Neutron · R.A.V.E.N. Living Encyclopedia

The neutron (n) is a baryon of spin ½, electric charge zero, and rest mass m_n = 1.674 927 500 56(85) × 10⁻²⁷ kg, equivalent to a rest energy of 939.565 421 94(48) MeV (Mohr et al. 2025). It is a colour-singlet bound state of the quark and gluon fields of quantum chromodynamics with valence content udd; the quark masses contribute of order 1% of the neutron mass, and the remainder is the kinetic and field energy of the confined system (Dürr et al. 2008). It is a quantum object, localised in detection and described in diffraction and in bound states by a wavefunction of de Broglie wavelength λ = h/p; in the deuteron it occupies a stationary state bound to a proton with a separation energy of 2.224 566 27(46) MeV (Wang et al. 2021). It carries no net electric charge, the measured value being (−0.4 ± 1.1) × 10⁻²¹ e (Baumann et al. 1988), and it sources a magnetic dipole field of moment −1.913 042 76(45) nuclear magnetons (Mohr et al. 2025). It participates in the strong, electromagnetic and weak interactions. Elastic scattering resolves an internal charge distribution of mean square radius ⟨r²⟩_E = −0.1155(17) fm², the negative sign indicating negative charge density at large radius, and a root-mean-square magnetic radius of 0.864(9) fm (Mohr et al. 2025; Navas et al. 2024). The free neutron decays by the weak interaction to a proton, an electron and an electron antineutrino with a mean lifetime of 878.4(5) s (Navas et al. 2024); a neutron bound in a stable nucleus does not decay. Neutron capture in the slow and rapid processes synthesises the elements beyond iron (Burbidge et al. 1957; Cowan et al. 2021), and degenerate neutrons constitute the interior of a neutron star above the nuclear saturation density 2.8 × 10¹⁷ kg m⁻³ (Lattimer & Prakash 2004). The neutron was identified by Chadwick (1932) from the recoil energies of nuclei struck by the neutral radiation emitted when beryllium is bombarded with alpha particles.

02 · Equations

Governing equations

The neutron is a composite state of quantum chromodynamics (QCD); its mass, magnetic moment and form factors follow from that theory, while its decay requires the electroweak interaction. Relations are written in SI units with neutron mass m_n and elementary charge e; numerical values are from the CODATA 2022 adjustment (Mohr et al. 2025) and the Particle Data Group review (Navas et al. 2024).

Master · QCD Lagrangian

QCD Lagrangian density

$$\mathcal L_{\rm QCD}=\sum_{q}\bar q\left(i\hbar c\,\gamma^\mu D_\mu-m_qc^2\right)q-\tfrac14\,G^a_{\mu\nu}G^{a\,\mu\nu},\qquad D_\mu=\partial_\mu-\frac{ig_s}{\hbar c}A^a_\mu T^a$$

The neutron is the colour-singlet ground state of valence content udd. Confinement, the mass scale, the magnetic moment and the elastic form factors given below follow from this Lagrangian; the neutron–proton mass difference and free-neutron decay require in addition quantum electrodynamics and the electroweak sector.

01 · Mass

Neutron–proton mass difference

$$\begin{gathered}\left(m_n-m_p\right)c^2=1.293\,332\,51(48)\ \mathrm{MeV},\\ \left(m_n-m_p\right)c^2=\Delta_{\rm QCD}+\Delta_{\rm QED}\end{gathered}$$

The neutron–proton rest energy difference is 1.293 332 51(48) MeV (Mohr et al. 2025). Lattice quantum chromodynamics combined with quantum electrodynamics separates it into a strong-isospin term of 2.52(41) MeV set by the down–up quark mass difference and an electromagnetic term of −1.00(16) MeV (Borsanyi et al. 2015).

02 · Decay

Free-neutron beta decay

$$\begin{gathered}n\to p+e^-+\bar\nu_e,\qquad Q=0.782\,333\ \mathrm{MeV},\\ \frac{1}{\tau_n}=\frac{G_F^2\,|V_{ud}|^2\,m_e^5c^4}{2\pi^3\hbar^7}\left(1+3\lambda^2\right)f\left(1+\Delta_R\right)\end{gathered}$$

The released energy Q = 0.782 333 MeV is the difference of the neutron, proton and electron rest energies (computed from Mohr et al. 2025). The rate is fixed by the Fermi constant, the quark mixing element |V_ud|, the phase-space factor f, the axial-to-vector ratio λ and the radiative correction Δ_R (Czarnecki et al. 2018). The measured mean lifetime is 878.4(5) s (Navas et al. 2024).

