STUDY OF THE TEMPORAL AND SPECTROMETRIC CHARACTERISTICS OF A CHERENKOV γ-SPECTROMETER

I. V. Glavanakov, V. I. Kryshkin, V. I. Stibunov,
V. N. Eponeshnikov

(Presented by the scientific-technical seminar of the High-Energy Laboratory of the Nuclear Physics Research Institute)

The principal requirement imposed on Cherenkov total-absorption spectrometers is high energy and time resolution. This problem can be solved in two ways:
a) by using in the instrument two types of photomultiplier tubes, one of which has good spectrometric characteristics and the other, timing characteristics;
b) by using a photomultiplier tube having satisfactory spectrometric as well as timing characteristics.

The purpose of the present work is to study the temporal and spectrometric characteristics of Cherenkov total-absorption γ-spectrometers in the γ-quantum energy range 200–700 MeV. The characteristics of three variants of γ-spectrometers with different types of photomultiplier tubes were investigated. In the first version of the spectrometer, one spectrometric photomultiplier tube of type FEU-49 and two timing tubes of type FEU-36 were used; in the second, one photomultiplier tube of type FEU-65; and in the third, one FEU-49. Below, the characteristics and designs of spectrometers with different types of photomultiplier tubes are described.

1. A γ-spectrometer with two types of photomultiplier tubes

The design of the spectrometer with separation of the timing and spectrometric functions is shown in Fig. 1. The radiator of the spectrometer consists of two blocks of TF-1 glass: a cylindrical block 340 mm in diameter and 100 mm high, and a conical block with base diameters of 340 and 300 mm and a height of 200 mm, bonded with OK-72 adhesive. The lateral surface of the radiator is polished and coated with an aluminum reflector. The front end is covered with aluminized Mylar. The radiator and the photomultiplier tubes are placed in a composite cylindrical holder made of mild steel. Optical contact between the radiator and the multiplier is provided by silicone grease. Fixing the positions of the multipliers on the end face of the radiator is achieved by means of a special system of soft clamping. To eliminate mutual electromagnetic pickup, the bulbs of the multipliers are placed in cylinders made of copper foil.

The spectrometric channel of the instrument consists of an FEU-49 multiplier on the end face of the radiator, an emitter follower, a linear gate with adjustable “gate” width, and an AI-256 pulse analyzer. The timing channel includes two FEU-36 tubes, an adder, and a shaper—

Fig. 1. Design of the Cherenkov spectrometer. 1 — radiator, 2 — housing, 3 — reflectors, 4 — FEU-36, 5 — electromagnetic shield, 6 — FEU-49, 7 — high-frequency connectors.

...a standard-pulse generator with a threshold of 0.25 V. The pulses from the two PMTs were summed across an active resistor.

2. Photomultipliers

One FEU-49 unit was selected for the best uniformity of the photocathode and the best intrinsic amplitude resolution, which were studied with an NaI crystal and a Co\(^{60}\) source. Both during selection of the PMT and in the spectrometer, the FEU-49 was powered by a standard voltage divider.

The main requirements imposed on the FEU-36 multipliers are high photocathode sensitivity and a low noise level. Preliminary selection of the FEU-36 was carried out with a plastic scintillator and a Co\(^{60}\) source on a special stand that made it possible to vary the first and last three resistances of the voltage divider. The final determination of the parameters of the optimal voltage divider was performed using a GaP light source. In this case, the light intensity corresponded to the extraction of several electrons from the PMT photocathode. The PMT supply voltage was chosen from the plateau of the counting characteristic, which was obtained with very weak illumination of the photocathode.

3. Calibration of the spectrometer

A collimated beam of bremsstrahlung from the internal target of the synchrotron, after passing through a cleaning magnet, was converted into electron–positron pairs in the target of a magnetic pair spectrometer (Fig. 2). The electrons selected by the magnet according to momentum were collimated and entered the front face of the \(\gamma\)-spectrometer. The momentum spread of the electrons was \(\pm 3\%\). A telescope consisting of two scintillation counters placed in front of the spectrometer entrance window was used as a monitor.

Figure 3 shows the dependence of the amplitude of the spectrometer output pulse on the energy of the registered electrons. As can be seen from the figure, this characteristic is linear in the energy range studied.

