PHY6040 Particle Detectors Dr C N Booth

Coherent Effect for Charged Particles

So far in this course, we have looked at the effect of charged particles on individual atoms, and seen that this leads to excitation (exploited in scintillation counters) and ionisation of atomic electrons.  However, when we looked at the Bethe-Bloch formula for energy loss
we introduced the "density effect", δ, which arises from a screening of the particle's field due to the polarisation of the medium as a whole.  As considered in the Bethe-Bloch formula, this primarily results in a decrease in energy loss (hence the negative sign).  However, the changing polarisation can also lead to observable coherent effects in the medium, which can produce an observable signal.  We will look at two manifestations of this, Cherenkov and Transition Radiation.  These notes only introduce the topics and provide a summary, with links to descriptions in the BriefBook.  For further details of the exploitation of these effects in detectors, it is necessary to see the lecture notes.

Cherenkov Radiation

As a particle passes through matter, the surrounding atoms polarise and subsequently depolarise, and a weak electromagnetic wave spreads out from the instantaneous position of the particle.  For a particle travelling more slowly than light, wave-fronts originating at different times can never meet, and no interference is possible.

For a particle travelling faster than light, the wave-fronts do overlap, and constructive interference is possible, leading to a significant, observable signal.

Click here to view animations of the radiation from a moving particle.

A particle can not, of course, travel faster than the speed of light in a vacuum.  In a medium of refractive index n, the speed of light is c/n, and there is no reason why the speed of the particle, βc,  cannot be greater than c/n.
A highly relativistic particle passing through a medium is observed to emit visible light known as Cherenkov radiation if β > 1/n.  As can be seen from the above diagram, a cone of light radiates out from each point on the particle's track.
It can be shown that the number of photons per unit length of track is given by

n is a function of the frequency ν, for most materials decreasing rapidly in the ultraviolet.  Most radiation is therefore in the visible, peaking at the blue end of the spectrum.  In the visible range, the number of photons is roughly 500 sin2θc per centimetre of track.

As a special case, consider a medium with n close to 1, and write n = 1 +  δ (with δ « 1).
Cherenkov radiation then only occurs for β very close to 1, say β = 1 − ε (with ε « 1).
The condition for Cherenkov radiation, β > 1/n, implies ε < δ.
The number of Cherenkov photons is then

for δ > ε.

Cherenkov Detectors

As mentioned in the introduction, Cherenkov detectors are used primarily for identifying the type of a particle (whose momentum or energy is, at least approximately, known), rather than for tracking the position of the particle.  The three main types of detector are described further in the notes (available here in PostScript and PDF forms), and summarised below.

Transition Radiation

When a particle crosses between two regions of very different dielectric constant, there is a sudden change in the polarisation of the surrounding medium, and transient currents and fields are set up.  If the relativistic γ of the particle is » 1, then X-radiation known as Transition Radiation can be produced, with an angular distribution which is very strongly peaked in the direction of the particle.  The amount of radiation is proportional to the γ of the particle, and to the plasma frequency of the medium.  In practice, it is only high energy electrons (with their very small mass) which normally have a high enough γ to be detected, so transition radiation detectors are typically electron detectors.

A practical detector consists of a stack of radiator foils, of low atomic number in order to reduce absorption of the X-rays.  The radiation is then detected in a special proportional chamber.  This contains a high-Z gas such as Xenon (to absorb the photons rapidly).  The passage of any charged particle through the chamber will also produce a small signal due to ionisation.  In order to distinguish between transition radiation and ionisation, an asymmetric chamber is often used, with a drift space before the amplification region.  Transition radiation photons are absorbed early in this space, so give a large, late signal, in contrast with ionisation which gives a small signal spread out in time.  (Further details of Transition Radiation Detectors can be found in the notes, available in PostScript and PDF forms.)

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