TOTAL-ABSORPTION SCINTILLATION SPECTROMETER FOR STUDYING BREMSSTRAHLUNG FROM A BETATRON

\[ E_{\max}=30\ \text{MeV} \]

V. B. Kuznetsov

(Presented by the scientific seminar of the Research Institute of Nuclear Physics, Electronics, and Automation)

For studying the passage of bremsstrahlung radiation from a betatron through various materials, a “total-absorption” scintillation spectrometer with a crystal of dimensions \(100 \times 200\ \text{mm}\) and an FEU-49A was developed. The spectrometer consists of the following elements (Fig. 1):

Fig. 1.

1 — lead shielding;
1a — boron shielding;
2 — collimating device;
3 — crystal;
4 — photomultipliers;
5 — 100-channel pulse analyzer;
6 — synchronization unit;
7 — power-supply unit.

The lead shielding consists of 30 rings 500 mm in diameter with openings for the crystal and the PMT 30 cm in diameter. The front shielding of the spectrometer is 30 cm thick, and the side shielding is 10 cm thick. The lead rings are assembled together on guides and form a single shielding block, whose total weight is about 3 tons.

Fig. 2.

To choose the optimal geometry for registering $\gamma$ quanta, an analysis was made of the passage of radiation through the front shielding and the collimating aperture (Fig. 2). In this case it is necessary to take into account the following factors (1):

$G_1$ — the purely geometrical attenuation factor (determined by the effective solid angle subtended by the collimator);

$G_2$ — the factor taking into account the passage of quanta through the edge of the collimator of variable thickness;

$G_3$ — the factor taking into account passage through the front shielding;

$G_4$ — the factor taking into account the fraction of quanta that were scattered in the collimator channel and reached the scintillation crystal.

Figure 2 shows trajectories of $\gamma$ quanta illustrating the above factors,

\[ G_1=\frac{\pi r^2}{l^2}. \tag{1} \]

To determine $G_2$ and $G_4$, it is necessary to find the solid angle in which the quanta propagating in the direction of the collimator edge are contained,

\[ G_2^*=\frac{1}{4\pi}\int_0^{2\pi}\int_{\operatorname{arctg}\frac{r}{L}}^{\operatorname{arctg}\frac{r}{l-L}} \sin\alpha\cdot d\varphi\cdot d\alpha, \tag{2} \]

Passing through the edge of the collimator, the quanta are attenuated in accordance with the path length traversed by them in lead. This path is equal to

\[ L_1=\frac{l}{\cos\alpha}-\frac{r}{\sin\alpha}, \tag{3} \]

then

\[ G_2=\frac{1}{2}\int_{\operatorname{arctg}\frac{r}{L}}^{\operatorname{arctg}\frac{r}{l-L}} \exp\left[-\mu_{pb}(E)\left(\frac{l}{\cos\alpha}-\frac{r}{\sin\alpha}\right)\cdot \sin\alpha\cdot d\alpha\right]. \tag{4} \]

This interval was calculated by Simpson’s rule, with division into 10 intervals for quantum energies from 1 to 30 MeV. Figure 3 presents the results of calculations for various \(l\) and \(r\). As is seen from the figures, the maximum value of \(G_2\) occurs at an incident-quantum energy \(E = 3\) MeV.

Fig. 3.

The quantity \(G_4\) is determined from the expression

\[ G_4 = \frac{1}{4}\cdot \frac{\mu_k}{\mu_{\text{ob}}}\cdot \nu \cdot G_2^{*}, \tag{5} \]

\(\mu_k\) is the Compton-effect cross section for quanta of the given energy;
\(\mu_{\text{ob}}\) is the total absorption cross section in lead;
\(\nu\) is the ratio of the area under the curve of the differential cross section for Compton scattering through an angle to the total Compton-scattering cross section for the given energy.

For low energies, where this ratio differs substantially from 1, the mean angle \(\overline{\beta}\) through which the quanta must be scattered in order to strike the crystal is determined from the following expression:

\[ \overline{\beta} = \frac{ \displaystyle \int_{0}^{L} \operatorname{arctg}\frac{p}{x}\,dx - \displaystyle \int_{0}^{L} e^{-(L-x)} \operatorname{arctg}\frac{r}{x}\,dx }{ \displaystyle \int_{0}^{L} \left(1 - e^{-\mu \rho (L-x)}\right)\,dx }. \tag{6} \]

For quantum energies \(E \geq 5\) MeV it may be considered practically equal to 1. The dependence of \(G_4\) on \(E_\gamma\) is shown in Fig. 4.

The determination of \(G_3\) can be substantially simplified by assuming that all quanta passing through the frontal shielding travel the same distance \(L\) in the lead,

\[ G_3 = \frac{S_{\text{cr}}}{l^2}\cdot e^{-\mu \rho b L}, \tag{7} \]

where \(S_{\mathrm{cr}}\) is the area of the front face of the crystal. The dependence of \(G_3\) on \(E_\gamma\) is shown in Fig. 5.

The factors \(G_2\), \(G_3\), and \(G_4\) lead, as it were, to an increase in the solid angle subtended by the collimator. The ratio

\[ \frac{G_2+G_3+G_4}{G_1}=f(E_\gamma) \tag{8} \]

is shown in Fig. 6.

Fig. 4.

Thus, for the chosen geometry and collimator parameters \((l=200\ \mathrm{cm};\ L=30\ \mathrm{cm};\ r=0.5\ \mathrm{cm})\), the effects of photons passing through the frontal shielding and the edge of the collimator may be neglected.

Fig. 5.

To eliminate the influence of the neutron background, a boron absorber is placed in front of the lead shielding. As already indicated, the detector used is an NaI(Tl) crystal coupled to a photomulti-

…of the venetian-blind type, FEU-49A. Pulses from the photomultiplier, through a cathode follower and a preamplifier, are fed to an AI-100 hundred-channel pulse analyzer. The input of the analyzer is gated by a pulse from the synchronization unit, which consists of a plastic scintillator, a FEU-33 time photomultiplier, and a pulse shaper. The leading edge of the synchronizing pulse is

Fig. 6.

several tens of nsec, which makes it possible to use a delay line and to record quanta in any part of the betatron radiation pulse, whose duration is 3–5 μsec. The use of synchronization makes it possible to reduce the background of the spectrometer to a negligibly small value.

A special feature of the spectrometry of betatron bremsstrahlung is that, over the course of several μsec at the nominal intensity, \(10^3\)–\(10^5\) \(\gamma\)-quanta may pass through the collimator aperture. To avoid pile-up of quanta in time, the spectrometer must have high time resolution, or else no more than one quantum must be recorded during a radiation pulse. We have chosen a regime in which 2–5 quanta/sec are recorded, which corresponds to an intensity of 0.1–0.2 μr/min per meter. This corresponds to a probability of coincidence of two quanta in time of 0.5–1%. As a result, recording one spectrum with satisfactory statistics requires 4–5 hours.

It should be noted that this type of spectrometer is universal, which is explained by its high registration efficiency, close to 100%. This makes it possible to study the energy and angular distributions of betatron bremsstrahlung generated by various targets. In addition, the wide limits for regulating the radiation intensity at \(E_{\max} = const\) make it possible to study the passage of bremsstrahlung through both thin and thick absorbers.