Dynamic geometric representation of the two-dimensional Compton effect.
Diagram in the space of energy / moment, modifiable in 4 ways:
1-Change the perspective simply by dragging the background with the mouse.
2-Moving the red point (I) around the lower circumference, changes the direction of incidence of the photon
3-Moving the red point (e2) around the upper ellipse, modifies the exit direction of the electron
4-Moving vertically the red point (V), changes the speed of the center of m / E of the collision
Image elements:
Natural units (c = h = m = 1)
Spatial coordinate axes: x (unit vector u1), y (unit vector u2)
base circumference: radius equal to the Compton length of the electron (or any other particle with mass which is struck by a photon)
Point C: It is the center of the figure, it is on the line of the collision cdm, and also in the center of the initial vectors (E, p) (f1, e1) as well as of the final vectors (f2, e2)
Elements corresponding to the electron:
initial (e1, at rest) and final (e2, in the upper ellipse) vectors
electronic ellipse passing through e1 and e2: locus of all possible vectors resulting from the collision
Elements corresponding to the photon (dotted lines):
initial (f1, in the direction of incidence indicated by the red dot I) and final (f2, in the lower ellipse) vectors
photon ellipse, passing through f1 and f2: locus of all possible photon vectors involved in the collision
The base points (f1 ', f2', e1 ', e2') are the projections in the moment space of the corresponding space-time vectors.
They are shown separately in the image at the right side.
Numerical values that are shown:
3d (1,2) view:
v (red color): corresponding to the velocity of the center of momentum/energy, as well as to the speed of the boost from the symmetric RS
Energy (E) and momentum (p) for the dispersed electron and photons
2d view (right side)
dispersion angles for the electron (de, in red color) and the scattered photon (d2, in blue color)