# Free neutron decay

When embedded in an atomic nucleus, neutrons are (usually) stable particles. Outside the nucleus, free neutrons are unstable and have a mean lifetime of 877.75+0.50 −0.44 s or 879.6±0.8 s (about 14 min and 37.75 s or 39.6 s, respectively). Therefore, the half-life for this process (which differs from the mean lifetime by a factor of ln(2) ≈ 0.693) is 611±1 s (about 10 min, 11 s).
The free neutron decays primarily by beta decay, with small probability of other channels. The beta decay of the neutron can described at different levels of detail, starting with the simplest:
    n$^0$ → p$^+$ + e$^−$ + ν $_e$
Quantitative measurements of the free neutron decay time vary slightly between different measurement techniques for reasons which have not been determined.

## Energy budget

For the free neutron, the decay energy for this process (based on the rest masses of the neutron, proton and electron) is 0.782343 MeV. That is the difference between the rest mass of the neutron and the sum of the rest masses of the products. That difference has to be carried away as kinetic energy. The maximal energy of the beta decay electron (in the process wherein the neutrino receives a vanishingly small amount of kinetic energy) has been measured at 0.782±0.013 MeV. The latter number is not well-enough measured to determine the comparatively tiny rest mass of the neutrino (which must in theory be subtracted from the maximal electron kinetic energy); furthermore, neutrino mass is constrained by many other methods.
A small fraction (about 1 in 1,000) of free neutrons decay with the same products, but add an extra particle in the form of an emitted gamma ray:
    n$^0$ → p$^+$ + e$^−$ + ν $_e$ + γ
This gamma ray may be thought of as a sort of "internal bremsstrahlung" that arises as the emitted beta particle (electron) interacts with the charge of the proton in an electromagnetic way. In this process, some of the decay energy is carried away as photon energy. Gamma rays produced in this way are also a minor feature of beta decays of bound neutrons, that is, those within a nucleus.
A very small minority of neutron decays (about four per million) are so-called "two-body (neutron) decays", in which a proton, electron and antineutrino are produced as usual, but the electron fails to gain the 13.6 eV necessary energy to escape the proton (the ionization energy of hydrogen), and therefore simply remains bound to it, as a neutral hydrogen atom (one of the "two bodies"). In this type of free neutron decay, in essence all of the neutron decay energy is carried off by the antineutrino (the other "body").
The reverse process of recombination of a proton and an electron into a neutron and a neutrino by electron capture occurs in neutron stars, under the conditions of neutron degeneracy. Similarly, in inverse beta decay, a proton and a sufficiently energetic antineutrino may combine into a neutron and a positron.

## Decay process viewed from multiple levels

Understanding of the beta decay process developed over several years, with the initial understanding of Enrico Fermi and colleagues starting at the "superficial" first level in the diagram below. Current understanding of weak processes rest at the fourth level, at the bottom of the chart, where the nucleons (the neutron and its successor proton) are largely ignored, and attention focuses only on the interaction between two quarks and a charged boson, with the decay of the boson almost treated as an afterthought. Because the charged weak boson ( W$^−$ ) vanishes so quickly, it was not actually observed during the first half of the 20th century, so the diagram at level 1 omits it; even at present it is for the most part inferred by its after-effects.
    1 superficial BARYON level   n$^0$ → p$^+$ + e$^−$ + ν $_e$    The neutron ( n$^0$ ) emits an electron ( e$^−$ ) and its antineutrino ( ν $_e$) and becomes a proton ( p$^+$ ). 2 deeper BOSON level n$^0$ → p$^+$ + W$^−$  The neutron ( n$^0$ ) emits a W$^−$ boson and becomes a proton ( p$^+$ ).  ⤷ e$^−$ + ν $_e$  The W$^−$ boson decays into an electron ( e$^−$ ) and its antineutrino ( ν $_e$). 3 deeper still intra-NUCLEON level  ( u d d ) → ( u d u ) + W$^−$  One of the down quarks in the neutron emits a W$^−$ boson and becomes an up quark.  ⤷ e$^−$ + ν $_e$  The W$^−$ boson decays into an electron ( e$^−$ ) and its antineutrino ( ν $_e$). 4 deepest QUARK level d → u + W$^−$  A down quark ( d ) emits a W$^−$ boson and becomes an up quark ( u ).  ⤷ e$^−$ + ν $_e$  The W$^−$ boson decays into an electron ( e$^−$ ) and its antineutrino ( ν $_e$).

## Neutron lifetime puzzle

While the neutron lifetime has been studied for decades, there currently exists a lack of consilience on its exact value, due to different results from two experimental methods ("bottle" versus "beam"). The "neutron lifetime anomaly" was discovered after the refinement of experiments with ultracold neutrons. While the error margin was once overlapping, increasing refinement in technique which should have resolved the issue has failed to demonstrate convergence to a single value. The difference in mean lifetime values obtained as of 2014 was approximately 9 seconds. Further, a prediction of the value based on quantum chromodynamics as of 2018 is still not sufficiently precise to support one over the other. As explained by Wolchover (2018), the beam test would be incorrect if there is a decay mode that does not produce a proton.
On 13 October 2021 the lifetime from the bottle method was updated to $\tau _{n}=877.75s$ increasing the difference to 10 seconds below the beam method value of $\tau _{n}=887.7s$ and also on the same date a novel third method using data from the past NASA's Lunar prospector mission reported a value of $\tau _{n}=887s$ but with great uncertainty.
Yet another approach similar to the beam method has been explored with the Japan Proton Accelerator Research Complex (J-PARC) but it is too imprecise at the moment to be of significance on the analysis of the discrepancy.