ON A METHOD FOR MEASURING EFFECTIVE NEUTRON ABSORPTION CROSS SECTIONS

At Wigner’s suggestion, a number of investigators have theoretically developed[^1] and practically implemented[^2] a method for measuring effective neutron absorption cross sections with the aid of a so-called “pile oscillator.” The method is based on the fact that, when an absorber is periodically moved in a neutron flux, the resulting value of the total neutron flux, as well as the value of the neutron flux at every point, undergoes a periodic change. Owing to the linearity of the equations for the neutron flux in a pile, the amplitude of the resulting oscillations of the neutron flux is proportional to the amount of absorption in the sample under study. Therefore, by comparing the action of the absorber under study with the action of a known absorber, one can measure the amount of absorption in the former.

Two variants of this method should be distinguished. Moving an absorber in a pile that is, on the average, at critical conditions leads to the fact that during part of the period of motion the conditions are below critical (the neutron yield decreases), and during another part they are above critical (the neutron yield increases). In other words, moving the absorber causes a corresponding change in the neutron multiplication factor in the pile. The multiplication factor determines the rate of increase of the intensity of the neutron flux; therefore the neutron flux itself, emerging from the pile, differs in phase from the displacement of the absorber by 90°, and the amplitude of its oscillations is proportional to the amount of absorption. Feenberg and Wigner[^1] calculated the oscillations of the neutron flux at any point of the pile under periodic motion of an absorber. In particular, for the magnitude of the oscillations of the total neutron flux from the pile—or, what is the same, for the oscillations of the flux at points sufficiently far from the absorber—their calculations confirmed that, at a sufficiently low oscillation frequency, the amplitude of the flux oscillations is proportional to the absorption in the sample, and the phase differs by 90° from the phase of the absorber’s motion. Thus, for sufficiently slow oscillations (the neutron delay times must be much smaller than the period of oscillation of the sample), the intensity of the neutron flux oscillates as a whole, synchronously at every point (except for the region close to the absorber). These oscillations of the neutron-flux intensity in the pile were used to measure effective neutron absorption cross sections in the experiments of Langsdorf.[^3]

In the other variant of the method described, local oscillations of the intensity near the absorber are used. Calculation and experiment show that the use of local oscillations of the neutron flux makes the method more sensitive, allowing the detector to be placed near the absorber, where its influence is stronger. It is true that the pattern of local oscillations ...

considerably more complicated than the above-considered oscillations of the total intensity of the neutron flux. Near the boiler oscillator (the oscillating absorber), strong damped neutron waves propagate from the oscillator, analogous to the known thermal waves in Ångström’s method of measuring thermal conductivity. However, the characteristic property of these oscillations of neutron-flux intensity—their proportionality to absorption in the sample—also remains valid here, which makes it possible to use this method for rapid and accurate measurement of effective cross sections.

Fig. 1.

The advantages of the boiler-oscillator method include the fact that it gives a result averaged over a large number of periods of oscillation, thereby excluding the influence of random deviations; moreover, the resulting alternating current is easily amplified.

In the paper by Suver et al.,² a detailed description is given of the latter method, used at Oak Ridge for the systematic measurement of effective cross sections of various isotopes.

The mechanical part of the boiler oscillator is shown in Fig. 1. A motor rocks a simple flywheel 75 cm in diameter. A drive belt fitted on the wheel is connected, by means of a system of pulleys, with a rectangular beryllium shuttle having a polonium strip measuring \(10 \times 10 \times 60\) mm. The sample under investigation is placed in this strip. The oscillations of the shuttle with the sample have a frequency of about 1 oscillation per second and an amplitude of 80 cm.

The neutron flux was measured with the aid of ionization chambers of two different types. The first type of chamber was an aluminum cylinder 25 cm long and 2.5 cm in diameter, internally coated with enriched boron (\(2\ \text{mg}/\text{cm}^2\)). The axis of this chamber was placed parallel to the axis of the shuttle, directly beneath it at a distance of 1 cm. The chamber of the second type, which proved more suitable, is shown in Fig. 1. Its active volume is bounded by two aluminum cylinders 28 cm long, with diameters of 2.2 and 5.0 cm. The collecting electrode of the chamber, insulated from the rest of the chamber by polystyrene, was 25 cm long and 3.8 cm in diameter. It was coated on both sides with enriched-

Fig. 2.

