How Do You Weigh a Particle Moving at Half the
Speed of Light?
There are basically two ways to weigh subatomic particles that are
moving at a substantial fraction of the speed of light.
1) You can slow down and stop the particles in a series of detectors
that measure the rate that the particles are slowing down (their energy
loss), or their velocity. The rate at which a particle slows down
is a strong function of the charge of the particle (which, since
these are bare nuclei with only protons and neutrons, tells you the
number of protons, i.e. the element). The energy loss is a much
weaker function of the mass (the number of protons + neutrons) of
the particle, but from the small differences in slowing down, you
can determine the mass. Typically, in order to measure the difference
between Iron-56 and Iron-57 for example, which differ by less than 2%
in mass, you need to get your error (sigma) in the mass measurement
down to about .25% or one in four hundred. The
CRIS (http://www.srl.caltech.edu/ACE/CRIS_SIS/cris.html) instrument on ACE
is an example of this type of detector system.
2) You can use a strong magnetic field to bend the track of the charged
particle (cosmic ray). If you measure the curvature of the track (with
drift chamber detectors for example) and have an independent measure of
the particle velocity (with a time-of-flight system or Cerenkov detector),
you can determine the mass.
ISOMAX (http://lheawww.gsfc.nasa.gov/docs/gamcosray/hecr/ISOMAX/) uses this method. It has a pair of superconducting
magnets that generates a magnetic field that is more than 1 Tesla