Subatomic Physics

5.3. Mass Measurements 89
Figure 5.7: Aston’s mass spectrometer.
short-lived isotopes, (9) an issue of great importance to understand the production
of elements in stars (see Chapter 19.)
Mass spectroscopy works well for nuclei, but it is difficult (or impossible) to
apply to most particles. In the mass spectrometer, all ions start with a very small
(thermal) velocity and are accelerated in the same field. Their relative masses
can therefore be determined very accurately. However, particles are produced in
reactions, and their initial velocities are not accurately known. Moreover, some of
the particles are neutral and cannot be deflected. Different approaches are necessary,
and they are based on Eqs. (1.2) and (1.7):
p = mγv
(1.2)
(1.7)
E 2 = p 2 c 2 + m 2 c 4
γ =
1
(1 − (v/c) 2 . (1.6)
) 1/2
These relations show that the mass of a particle can be computed if momentum
and energy or momentum and velocity are known. Many techniques are based on
this fact, and the arrangement shown in Fig. 5.8 provides an example. A magnet
selects particles with momentum p. Two scintillation counters, S1 and S2, record
the passage of a particle. The time delay between pulses S2 and S1 can be measured
and, with the distance between S1 and S2 known, the velocity can be computed.
Together, momentum and velocity give the mass.
The method just discussed fails if the particle is neutral or if its life-time is so
9 These techniques have been brought to a fine point by H.-J. Kluge and collaborators, see K.
Blaum, Phys. Rep. 425, 1 (2006).