### Experimental Examples (continued)

#### Particle Identification

We'd like to know whether a charged track is due to a e+, μ+, π+, K+, or p. This is the task of particle identification. There are several ways to differentiate particle types:

• differences in the way they interact -- electrons readily bremstrahl and compton scatter, pions, kaons, and protons interact strongly, muons do neither.
• sort out the possibilities by the kinematics of a decay.
• differences in mass.

### Energy loss formula

The Bethe-Bloch formula:

-dE/dx = Kz2(Z/A)(1/β2)[(1/2)ln(2mec2β2γ2Tmax/I2) - β2 - δ/2]

Taking a look at Fig. 26.1 in the Review of Particle Properties handout, we can see the range over which the Bethe-Bloch formula is applicable, from βγ of about 0.1 to several hundred. This plot is for μ+, but the conclusion about the range of applicability of the Bethe-Block formula is true for all heavy charged particles, μ, π, K, p, and d. I will ignore the region of βγ<0.1 as it is not generally important in particle physics experiments.

The region of βγ> few hundred is where radiative losses (bremstrahlung) turns on. For corresponds to muon momenta greater than about 100 GeV/c. Again, most experiments don't have muons of such high momentum, so that bremstrahlung by muons and heavier particles is basically ignored. (There are people now considering the effects of muon bremstrahlung in the next generation of experiments.) Bremstrahlung is an important effect for electrons.

The energy loss function has a minimum around βγ=3. The energy loss at this point is known as minimum ionizing, and a particle with this energy is called a minimum ionizing particle or MIP. This value is important, since it quantifies the smallest signals that a particular detector expects to see.

The quantity I is the mean excitation energy for the material. As can be seen in Figure 26.5, I depends on the material composition. This plot demonstrates that the I is approximately given by:

I = [(10±1)eV] Z
This relation works

For a particle of mass M and speed βc, Tmax is given by

Tmax = (2mec2β2γ2)/(1 + 2γme/M + (me/M)2).

Again looking at Figure 26.3, we see that the mean energy loss decreases for heavier elements. This counterintuitive effect is compensated for by the (normally) higher density of material composed of heavy elements.

### Multiple Coulomb Scattering (MCS)

Particles lose little energy in collisions with atomic nuclei, but their trajectory will be perturbed. We say that particles are scattered when passing through matter due to electromagnetic interactions with the nucleus (Coulomb scattering). This scattering is analogous to Rutherford scattering. For single interactions, the resulting distribution of scattered angles can be calculated similarly to the Rutherford scattering formula.

Normally particles must traverse modest thicknesses of material in which they can experience many scatters. This is the case we are now interested in and it is called multiple coulomb scattering or MCS for short. After many scatters, the resulting distribution of scattered angles is roughly Gaussian:

P(θ)dθ = (2π)-1/2θ0-1 exp(θ2/2θ02)dθ
with θ0 given by:
θ0 = (13.6MeV/βcp)z(x/X0)1/2 [1 + 0.038ln(x/X0)].
The quantity X0 is called the radiation length of the material. It characterizes electromagnetic interactions with nuclei of the material.