03 · Weak couplings

Axial-to-vector ratio

$$\begin{gathered}\lambda=\frac{g_A}{g_V}=-1.276\,41(56),\\ a=\frac{1-\lambda^2}{1+3\lambda^2},\qquad A_0=-2\,\frac{\lambda^2+\lambda}{1+3\lambda^2}\end{gathered}$$

The ratio λ governs the angular correlations in neutron decay: a is the electron–antineutrino correlation coefficient and A₀ is the electron asymmetry with respect to the neutron spin. The value λ = −1.276 41(56) comes from A₀ measured with polarised cold neutrons (Märkisch et al. 2019); taken with the lifetime it determines |V_ud| without nuclear-structure corrections (Czarnecki et al. 2018).

04 · Magnetism

Magnetic moment

$$\begin{gathered}\mu_n=g_n\,\frac{e\hbar}{4m_n}=-1.913\,042\,76(45)\,\mu_N,\\ g_n=-3.826\,085\,52(90),\qquad \frac{\mu_n}{\mu_p}=-0.684\,979\,34(16)\end{gathered}$$

A neutral point-like Dirac particle has no magnetic moment. The measured value −1.913 042 76(45) nuclear magnetons is a consequence of the charged constituents (Mohr et al. 2025); the non-relativistic quark model with valence content udd predicts μ_n/μ_p = −2/3, which reproduces the measured ratio to 3% (Bég et al. 1964).

05 · Size

Charge and magnetic form factors

$$\begin{gathered}\frac{d\sigma}{d\Omega}=\left(\frac{d\sigma}{d\Omega}\right)_{\!\rm Mott}\frac{G_E^2+\tau G_M^2}{1+\tau}+2\tau G_M^2\tan^2\frac{\theta}{2},\\ \langle r^2\rangle_E=-6\hbar^2\left.\frac{dG_E}{dQ^2}\right|_{Q^2=0}\end{gathered}$$

The Sachs form factors G_E and G_M describe the distributions of charge and magnetisation, with τ = Q²/4m_n²c². For the neutron G_E(0) = 0, and the slope at zero momentum transfer gives ⟨r²⟩_E = −0.1155(17) fm², obtained from the scattering of low-energy neutrons by atomic electrons; the root-mean-square magnetic radius is 0.864(9) fm (Mohr et al. 2025; Navas et al. 2024).

06 · Bound state

The deuteron

$$\begin{gathered}\left[-\frac{\hbar^2}{2\mu}\frac{d^2}{dr^2}+V(r)\right]u=-Bu,\\ B=2.224\,566\,27(46)\ \mathrm{MeV},\qquad \mu=\frac{m_nm_p}{m_n+m_p}\end{gathered}$$

The deuteron is the single bound state of two nucleons, with separation energy B = 2.224 566 27(46) MeV (Wang et al. 2021) and spin-parity 1⁺ (Navas et al. 2024). Its electric quadrupole moment 0.2859(3) fm² requires an admixture of the D state of about 4%, which measures the tensor component of the nucleon–nucleon interaction (Ericson & Rosa-Clot 1983).

07 · Neutron optics

de Broglie wavelength and Bragg condition

$$\begin{gathered}\lambda=\frac{h}{m_nv},\qquad \lambda\!\left(2200\ \mathrm{m\,s^{-1}}\right)=0.1798\ \mathrm{nm},\\ n_{\rm ref}=1-\frac{\lambda^2}{2\pi}Nb_c,\qquad 2d\sin\theta=m\lambda\end{gathered}$$

A neutron in thermal equilibrium at 293.6 K moves at 2200 m s⁻¹ and has a de Broglie wavelength of 0.1798 nm, comparable to interatomic spacings, so crystals diffract neutrons (Wollan & Shull 1948; computed from Mohr et al. 2025). The coherent scattering length b_c varies between isotopes and does not increase with atomic number, so the method locates light nuclei in a lattice.