Fig. 2. Layout of the apparatus. 1—internal target of the synchrotron, 2—vacuum chamber of the synchrotron, 3—lead collimators, 4—concrete shielding, 5—cleaning magnet, 6—magnetic pair spectrometer, 7—target, 8—quantometer, 9—scintillation counter, 10—Cherenkov γ-spectrometer, 11—lead shielding.

The dependence of the energy resolution of the spectrometer on the electron energy is shown in Fig. 4. The somewhat poorer resolution of our instrument in comparison with the spectrometer of [1] is apparently explained by the presence of cementing and by the geometry of the radiator. The spectrometer was calibrated with a lead converter 8 mm thick, placed at a distance of 4.5 cm from the radiator. In the investigated energy range the amplitude of the output pulses decreased by 15–20%, and the resolution worsened by 2–3%.

Fig. 3. Dependence of the spectrometer pulse amplitude on the electron energy.

Fig. 4. Dependence of the energy resolution of the spectrometer on the electron energy.

4. Time Characteristics

The time characteristics of the spectrometer were studied with the aid of a time-amplitude converter (Fig. 5). Figure 6 shows a typical distribution of time intervals between the pulses of counters \(S\) and \(C\). Previously, analogous distributions were obtained using the pulses of individual FEU-36 photomultipliers as the “start” pulse; then, with the aid of delay lines, the maxima of the time—

Fig. 5. Diagram for measuring the temporal characteristics of the spectrometer. \(\Sigma\) — summator, \(\square\) — shaper, \(\cup\) — coincidence circuit, \(t \to A\) — time-to-amplitude converter, AI — pulse-amplitude analyzer, DL — delay lines, S — scintillation counter.

Fig. 6. Distribution of the time intervals between the signals of the transmission scintillation counter and the spectrometer.

The time distributions were aligned with an accuracy of \(\pm 0.3\) ns. No noticeable shift of the maximum of the time distribution was observed when the electron energy was changed. The asymmetry of the time distributions and their relatively large width can be explained by the low intensity of the light reaching the FEU-36 photocathodes and by the wandering of the light in the radiator. The stability of operation of both the time channel and the spectrometric channel was monitored with GaP light-emitting diodes.

5. Detection efficiency

The detection efficiency of the system when summing the pulses of two FEUs is related to the detection efficiency of the individual FEUs by the following expression:

\[ \sigma_{\Sigma} = \varepsilon_1 + \varepsilon_2 - \varepsilon_1 \varepsilon_2, \]

that is, the necessary condition for 100% efficiency is 100% efficiency of at least one multiplier, which in our case is difficult to achieve. However, a practically reasonable efficiency can be obtained even without satisfying this condition. An estimate of the detection efficiency of one FEU-36 can be obtained from the value of the mean number of photoelectrons entering the FEU multiplying system [1], which at an electron energy of 100 MeV is approximately 1.5. This indicates the fundamental possibility, using the FEU-36, of detecting electrons and \(\gamma\)-quanta with energies greater than 100 MeV.

The measurement of the detection efficiency of the spectrometer was carried out according to the scheme shown in Fig. 7. The efficiency was calculated from the ratio of the areas of the spectra under the control of the linear gate either from the scintillation telescope (SS1) or from (SS2). Za-

Fig. 7. Circuit for measuring the registration efficiency of the spectrometer. \(\Sigma\) — summator, \(\square\) — shaper, 1, 2 — coincidence circuits, EP — emitter follower, LP — linear gate, AI — pulse-amplitude analyzer, \(S_1S_2\) — scintillation counters.

Fig. 8. Dependence of the spectrometer registration efficiency on electron energy.

The dependence of the spectrometer registration efficiency on energy is shown in Fig. 8. A noticeably sharp decrease in efficiency at electron energies below 100 MeV is due to the relatively high threshold of the shaper and the low intensity of Cherenkov light. Lowering the shaper threshold, however, leads to a significant increase in the noise level.

II. \(\gamma\)-spectrometer with an FEU-65

Because of the relative novelty of the FEU-65 multiplier, a preliminary estimate was made of the energy resolution of the spectrometer and of the range of pulse amplitudes from the FEU-65 anode.

