Measurement of the Thresholds of \((\gamma, n)\) Reactions in Silicon Isotopes

A. K. Berzin, R. N. Meshcheryakov

The measurement of the threshold of the \((\gamma, n)\) reaction in silicon isotopes, especially in the most abundant of them, \(\mathrm{Si}^{28}\), is associated with considerable difficulties. The method of “direct registration” does not make it possible to obtain reliable data in the immediate vicinity of the threshold because of the large number of background neutrons.

With the “residual activity” method, a large statistical error near the threshold is inevitable, despite the high energy of the decay positrons \((E_{\beta^+}=3760\ \text{keV})\), which permits the use of thick samples. The short half-life \((4.07\ \text{s})\) rules out activity measurements in adjacent rooms, while the use of “falling” or “swinging” apparatus is inevitably connected with placing the irradiated sample at a distance from the target and thereby with a reduction in the bremsstrahlung dose.

In addition, the small reaction cross section near the threshold and the short half-life do not, in principle, make it possible to obtain a large count in a single irradiation, since the total number of radioactive nuclei corresponding to the saturation activity proves to be very small. With repeated irradiation, the accuracy is reduced because of fluctuations in the maximum radiation energy (temperature effect), fluctuations in intensity from count to count, and registration conditions that are not strictly identical.

For a reliable determination of the threshold energy for the production of photoneutrons of this isotope, we used apparatus developed by one of the authors for measuring short-lived isomeric transitions and described earlier in its essentials [1]. It makes it possible to obtain activity counts at a given energy with a small statistical error, independently of the magnitude of the reaction yield and the half-life of the radioactive nucleus [2].

Since, in the case of measuring the \(4.08\ \text{s}\) activity, it is advantageous to operate the betatron with a smaller number of radiation pulses per second, the control unit of the accelerator was modified.

The parameters of the circuit are given in Fig. 1.

As can be seen from the figure, the frequency of the trains of bremsstrahlung pulses is determined by the duration of the counting interval of the time analyzer and can be varied over a wide range.

The detector for the decay products of \(Si^{27}\) was an FEU-13B photomultiplier with a stilbene crystal.

Registration of short-lived products over a long time interval leads to a considerable increase in the background owing to the accumulation of long-lived radioactive elements in the materials of the collimator, the accelerator, and other objects surrounding the apparatus.

Fig. 1.

To reduce the number of false counts, the detector together with the sample was shielded by an 80-mm-thick bismuth screen. The latter, reliably protecting the detector from the background of long-lived activity, is itself a source of \(\gamma\)-quanta with energies of 930 and 500 keV, arising as a result of the reaction \(Bi^{208}(\gamma,n)Bi^{207m}\), with a half-life of \(3.4 \cdot 10^{-3}\) sec. Such a short half-life makes it possible to separate the background arising as a result of this reaction by means of time selection. For this purpose the beam-pulse width was chosen to be 4096 \(\mu\)sec, which corresponds to an operating mode with a frequency of 14 Hz. Counting was carried out separately in channels 2–7 and 15 to determine the background level. Channels 8–14 operated into the common recalculating device. The total delay time, equal to the duration of the first channel and the blanking time, was thus slightly more than 4100 \(\mu\)sec. The total duration of the measurements depended on the readings of the monitor chamber and varied in the interval from 50 min to 1.5 hours, depending on the maximum energy of the accelerated electrons. The contribution of the long-lived activity was taken into account by measuring the background after switching off the accelerator intensity.

In the chosen operating regime, the number of counts for each measured point was 20–25 times greater than the value corresponding to saturation activity.

A further increase in accuracy is limited by the error arising from fluctuations in the intensity and from switching off the counting device before the end of the decay of the element under study.

The total number of decay events that can be registered by the setup at a fixed maximum bremsstrahlung energy can be written in the form

\[ N = \frac{m(1-e^{-\lambda \tau})(1-e^{-\lambda T_c})e^{-\lambda T_s}} {\lambda(1-e^{-\lambda T_n})} \sum J_k - \frac{J_{\mathrm{cp}}\cdot m(1-e^{-\lambda \tau})(1-e^{-\lambda T_c})e^{-\lambda T_s}} {\lambda(1-e^{-\lambda T_n})^2}. \]

where \(\tau\) is the duration of the irradiation pulse,

\(\lambda\) is the decay constant,

\(T_n\) is the time interval between accelerator pulses,

\(T_c\) is the counting time interval,

\(T_s\) is the delay-time interval,

\(J_k\) is the intensity in the \(k\)-th accelerator pulse.

The second term of the expression given gives the magnitude of the error arising because the counting device is switched off before the end of the decay of the element under study.

Since the intensity recorded by the monitor chamber can be written in the form \(g_1 \cdot k \cdot J_{\mathrm{cp}}\), where \(g_1\) is a proportionality coefficient, and the expression given above in the form \(g_2 \cdot J_{\mathrm{cp}} \cdot (k-1)\), then, for a sufficiently long experiment time, the error arising from the second term in the expression for the total number of decay events may be neglected.

More serious limitations on the accuracy of the measurements are imposed by fluctuations of the intensity and, owing to the finite time constant of the dosimeter, the associated inaccurate determination of the dose received by the sample. The integrating dosimeter used in our experiments had a discharge time under natural-background conditions of about three hours.

Calculation shows that this limits the reproducibility of the readings to \(\pm 0.3\%\).

All measurements were carried out with samples of natural isotopic composition. The thresholds of the \((\gamma,n)\)-reaction of the two other isotopes were determined by the method of direct registration.

The results of the measurements are given in the table.

Table

REFERENCES

1. Kislyov, Meshcheryakov et al. Proceedings of the III Interuniversity Conference on Accelerators, Tomsk, 1961.
2. F. Ferrero, R. Malvano, C. Tribuno. Nuovo Cimento, 2, No. 5, 1135–36, 1955.