Resolution of the neutron lifetime puzzle and the conceptual design of its experimental confirmation

The lifetime of free neutrons was a long-standing puzzle: in the beam experiments it significantly exceeded the corresponding result from the trap experiments. The difference far exceeded the experimental error margins. While the results of the trap experiments were based on counting neutrons, the results of the beam experiments were based on counting protons stemming from the three-body decay of a neutron into a free proton and a free electron (plus antineutrino). It was well-known that there is a relatively small probability for the two-body decay of a free neutron into a hydrogen atom (plus antineutrino). For explaining the above puzzle, the Branching Ratio (BR) for this two-body decay – compared to the usual three-body decay – should have been ∼ 1 %. However, the theoretical BR for such two-body decay was previously known to be smaller by several orders of magnitude: 4 × 10^–6. In one of our papers of 2024 (hereafter paper I) it was pointed out that after taking into account the second solution of the Dirac equation for hydrogen atoms, the theoretical BR for the two-body decay of free neutrons (into hydrogen atoms and antineutrinos) got enhanced by a factor ∼ 3000 to become ∼ 1 %. Thus, the neutron lifetime puzzle appeared solved completely. In the present paper, the resolution of the neutron lifetime puzzle in this way is just the “stepping stone” leading to the “keystone” (i.e., to the central idea): to the proposed conceptual design of the experiments that will constitute both the first experimental detection of the two-body decay of free neutrons and the experimental confirmation that the two-body decay of free neutrons produces overwhelmingly the hydrogen atoms described by the second solution of the Dirac equation.