Subatomic Physics

70 Detectors
energy Ē = E0/2 n . The shower stops when Ē = Ec, when loss of energy by
ionization becomes important.
The impact point of any particle can be obtained from the lateral spread of the
shower. In the case of an incident electron, the shower is well defined and can be
traced back.
High energy hadrons are generally not contained in an electron calorimeter, so
that a hadron calorimater tends to surround or be placed behind an electron one.
Hadrons slow through collisions with nuclei and give rise to secondary hadrons which
produce more hadrons. The exception is a particle like a π 0 , which decays primarily
into two photons and thence produces an electron shower. The mean free path of
a hadron depends on the cross section for collisions with nuclei and on the density
of the material. A typical hadron will traverse about 135 g/cm 2 in Fe. A typical
calorimater of Fe may be 2 m deep and 1/2 m in a transverse direction. For 95%
containment of the particle in the calorimeter, its length L ∼ (9.4lnE(GeV) + 39)
cm.
The shower development for electrons and for hadrons is a statistical process.
Thus, the relative accuracy increases with energy, the error being proportional to
1/ √ E0, whereE0 is the incident energy.
Muons, tauons, and neutrinos do not produce showers. Muons leave an ionization
trail which can be identified and then detected in a muon chamber (like a
calorimeter, but the muons have a high probability of not being absorbed and reaching
the layers of the chamber). In Fig. 4.19 we show examples of expected tracks
of particles through a detector planned for the LHC showing the calorimeters. The
size of the detector can be gauged by the scale on top.
4.11 Counter Electronics
The original scintillation counter, and even the original coincidence arrangement
(Fig. 4.1), needed no electronics; the human eye and the human brain provided the
necessary elements, and recording was achieved with paper and pen. Nearly all
modern detectors, however, contain electronic components as integral elements. A
typical example is the circuitry associated with the scintillation counter (Fig. 4.22).
A well-regulated power supply provides the voltage for the photomultiplier. The
output pulse of the multiplier is shaped and amplified in the analog part. The
height V of the final pulse is proportional to the height of the original pulse. In the
ADC, the analog-to-digital converter, the information is transformed into digital
form. The output is an integer number (usually expressed in binary units) that is
proportional to the pulse height (or area) and can be recorded by a computer.
The example here is a simple one in which only one parameter, the height of
the pulse, is digitized and stored. In most experiments, for every event, many
parameters are recorded. In modern experiments events rates can be too large
for all of them to be recorded, so an electronic system to decide which events are