2D companion to the 3D Mössbauer Effect Lab, driven by the same real Debye-model physics for Fe‑57 (14.4 keV gamma, natural linewidth 4.55 neV):
- Recoil energy: E_R = E_γ² / (2 M_eff c²). A free nucleus recoils with its own mass; a lattice-bound nucleus effectively recoils with a cluster of the crystal's mass, so E_R is far smaller.
- Recoil-free fraction (Lamb–Mössbauer factor): f = exp[ −(6E_R)/(k_B Θ_D) · (1/4 + D₁(Θ_D/T)/(Θ_D/T)) ], the standard Debye-model formula, evaluated live from the temperature slider and the Debye integral D₁.
- Effective linewidth: Γ = Γ_nat / f — as fewer decays are recoil-free, the visible resonance effectively broadens.
- Doppler scan: sliding the source at velocity v shifts the emitted photon energy by ΔE = E_γ·v/c. Transmission through the absorber follows a Lorentzian dip, T(v) = 1 − f·Γ²/(ΔE² + Γ²), narrowest and deepest exactly when f is largest — the real scanning technique used in Mössbauer spectroscopy.