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 Incoming links: Reduced Compton wavelength

Past exam of the particle and nuclear physics course of the University of Cambridge / 2012 / Paper 1 / 1 / a / Solution 2026-10-20

The static one-pion exchange propagator gives a Yukawa potential proportional to

e^{- m_{π} cr /ℏ} / r

. Its characteristic range is therefore the Reduced Compton wavelength,

R \sim \frac{ℏ c}{m _{π} c ^{2}} = \frac{197.3}{140} fm ≃ 1.4 fm .

This is an exponential falloff scale, not a sharp interaction cutoff. The ordinary Compton wavelength would introduce an unwanted factor

2 π

.

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