A Simple Estimate of the Mass of the Positron
Fig.1 A positive track curling to the left seems to change its sign (red). What is happening is that a positron collides head-on a stationary electron and loses all its momentum. this shows that the positron has the same mass as the electron.
The curves measurements performed at CERN give a magnitude
of 54
15MeV/c for the incident positron and 54
13MeV/c for the leaving electron ( Systematic errors are negligible in
comparison with the large statistical errors, forced upon us by the short lengths
of track that can sensibly be used for measurements, typically 3 cm.)
Momentum and energy conservation in the head-on collision of a positron and an electron give:
(1)
(2)
Eliminating the final momentum of the positron,
, and solving eq. (1) and (2), one can calculate the fraction of the
positron’s momentum that is imparted to the electron:
(3)
For equal masses, the target (electron) picks up all the
projectile’s momentum, so the ration
.
If the positron is stopped dead in the collision, it would then be annihilate with an electron to produce two 0.511 -MeV photons, back to back. Such low-energy photons cannot materialize into electro-positron pairs (this would violate energy conservation). However, our measurements errors allow the positron to keep » 10MeV in the bubble chamber, which could be passed on the annihilation photons.
electron-positron annihilation