Annotations visible in the figure:

• \(+250\,V\,D.C.\)
• \(110\,V\,A.C.\)
• To the channel filaments
• To the 6V6 panel
• Electronic switch
• All resistors are \(0.5\) watt unless otherwise indicated.

boron ($1\ \mathrm{mg/cm^2}$). Along the axis of the chamber there was placed a graphite rod, inside which was a shuttle carrying the specimen under investigation. The graphite rod served to reduce the effect of scattering of the neutron flux penetrating through the ionization chamber.

The voltage pulse from the ionization chamber was measured with a resonance galvanometer or with an integrator. The latter method proved more convenient. The circuit of the amplifier and integrator is shown in Fig. 2. The signal from the ionization chamber was amplified by a narrow-band feedback amplifier, rectified by a synchronous switch, and integrated in an integrator circuit. The voltage across the integrator capacitor was measured with a vacuum-tube voltmeter. The use of a synchronous rectifier and integrator leads to the rejection of frequencies other than the desired one, so that the effect of noise caused by statistical fluctuations of the ionic current in the chamber is greatly reduced. The rectifying switch is controlled by a cam connected to the mechanism that moves the shuttle. By means of adjustment one can make use of any part of the period of oscillation of the shuttle. This is essential from the point of view of eliminating the influence of neutron scattering.

Experience shows that the oscillations of the neutron flux through the ionization chamber can be due not only to absorption in the oscillating specimen, but also to scattering by this specimen. If, for example, graphite is taken as the specimen, for which absorption is negligibly small, the ionization chamber nevertheless registers oscillations of the neutron flux. Therefore an accurate measurement of absorption in a specimen is possible only when the influence of scattering is excluded. For this purpose use is made of differences in the form of the voltage pulse for a scattering specimen and for an absorbing specimen. In a chamber of the first type (see above) these pulses are so close in form that their separation is impossible. It was therefore necessary to abandon this type of chamber in favor of a chamber of the second type. In this chamber the pulses from absorption and scattering differ in sign, in the steepness of the voltage rise and, most importantly, differ somewhat in phase. By choosing the position of the rectifying switch, it is possible to ensure that predominantly the signal caused by absorption in the specimen is passed. With suitable adjustment one can find such a position of the switch that, for equal effective cross sections of scattering and absorption, the corresponding pulses differ by a factor of 200 (in a chamber of the first type the pulses are distinguished by only a factor of 20). This makes it possible to measure the absorption of specimens with effective absorption cross sections of the order of fractions of a barn*.

The effective absorption cross section of the specimen under study was determined by comparing the effect produced by this specimen with the effect of a standard absorber, for which gold was chosen, since its effective cross section is well known and, in addition, it obeys the $1/v$ law in the thermal region.

As in all measurements of effective cross sections, the purity of the specimen, its shape, and its position are of special importance. The specimen must be sufficiently thin for the correction for self-absorption to be small. Since the measurements are based on comparison with a standard, the best results are obtained when the specimen and the standard have the same dimensions, shape, position in the shuttle, and the same magnitude of self-absorption.

With the aid of the apparatus described, the effective cross sections of a whole series of elements and isotopes were measured; however, the results of the measurements are not published in the paper being reviewed. The method makes it possible to measure total

* $1$ barn $= 1\cdot 10^{-24}\ \mathrm{cm^2}$.

effective cross sections of the order of \(10^{-3}\ \text{cm}^2\). Such high sensitivity makes it possible to use it for the investigation of effective cross sections of isotopes present only in small quantities. The results cited as an example for measurements of absorption cross sections for In (191.2 barns), Ag (29.9 barns), and Ag\(^{109}\) (83.7 barns) testify to the good sensitivity and accuracy of the method described.

E. Burshtein

References Cited

1. A. M. Weinberg and H. C. Schweinler, Phys. Rev. 74, 851 (1948).
2. J. I. Hoover, W. H. Jordan, C. D. Moak, L. Pardue, H. Pomerance, J. D. Stron and E. O. Wollan Phys. Rev. 74, 864 (1948).
3. A. Langsdorf, Bull. Amer. Phys. Soc. 23 No. 3, 20 (1948).