Reduced Compton wavelength of the electron

Where λ_C = h/(m_e c) is the wavelength that appears in Compton's scattering formula, the reduced version ƛ_C = ħ/(m_e c) is the one that appears in field theory: it is the range of the Yukawa potential for an exchanged particle of mass m_e, and the length at which the Dirac equation's zitterbewegung operates. The same construction applied to the pion mass gives about 1.4 fm, which is why the strong nuclear force reaches roughly that far and no further.

It slots neatly into the hierarchy of atomic lengths, each rung a factor of α = 1/137 apart: the Bohr radius 5.29 × 10⁻¹¹ m, then ƛ_C = α a₀ = 3.86 × 10⁻¹³ m, then the classical electron radius r_e = α ƛ_C = 2.82 × 10⁻¹⁵ m. The trap is simply which one a formula wants: a stray 2π between λ_C and ƛ_C is the same mistake as confusing h with ħ.