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…