recoil energy of the daughter 7Li atom. There are two decay channels for the 7Be atoms: a direct decay to the nuclear ground state of the daughter atom with neutrino radiation and decay to the nuclear excited state of the daughter atom with neutrino radiation, followed by decay to the nuclear ground state with radiation of a γ-ray photon. For the first channel, the exact analytical expression for the recoil kinetic energy of the daughter atom is available in the literature. We derived exact analytical expressions for the recoil kinetic energy in the second decay channel. This recoil energy depends on the angle between the directions of motion of the neutrino and the photon. We point out that for a massless neutrino, the difference between the recoil energy in the first channel and the maximum recoil energy in the second channel is exactly zero. Thus, detection of a finite difference between the two energies would confirm the radiation of a massive neutrino. We also suggest another approach to the detection of massive neutrinos: the difference between the maximum and minimum recoil energies for the second channel changes significantly when a sterile neutrino is radiated. This effect could potentially be used for the detection of a sterile neutrino.