Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

R/M (g cm −2 GeV −1 )
50000
20000
10000
5000
2000
1000
500
200
100
50
20
10
5
2
27. Passage of particles through matter 233
Pb
H 2 liquid
He gas
1
0.1 2 5 1.0 2 5 10.0 2 5 100.0
βγ = p/Mc
0.02 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0
Muon momentum (GeV/c)
0.02 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10.0
Pion momentum (GeV/c)
0.1 0.2 0.5 1.0 2.0 5.0 10.0 20.0 50.0
Proton momentum (GeV/c)
Figure 27.4: Range of heavy charged particles in liquid (bubble
chamber) hydrogen, helium gas, carbon, iron, and lead. For example:
For a K + whose momentum is 700 MeV/c, βγ =1.42. For lead we
read R/M ≈ 396, and so the range is 195 g cm−2 .
�ωp. Since the plasma frequency scales as the square root of the electron
density, the correction is much larger for a liquid or solid than for a gas,
as is illustrated by the examples in Fig. 27.2.
The remaining relativistic rise comes from the β2γ 2 growth of Tmax,
which in turn is due to (rare) large energy transfers to a few electrons.
When these events are excluded, the energy deposit in an absorbing
layer approaches a constant value, the Fermi plateau (see Sec. 27.2.6
below). At extreme energies (e.g., > 332 GeV for muons in iron, and
at a considerably higher energy for protons in iron), radiative effects are
more important than ionization losses. These are especially relevant for
high-energy muons, as discussed in Sec. 27.6.
27.2.5. Energetic knock-on electrons (δ rays) : The distribution of
secondary electrons with kinetic energies T ≫ I is [2]
d2N 1 Z 1
= Kz2
dT dx 2 A β2 F (T )
T 2
(27.7)
for I ≪ T ≤ Tmax, whereTmax is given by Eq. (27.4). Here β is the
velocity of the primary particle. The factor F is spin-dependent, but is
about unity for T ≪ Tmax. For spin-0 particles F (T )=(1−β2T/Tmax); forms for spins 1/2 and 1 are also given by Rossi [2]. For incident
electrons, the indistinguishability of projectile and target means that the
Fe
C