Neutron physics — the use of slow / thermal / cold neutrons as a condensed-matter probe, exploiting (i) electrical neutrality (deep penetration, no Coulomb scattering), (ii) wavelength comparable to interatomic spacing for thermal neutrons…
neutron-physics
de Broglie wavelength: λ = h/(m_n·v)
The de Broglie 1924 matter-wave hypothesis assigns every massive particle of momentum p = m·v a quantum-mechanical wavelength λ = h/p =…
Bragg diffraction: n·λ = 2·d·sin(θ)
W. L. Bragg 1913 derivation (Nobel 1915): coherent scattering off a crystal's parallel lattice planes at spacing d has constructive…
SANS: |Q| = (4π/λ)·sin(θ/2)
Small-angle neutron scattering (SANS) measures the coherent elastic-scattering differential cross-section dσ/dΩ as a function of…
de Broglie velocity ratio: λ(2v)/λ(v) = 1/2
Sympy-exact witness of the de Broglie wavelength-velocity inverse proportionality. Setup: λ = h/(m_n·v). Identity: doubling v halves λ —…
Bragg anchor: d(n=1, θ=π/6) = λ
Sympy-exact witness of the Bragg-law canonical anchor. Setup: d = n·λ/(2·sin(θ)); specialise to n=1 → d = λ/(2·sin(θ)). Identity: at θ =…
SANS extremes: Q(θ=0)=0; Q(θ=π)=4π/λ
Sympy-exact witness of the SANS scattering-vector extreme limits. Setup: |Q| = (4π/λ)·sin(θ/2). Identity 1 (forward, θ=0): sin(0) = 0, so…
Maxwell-Boltzmann thermal-neutron speed distribution; Schwartz-distribution
Maxwell-Boltzmann thermal-neutron-distribution framework (Maxwell 1860 Phil Mag 19, 19; Boltzmann 1872 Wien Sitzber 66, 275). Setup:…
1/v law absorption cross-section sigma(v) = sigma_0 v_0/v; Riemann-integrable
1/v-law neutron-absorption framework (Bohr 1936 Nature 137, 344; Bethe 1937 Rev Mod Phys 9, 69). Setup: for thermal neutrons (E < 1 eV),…
Neutron-diffusion length L^2 = D/Sigma_a; vector-field flux
Neutron-diffusion-length framework (Fermi 1936 Ricerca Sci 7, 13; Glasstone-Edlund 1952). Setup: thermal-neutron flux phi(r) in a…
Theorem: v_p^2 - 2 k T/m = 0 (Maxwell-Boltzmann most-probable-speed identity)
Theorem (Maxwell-Boltzmann v_p canonical): v_p = sqrt(2 k T/m) squared yields v_p² = 2 k T/m; residual v_p² - 2 k T/m = 0 identically.…
Theorem: sigma(v) v - sigma_0 v_0 = 0 (1/v-law product invariance)
Theorem (1/v-product canonical): sigma(v) = sigma_0 v_0/v multiplied by v yields sigma(v) v = sigma_0 v_0 = constant. Residual: sigma(v) v…
Theorem: L^2 Sigma_a - D = 0 (neutron-diffusion-length identity)
Theorem (diffusion-length canonical): L = sqrt(D/Sigma_a) squared and multiplied by Sigma_a gives L² Sigma_a = D, residual L² Sigma_a - D =…
Neutron (Chadwick 1932)
J Chadwick 1932 (Nobel 1935) neutron-discovery; alpha + Be -> C + n; modern thermal-neutron + cold-neutron + ultracold-neutron sources.
Fermi pile (CP-1 1942)
E Fermi 1942 Chicago Pile-1 first self-sustaining nuclear chain reaction; modern Generation IV + thorium reactor designs; ITER-fusion…
Ultracold neutrons (UCN)
ILL + LANL + PSI UCN sources; 200 neV kinetic-energy storable in material/magnetic traps; basis of EDM + neutron-lifetime + gravity…
Neutron EDM
ILL-PNPI 2020 |d_n| < 1.8e-26 e cm; CP-violation strict-limit; modern N2EDM at PSI + Crystal at ORNL aim for 10^-28 sensitivity.
Neutron lifetime
Bottle ~ 877 s vs beam ~ 888 s ~10 sigma discrepancy; modern UCNtau 2021 ultracold-magnetic 877.7 +/- 0.7 s tightest measurement.
Neutron scattering (Nobel 1994)
C Shull-B Brockhouse Nobel 1994 elastic + inelastic neutron-scattering; modern SNS + ILL + JPARC/MLF; magnetic + phonon + biological…
Neutron (Chadwick 1932)
J Chadwick 1932 (Nobel 1935) neutron-discovery; modern modern foundational + ESS 2024 + ISIS-pulsed-source + 14-MeV-DT-fusion-source.
Neutron scattering (Shull-Brockhouse 1994)
C Shull-B Brockhouse 1994 (Nobel 1994) elastic / inelastic-neutron-scattering; modern modern foundational text + 2024 SANS…
UCN (Fermi 1934)
E Fermi 1934 (Nobel 1938) UCN; modern modern foundational + UCN-EDM + 2024 LANSCE NIST-EDM neutron lifetime 887 s β-decay tension.
Neutron lifetime (Wietfeldt-Greene 2011)
F Wietfeldt-G Greene 2011 + 2024 4σ tension beam-vs-bottle 887.7±0.3 vs 877.7±0.7 s; modern modern foundational text + sterile-neutron…
Fission (Meitner-Frisch 1939)
L Meitner-O Frisch 1939 fission interpretation; modern modern foundational + Hahn-Strassmann 1938 + 2024 fast-reactor + thorium SMR design.
Breit-Wigner (1936)
G Breit-E Wigner 1936 resonance σ(E) = πλ²/(E-E_0)²+Γ²/4; modern modern foundational + 2024 nuclear-data-evaluation ENDF / TENDL.