08 · Bulk matter

Degenerate neutron matter

$$\begin{gathered}P_{\rm deg}=\frac{\hbar^2}{15\pi^2m_n}\left(3\pi^2n\right)^{5/3},\\ \frac{dP}{dr}=-\frac{G\left(\varepsilon+P/c^2\right)\left(m+4\pi r^3P/c^2\right)}{r\left(r-2Gm/c^2\right)}\end{gathered}$$

The first relation is the pressure of a non-relativistic degenerate neutron gas of number density n; the second is the relativistic equation of hydrostatic equilibrium (Tolman 1939; Oppenheimer & Volkoff 1939). Integration with a nuclear equation of state fixes the mass–radius relation, and the measured mass of PSR J0740+6620 is 2.08(7) solar masses (Fonseca et al. 2021).

03 · Numbers

Measured properties

Recommended values from the CODATA 2022 adjustment (Mohr et al. 2025), the exact 2019 SI definition of the elementary charge, and Particle Data Group averages and limits (Navas et al. 2024). Parenthesised digits give the standard uncertainty in the final digits shown.

(−0.4 ± 1.1) × 10⁻²¹ e

Charge · measured · Baumann et al. 1988

939.565 421 94 MeV

Rest energy m_nc² · Mohr et al. 2025

⟨r²⟩_E = −0.1155(17) fm²

Mean square charge radius · Mohr et al. 2025

|d_n| < 1.8 × 10⁻²⁶ e·cm

Electric dipole moment · limit · 90% CL · Abel et al. 2020

Quantity	Value	Status	Meaning & convention
Electric charge	(−0.4 ± 1.1) × 10⁻²¹ e	measured · ± 1.1 × 10⁻²¹ e	Deflection of a cold neutron beam in an electric field gives q_n = (−0.4 ± 1.1) × 10⁻²¹ e, consistent with zero (Baumann et al. 1988).
Mass	1.674 927 500 56(85) × 10⁻²⁷ kg	measured · 5.1 × 10⁻¹⁰	Equivalently 1.008 664 916 06(40) u (Mohr et al. 2025).
Rest energy	939.565 421 94(48) MeV	derived · m_nc²	Energy of one neutron at rest (Mohr et al. 2025).
Neutron–proton mass difference	1.293 332 51(48) MeV	derived · (m_n−m_p)c²	Sets the energy released in beta decay and the neutron fraction entering primordial nucleosynthesis (Mohr et al. 2025).
Spin	½ ℏ	exact · representation	Intrinsic angular momentum; a fermion, obeying the Pauli exclusion principle (Navas et al. 2024).
Valence quark content	udd	exact · flavour assignment	One up quark and two down quarks in a colour singlet; isospin partner of the proton (Navas et al. 2024).
Magnetic moment	−9.662 3653(23) × 10⁻²⁷ J T⁻¹	measured · 2.4 × 10⁻⁷	Equivalently −1.913 042 76(45) nuclear magnetons; antiparallel to the spin (Mohr et al. 2025).
g-factor	−3.826 085 52(90)	measured · 2.4 × 10⁻⁷	A neutral point-like Dirac particle would have g = 0; the measured value reflects the charged constituents (Mohr et al. 2025).
Gyromagnetic ratio	1.832 471 74(43) × 10⁸ s⁻¹ T⁻¹	measured · 2.4 × 10⁻⁷	Equivalently γ_n/2π = 29.164 6935(69) MHz T⁻¹, the Larmor frequency per unit field (Mohr et al. 2025).
Mean square charge radius	−0.1155(17) fm²	measured · 1.5 × 10⁻²	From the neutron–electron scattering length; the negative sign indicates negative charge density at large radius (Mohr et al. 2025).
Magnetic radius	0.864(9) fm	measured · 1.0 × 10⁻²	Root-mean-square radius from the magnetic form factor G_M (Navas et al. 2024).
Compton wavelength	1.319 590 903 82(67) fm	derived · h/m_nc	Length scale at which pair creation becomes relevant; not a spatial extent (Mohr et al. 2025).
Mean lifetime	878.4(5) s	measured · 5.7 × 10⁻⁴	Free-neutron beta decay; a neutron bound in a stable nucleus does not decay (Navas et al. 2024).
Electric dipole moment	\|d_n\| < 1.8 × 10⁻²⁶ e·cm	limit · 90 % CL	Abel et al. (2020), ultracold neutrons. A non-zero value would violate time-reversal symmetry.

Sources · NIST CODATA 2022 (physics.nist.gov/constants) · PDG 2024 neutron listing S017 · Abel et al. PRL 124, 081803 (2020) · Märkisch et al. PRL 122, 242501 (2019) · Borsanyi et al. Science 347, 1452 (2015)

04 · Situations

Representative configurations

Six configurations computed from CODATA 2022 constants: the deuteron, Larmor precession in a uniform magnetic field, Bragg diffraction from a crystal, free-neutron beta decay, the recoil experiment of Chadwick (1932), and degenerate matter in a neutron-star interior. Each scene states any scale factor applied to the rendering.

