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 based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...

neutrons The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behave ...

are (usually) stable particles. Outside the

nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom * Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucl ...

, free

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...

s are unstable and have a

mean lifetime A quantity is subject to exponential decay if it decreases at a rate Proportionality (mathematics), proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ...

of (about , ). Therefore, the

half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...

for this process (which differs from the mean lifetime by a factor of ) is (about , ). (An article published in October 2021, arrives at for the mean lifetime). The

beta decay In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to an isobar of that nuclide. For ...

of the neutron described in this article can be notated at four slightly different levels of detail, as shown in four layers of

Feynman diagrams In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduce ...

in a section below. : The hard-to-observe quickly decays into an

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...

and its matching

antineutrino A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...

. The subatomic reaction shown immediately above depicts the process as it was first understood, in the first half of the 20th century. The

boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer s ...

() vanished so quickly that it was not detected until much later. Later, beta decay was understood to occur by the emission of a

weak boson In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , and ...

(), sometimes called a charged weak current. Beta decay specifically involves the emission of a boson from one of the

down quark The down quark or d quark (symbol: d) is the second-lightest of all quarks, a type of elementary particle, and a major constituent of matter. Together with the up quark, it forms the neutrons (one up quark, two down quarks) and protons (two up q ...

s hidden within the

, thereby converting the down quark into an

up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...

and consequently the

into a

proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

. The following diagram gives a summary sketch of the beta decay process according to the present level of understanding. Beta Negative Decay

: For diagrams at several levels of detail, see § Decay process, below. :

Energy budget

For the free neutron, the

decay energy The decay energy is the energy change of a nucleus having undergone a radioactive decay. Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy ...

for this process (based on the

rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...

es 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 energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...

. 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 a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...

(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 γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...

: : This gamma ray may be thought of as a sort of "internal

bremsstrahlung ''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typicall ...

" that arises as the emitted beta particle (electron) interacts with the

charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...

of the proton in an electromagnetic way. In this process, some of the decay energy is carried away as

photon energy Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, ...

. 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 Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...

hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...

), and therefore simply remains bound to it, as a neutral

hydrogen atom A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen consti ...

(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 transformation of a free proton to a neutron (plus a positron and a neutrino) is energetically impossible, since a free neutron has a greater mass than a free proton. However, see

proton decay In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov ...

Decay process viewed from multiple levels

Understanding of the beta decay process developed over several years, with the initial understanding of

Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...

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 (nucleon number). Until the 1960s, nucleons we ...

(the

and its successor

) 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

() 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 In science and history, consilience (also convergence of evidence or concordance of evidence) is the principle that evidence from independent, unrelated sources can "converge" on strong conclusions. That is, when multiple sources of evidence are ...

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 The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the ent ...

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 theory 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 ...

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 ''Lunar Prospector'' was the third mission selected by NASA for full development and construction as part of the Discovery Program. At a cost of $62.8 million, the 19-month mission was designed for a low polar orbit investigation of the Moon, ...

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.

Footnotes

References

Bibliography