How this calculator works
Energy and momentum conservation give a photon wavelength increase that depends on target rest mass and photon deflection angle. The target is assumed free and at rest before collision. The deflection angle is between the incoming and outgoing photon directions. Forward scattering has zero shift and cannot determine a mass. Backscattering gives the largest increase, twice the ordinary Compton wavelength. Binding, moving targets and multiple scattering require a different model.
Formula
Delta lambda = h(1-cos theta)/(mc) = 2h sin²(theta/2)/(mc); 0 <= theta <= pi. Picometres use 1 pm = 1e-12 m.
Worked example
For an electron of mass 9.1093837015e-31 kg, a 90 degree scatter adds about 2.426310239 pm. A 180 degree scatter adds 4.852620477 pm.
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Frequently asked questions
Does the incoming wavelength matter?
It affects the outgoing photon energy, but the wavelength increase in this model depends only on mass and angle.
Can the shift be negative?
Not for a free target initially at rest. A moving target can transfer energy to the photon.
Why can zero shift not give a mass?
At zero angle every positive mass gives zero shift, so there is no unique inverse.