05 · Latest research

Recent literature

Preprints and papers retrieved at page load, ordered by submission date. arXiv: categories nucl-ex, nucl-th, hep-ex, hep-ph and astro-ph.HE, abstracts matching the neutron lifetime, the neutron electric dipole moment, beta-decay correlations, ultracold neutrons, neutron scattering lengths or neutron-star matter. INSPIRE-HEP: the same terms in titles of high-energy-physics records. Dates are arXiv submission dates and INSPIRE record dates; no publisher issue dates are used.

Querying arXiv · INSPIRE-HEP …

Date	Source	Title and authors	Reference
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06 · References

References

Declared representations

Valence quarks are illustrativeThe three points inside the hero are the valence quarks of content udd moving within the confinement radius; their positions are illustrative and their colours cycle to indicate colour exchange.

The charge distribution has no edgeThe inner positive and outer negative shells indicate the sign of the charge density implied by the negative mean square charge radius (Mohr et al. 2025); the neutron has no surface, and the density falls off smoothly.

The spin axis is a quantum numberNothing rotates. The axis shows the spin direction, and the magnetic dipole field is drawn antiparallel to it because the g-factor is negative (Mohr et al. 2025).

Declared scalingWhere a physical rate or ratio is below display resolution (the Larmor period, the decay time, the stellar interior), the applied scale factor is stated in the scene.

Sources

J. Chadwick (1932). The existence of a neutron. Proc. R. Soc. A 136, 692.

R. C. Tolman (1939). Static solutions of Einstein’s field equations for spheres of fluid. Phys. Rev. 55, 364.

J. R. Oppenheimer & G. M. Volkoff (1939). On massive neutron cores. Phys. Rev. 55, 374.

E. O. Wollan & C. G. Shull (1948). The diffraction of neutrons by crystalline powders. Phys. Rev. 73, 830.

E. M. Burbidge, G. R. Burbidge, W. A. Fowler & F. Hoyle (1957). Synthesis of the elements in stars. Rev. Mod. Phys. 29, 547.

M. A. B. Bég, B. W. Lee & A. Pais (1964). SU(6) and electromagnetic interactions. Phys. Rev. Lett. 13, 514.

T. E. O. Ericson & M. Rosa-Clot (1983). The deuteron asymptotic D-state as a probe of the nucleon–nucleon force. Nucl. Phys. A 405, 497.

J. Baumann et al. (1988). Experimental limit for the charge of the free neutron. Phys. Rev. D 37, 3107.

J. M. Lattimer & M. Prakash (2004). The physics of neutron stars. Science 304, 536.

S. Dürr et al., BMW (2008). Ab initio determination of light hadron masses. Science 322, 1224.

S. Borsanyi et al. (2015). Ab initio calculation of the neutron–proton mass difference. Science 347, 1452.

A. Czarnecki, W. J. Marciano & A. Sirlin (2018). Neutron lifetime and axial coupling connection. Phys. Rev. Lett. 120, 202002.

B. Märkisch et al., PERKEO III (2019). Measurement of the weak axial-vector coupling constant in the decay of free neutrons. Phys. Rev. Lett. 122, 242501.

C. Abel et al., nEDM (2020). Measurement of the permanent electric dipole moment of the neutron. Phys. Rev. Lett. 124, 081803.

E. Fonseca et al. (2021). Refined mass and geometric measurements of the high-mass PSR J0740+6620. Astrophys. J. Lett. 915, L12.

T. E. Riley et al. (2021). A NICER view of the massive pulsar PSR J0740+6620. Astrophys. J. Lett. 918, L27.

J. J. Cowan et al. (2021). Origin of the heaviest elements: the rapid neutron-capture process. Rev. Mod. Phys. 93, 015002.

M. Wang et al. (2021). The AME 2020 atomic mass evaluation (II). Tables, graphs and references. Chin. Phys. C 45, 030003.

S. Navas et al., Particle Data Group (2024). Review of particle physics. Phys. Rev. D 110, 030001.

P. J. Mohr et al. (2025). CODATA recommended values of the fundamental physical constants: 2022. Rev. Mod. Phys. 97, 025002 · physics.nist.gov/constants · PDG neutron listing.