1. Estimate of the energy resolution

If it is assumed that the intensity of the light emitted by an individual shower particle is, on average, the same for all particles, then the expression for the energy resolution of the spectrometer will have the form [2]

\[ \delta^2=\delta_1^2+\delta_3^2+\delta_4^2, \]

where \(\delta_1\) is the contribution to the spectrometer resolution from fluctuations in the number of shower particles;

\(\delta_3\) is the spread introduced by the light collector;

\(\delta_4\) is the spread associated with multiplication of photoelectrons.

The required dependence \(\delta_1(E)\) for a radiator of our dimensions (12 r.u.) can be obtained by interpolating the data of Ref. [2]. From the same work it follows that, for a radiator length of 12 radiation units, the contribution to the energy resolution from fluctuations of the light collector depends only weakly on the energy of the primary \(\gamma\)-quantum, and it may be taken as equal to 7%. It remains to take into account the contribution to the resolution from fluctuations of the gain coefficient of the FEU, \(\delta_4\). Since \(\delta_4\) is practically independent of the length of a radiator having sufficient transparency [2], we can use the dependence of \(\delta_4\) on energy for a radiator 10 radiation units thick [2], taking into account the difference in the characteristics of the FEUs used. The final dependence of the energy resolution of the Cherenkov \(\gamma\)-spectrometer on the \(\gamma\)-quantum energy is shown in Fig. 9 by the dashed curve.

2. Estimation of the range of pulse amplitudes from the anode of the FEU-65

To justify the choice of the electronic circuits constituting the spectrometric and time channels of the instrument, the possible range of pulse amplitudes from the anode of the FEU-65 was estimated. The number of photoelectrons \(d\Phi\) knocked out from the photocathode by Cherenkov radiation emitted over 1 cm of the path of a charged particle can be determined by the expression [3]:

\[ \frac{d\Phi}{dl} = \frac{2\pi}{137}\lambda_m \eta(\lambda_m)\varepsilon S_0 \left(1-\frac{1}{\beta^2 n^2(\lambda)}\right) \int \frac{S(\lambda)\,d\lambda}{\lambda^3}, \tag{1} \]

where \(\eta(\lambda_m)\) is the quantum efficiency of the photocathode at the maximum of spectral sensitivity;

\(S'(\lambda)\) is the relative spectral characteristic;

\(S_0\) is the integral sensitivity of the photocathode;

\(\varepsilon\) is a factor accounting for losses of Cherenkov light.

For the FEU-65 the integral in expression (1) is equal to \(3\times10^8\ \text{cm}^{-2}\) and \(\eta(\lambda_m)=3.5\times10^{-3}S_0\) photoelectrons/quantum. Taking \(\beta=1\), \(S_0=50\ \mu\text{A/lm}\), \(\varepsilon=0.1\), and substituting into (1), we obtain \(d\Phi/dl=16\) photoelectrons/cm.

The path length of the charged component of the shower in approximation B is equal to

\[ T=\frac{e}{e_k}x_0, \tag{2} \]

where

\(e_k\) is the critical energy;

\(x_0\) is the radiation unit.

For electrons with an energy of 500 MeV, \(T=79\) cm. Consequently, the total number of photoelectrons \(\Phi\) is equal to 1260, and the charge \(Q\) on the FEU anode will be \(2\times10^{-10}\) coulomb. The corresponding pulse amplitude at the FEU anode is [4] 1.2 volts; i.e., when the electron energy changes up to 1 GeV, the upper limit of the range of pulse amplitudes, without taking into account the energy threshold of Cherenkov radiation, will not exceed 2.5 volts.

3. Design features of the spectrometer and calibration results

The design of the Cherenkov spectrometer with one FEU-65 multiplier differs from the design of the preceding spectrometer only in the sys-

Fig. 9. Dependence of the energy resolution of the spectrometer on electron energy.

Fig. 10. Design of the spectrometer with the FEU-65

...with a soft compression system for the FEU (Fig. 10). In this case the procedure for selecting the optimum operating mode of the FEU is somewhat more complicated. This is associated with the need to obtain satisfactory timing and spectrometric pulses. The FEU-65 was selected as follows. For each FEU specimen, a supply-voltage divider was chosen that provided minimum amplitude fluctuations and maximum steepness of the rise of the anode current. The specimens that were best in this respect were subjected to the following test: the amplitude fluctuations were measured under pulsed illumination of the entire photocathode area by scattered light from a GaP light-emitting diode. The selected FEU-65 specimen has the following characteristics: photocathode uniformity 0.82; energy resolution with a NaI crystal of Ø 60 mm and \(h = 20\) mm and a \(Cs^{137}\) source—13%.

