MEASUREMENT OF THE VELOCITY OF $\gamma$-QUANTA IN AIR

The development of methods for measuring time intervals of the order of $10^{-9}$ sec has now made possible a direct determination of the velocity of propagation of $\gamma$-quanta. For this purpose, in the paper under review[^1] use is made of $\gamma$-quanta arising in the annihilation of a positron and an electron. Two such $\gamma$-quanta are emitted simultaneously in opposite directions, and the problem of determining their velocity of propagation is reduced to measuring the time interval between the arrival of these two quanta at the corresponding detectors, the distance of which from the radiation source is known. Of course, there is no reason to expect that the determination of the velocity of $\gamma$-quanta would give a value of the velocity different from those obtained in measuring the velocity of propagation of electromagnetic waves in the visible region of the spectrum (frequencies of about $10^{14}$ c/s) or at radio-location frequencies ($10^{10}$ c/s). Nevertheless, such measurements are of interest in that they extend the region of frequencies used for determining the velocity of light up to $10^{20}$—$10^{21}$ c/s. Such frequencies are extremely far removed from all resonance frequencies of atoms and molecules, and for them the air medium is equivalent to a vacuum. However, the value of the work referred to lies chiefly in the fact that it develops an experimental method which may find application in determining the velocity of fast charged particles from their time of flight. Such a method proves extremely convenient for identifying particles with a definite velocity in the presence of a considerable number of other particles with different velocities.

A diagram of the experiment is shown in Fig. 1. The detectors of the $\gamma$-quanta were liquid scintillation counters (a solution of terphenyl in phenylcyclohexane). The radioactive source emitting positrons (1 curie of Cu$^{64}$) was enclosed in a metal shell, which also served as the source of annihilation $\gamma$-quanta (with an energy of about 0.5 MeV). As may be seen from Fig. 1, the source and both counters were arranged in a straight line, the source and one of the counters being mounted on a common base, which

Fig. 1.

Fig. 2.

could be moved relative to the other counter. The radio-engineering coincidence circuit measured the time interval $\Delta t$ between the arrival, in the detectors, of two $\gamma$ quanta. The resolving time of the coincidence circuit was equal to $5\cdot 10^{-9}$ sec. The delay between the pulses from the two detectors entering the coincidence circuit was equal to the difference in distances between the counters and the source, divided by the propagation velocity of the $\gamma$ quanta. To obtain coincidences between the pulses from both detectors, an additional delay was introduced into the short arm of the circuit by means of a high-frequency cable serving as a delay line. The delay time was measured from the length of the cable necessary to obtain the maximum number of coincidences; for a given cable length the counter with the source, placed on a movable base, was shifted until coincidences were obtained. Refinement was achieved by inserting additional short pieces of cable. In this way, for a given distance between the source and the counters, the dependence of the number of coincidences on the cable length was recorded. One of the curves obtained is shown in Fig. 2 (the abscissa gives the delay due to the cable, and the ordinate gives the number of coincidences per second). The position of the maximum of this curve determines the delay time. Measurements were made for five distances between the left detector and the source, equal to 2.3; 4.8; 7.3; 14.9; and 34.8 m. Plotting along the abscissa the magnitude of the measured time interval, and along the ordinate the corresponding distance between the counters, the authors obtain five points lying on a straight line. The tangent of the angle of inclination of this line with respect to the abscissa gives the velocity of the $\gamma$ quanta. As a result of the measurements described, for the velocity of the $\gamma$ quanta the value $c=(2.983\pm 0.010)\cdot 10^{10}$ cm/sec was obtained, in agreement with the value $2.998\cdot 10^{10}$ cm/sec adopted at the present time.^2

The cable used in these measurements was tested for dispersion. In the frequency interval from 2 to 400 Mc, not the slightest dispersion was found. The magnitude of the delay produced by short pieces of cable was measured by the resonance method, with one end short-circuited. It is of interest to note that the change in the flight time of electrons in the photomultiplier, caused by a change in the voltage applied to it, can have a substantial influence on the accuracy of such measurements. The authors point out that, for a potential difference on the photomultiplier of 2000 V, a change of 20 V changes the flight time by $4\cdot 10^{-10}$ sec.

References

1. M. R. Cleland and P. S. Jastram, Phys. Rev. 84, No. 2, 271 (1951).
2. J. W. M. DuMond and E. R. Cohen, Phys. Rev. 82, 555 (1951).

A. Weisenberg