Figure 6.2. Proportional counter. (a) The incident x ray penetrates the thin window and ejects a photoelectron from an argon atom. Secondary electrons may also carry some of the energy. The electrons travel about 1 mm or less and create ion pairs (electrons and positive ions) along their tracks. One such track is shown as the short dark line. The electrons are attracted to the anode, near which they multiply by ionizing other argon atoms. (b) Position-sensitive proportional counter. The anode is resistive and the deposited charge is fed to preamplifiers at each end. The ratio of detected voltages yields the position along the wire of the deposited charge. The anode may be kept at ground potential to avoid large high-voltage capacitors, e.g., C1 in (a); in this case the body is run at high negative voltage (don't touch!).

is most probably ejected from the ground state of the argon atom, known as the K shell or n = 1 state. It takes 3.2 keV of energy to ionize the atom from this state, that is, for the ejected electron to overcome the potential energy of the bound state. Thus the photoelectron will emerge from the atom with only 6.0 — 3.2 = 2.8 keV of kinetic energy. It is this photoelectron that gives rise to the ion pairs.

In contrast to the catastrophic interactions of photons, a charged particle traversing material such as a gas will lose energy gradually through many ionizations of the atoms along its track. Its electric field ejects outer shell electrons from the gas atoms with which it has near encounters, thus creating a track of ions and electrons. An electron in argon gas loses about 25 eV of energy for each electron-ion pair it produces. It dissipates all its energy and comes to a stop in 1 mm or less. In our case, it will have created about 2800/25 = 112 ion pairs, with statistical fluctuations of 112 (see discussion of statistics below in Section 3). These ion pairs represent only 2.8 keV of the original 6.0 keV energy. Thus, so far, less than half of the x-ray energy is in a form that can be recorded by the detector.

Most or all of the missing energy may also be recovered through the relaxation of the originally disturbed atom with the missing K shell electron back to its neutral state. First, it fills its vacated ground state, probably with an electron from the n = 2 (L) shell. This transition to a lower energy state results in the release of a Ka x ray (fluorescence) of energy 3/4 the K shell ionization energy, or 2.4 keV, or it may eject an electron from the L shell (Auger effect). In the former case, the fluorescent x ray will likely interact with another gas atom, ejecting a photoelectron from the n = 2 or higher state.

Thus, in either case, another electron is traveling through the gas, and it produces more ion pairs. The Auger electron will not have the full 2.4 keV because, as before, it had to expend energy climbing out of the electric potential of its parent atom, namely 1/4 x 3.2 = 0.8 keV for the n = 2 state of argon. The remaining kinetic energy of the electron, 1.6 keV, creates —64 ion pairs along its track and these are recorded along with the first —112 ion pairs.

There is still missing energy, and it is stored in the atom or atoms that have L shell, or higher shell, vacancies. The involved atoms continue to relax with the emission of electrons until most or all of the original 6.0 keV has been converted into about (6 keV)/(25 eV) = 240 ion pairs. All of this happens extremely rapidly, in nanoseconds. The ion pairs from all these interactions are now waiting to be recorded. The recording process takes microseconds.

The electric field in the detector causes the electrons to drift inward toward the central anode while the ions drift outward toward the walls of the counter. The electrons will suffer many elastic collisions with gas atoms as they proceed toward the anode. The electric field strength increases rapidly as the distance to the anode decreases and is extremely strong in the immediate vicinity of the anode. When the electrons are close to the anode, they gain sufficient energy between collisions to ionize the atoms with which they collide. Each such inelastic collision produces another electron, thus doubling the number of electrons. Subsequent collisions continue the doubling until the number of electrons has been increased by a factor of several thousand when they strike the anode. This multiplication creates sufficient charge for registration by electronic circuits. The deposited charge is recorded electronically as a voltage or current and then as a digital number.

This entire process is fairly linear throughout: a more energetic x ray will result in more energy being deposited in the gas as ion-electron pairs, and the multiplication by the electric field is by an approximately fixed factor if the detector voltage is not too great. Thus the recorded charge will be a rough measure of the energy of the incident x ray; thus the name "proportional counter".

Statistical fluctuations in the number of ion pairs lead to fluctuations in the recorded charge (pulse height) for a given x-ray energy. If one plots the distribution of recorded pulse heights for incident 6.0 keV x rays, the result will be a peak at the pulse height corresponding to 6.0 keV, with a full width at half maximum (FWHM) of ~20% of 6.0 keV. The proportional counter is a low resolution spectroscope.

If the voltage is too high, each x ray will lead to a breakdown in the counter. It thus behaves as a Geiger counter which counts the x rays (or other charged particles) but does not reveal their energies because all the voltage pulses are more or less identical, independent of the energy of the detected particle or photon.

Sometimes, in the proportional counter, the secondary 2.4 keV fluorescent x ray, discussed above for argon gas, will occasionally escape from the detector volume without being absorbed. Its energy is thus lost. This leads to an escape peak in the pulse height distribution. For incident 6.0-keV x rays in argon, this would appear as a secondary peak at 6.0 — 2.4 = 3.6 keV. The strength of the peak depends on the counter geometry as well as on the fluorescent yield of the element in question, that is, the probability that a vacancy in the K shell will be filled via the emission of an x ray, in contrast to the direct emission of an electron via the Auger effect. In heavy elements, such as xenon, fluorescence dominates. The escape peak can be substantial in this case. In argon, the Auger effect dominates, and the escape peak is much less pronounced.

Proportional counters are very efficient detectors in that they count a high proportion of the incident x rays, until at high energies the gas becomes transparent. They can be made with rather large areas so they can collect x rays from a celestial source at a high rate, and they can be made to respond to energies as high as ~60 keV. They thus were the backbone of early x-ray detectors and as well as of the recent Rossi X-ray Timing Explorer, despite their relatively high backgrounds compared to focusing systems (Section 5.3).

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