When embedded in an

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester ...

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

s are (usually) stable particles. Outside the nucleus, free neutrons are unstable and have a mean lifetime of or (about and or , respectively). Therefore, the

half-life Half-life is a mathematical and scientific description of exponential or gradual decay. Half-life, half life or halflife may also refer to: Film * Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang * ''Half Life: ...

for this process (which differs from the mean lifetime by a factor of ) is (about , ). The free neutron decays primarily by

beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron ...

, with small probability of other channels. The beta decay of the neutron can be described at different levels of detail, starting with the simplest: : 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 . 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 In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

. 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 . The latter number is not well-enough measured to determine the comparatively tiny rest mass of the

neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...

(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 A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...

: : 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 In physics and chemistry, ionization energy (IE) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, Ion, positive ion, or molecule. The first ionization energy is quantitatively expressed as : ...

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

), 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 Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. Th ...

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 The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...

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 In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number. Until the 1960s, nucleons were thought to be ele ...

(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 () 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. :

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 In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of ...

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=877.75 s

increasing the difference to 10 seconds below the beam method value of

\tau_n=887.7 s

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=887 s

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. One possible explanation for the difference is multiple elastic neutron scattering between neutrons, and between neutrons and the trap walls. This would decrease the lifetime of the involved neutrons only in the bottle method, and the effect would depend on the shape of the bottle.

Footnotes

References

Bibliography