Fig. 11. Dependence of the spectrometer pulse amplitude on electron energy.

Fig. 12. Delayed-coincidence curve for signals of the spectrometer and of the transmission scintillation counter.

The pulse for amplitude analysis is taken from the last dynode of the FEU, passes through a linear gate, is converted by an integrator, and is analyzed by an AI-256 amplitude analyzer. The timing sig-

is taken from the FEU anode and fed to a standard-pulse shaper. Figs. 9 and 11 show experimental dependences characterizing the linearity of the instrument and its energy resolution. The discrepancy between the calculated curve and the experimental data can be explained by the fact that the radiator glass has a somewhat lower transparency than was assumed in the calculation, and by the poorer light-collection conditions from the first block. Fig. 12 gives the curve of delayed coincidences of the signals of the γ-spectrometer and the scintillation counter, from which one can judge the time resolution of the instrument.

III. γ-spectrometer with one FEU-49 multiplier

The use in the spectrometer of a single spectrometric multiplier of the FEU-49 type makes it difficult to obtain a sufficiently good time resolution of the counter. When the FEU-49 is powered by means of a passive voltage divider, the duration of the pulse at the base from the anode is about 80 ns. Changing the first three resistances made it possible, without degrading the amplitude resolution of the FEU, to reduce the pulse duration by a factor of 2. As the shaper of standard pulses in the “time” channel of the spectrometer, a circuit with compensation of the amplitude dependence by the “zero-crossing” method was used.

Fig. 13 shows the distribution of time intervals between the signals of the spectrometer and of the through scintillation counter, obtained with the aid of a time-to-amplitude converter. The use of shapers without amplitude compensation with timing referred to the leading edge of the pulse led to a shift of the time distributions by 3–4 ns when the electron energy was changed from 200 to 600 MeV.

Fig. 13. Distribution of time intervals between the signals of the spectrometer and the through scintillation counter.

In conclusion, let us note the advantages of the different variants of γ-spectrometers and their observed shortcomings.

The first variant of the spectrometer, being structurally the most complex, has good time resolution and has two time signals, which makes it possible, with the use of a coincidence circuit, to reduce to a minimum the level of noise loads in the “time” and spectrometric-

... in the spectrometer’s channels. But this is associated with a decrease in the registration efficiency of the spectrometer.

Despite the electromagnetic shielding of the FEU tubes, it was not possible to eliminate completely the pickup of the FEUs on one another. Time-shifted signals and their pickup slightly increased the level of random coincidences. The use in this spectrometer of a spectrometric multiplier of the FEU-49 type made it possible to obtain relatively good energy resolution.

The next two versions of the spectrometer differ from the preceding one by their considerable simplicity. The spectrometer with an FEU-65-type multiplier has better time resolution and poor energy resolution, especially at low energies. Its drawback is, moreover, the high level of low-energy noise loading, which makes it difficult to use the spectrometer at energies of $\sim 100$ MeV. The short duration of the FEU-65 pulse ($\sim 20$ ns at the base) may prove to be a decisive factor in choosing the type of spectrometer for operation under loading conditions up to 20 MHz. The version of the spectrometer with one FEU-49-type multiplier has good energy resolution. The time resolution, equal to 13 ns (the width at half-height of the time distribution), permits sufficiently rapid and effective selection of events.

REFERENCES

1. Yu. A. Aleksandrov, A. V. Kushchenko, V. N. Maikov, V. V. Pavlovskaya. Trudy FIAN, 40, 3, 1968.
2. V. F. Grushin, E. M. Leikin. Trudy FIAN, 34, 187, 1966.
3. V. P. Zrelov. Vavilov-Cherenkov Radiation and Its Applications in High-Energy Physics. Vol. 2, Atomizdat, 1968.
4. Yu. K. Akimov. Scintillation Methods for Recording High-Energy Particles. Moscow State University Press, 1963.