A DEMONSTRATION EXPERIMENT ON THE ANNIHILATION OF A POSITRON–ELECTRON PAIR

The annihilation of an electron–positron pair with the emission of γ-quanta, like other transformations of elementary particles, is among the most interesting phenomena of modern physics.

Among other things, the fulfillment of four conservation laws is vividly illustrated here:

1) the law of conservation of energy (two quanta of 0.5 MeV each are emitted);

2) the law of conservation of momentum (not one, but two quanta are emitted, flying off in opposite directions);

3) the law of conservation of angular momentum—spin: particles in the para-state (the total spin is zero) are transformed into γ-quanta with mutually opposite spin directions*);

4) the law of conservation of charge.

Therefore, a demonstration of this effect before a broad student audience is highly desirable.

The paper being reviewed[^1] describes the scheme of an apparatus that makes it possible to carry out this kind of demonstration experiment (see the figure).

Sources of positrons may be Cu⁶⁴ ($\tau \sim 12.4$ hours), Co⁵⁸ ($\tau \sim 80$ days), Na²² ($\tau \sim 2.6$ years). The most convenient are the longer-lived isotopes, since installations for obtaining them shortly before the demonstration are usually not available. However, if the latter is possible, it is better to use Cu⁶⁴, since it gives very few nuclear γ-quanta that create an undesirable background. The source is placed

*) The probability of annihilation into 3 γ-quanta is only $\sim \dfrac{1}{200}$ of the two-quantum probability.

inside a bored-out lead cylinder. Most of the positrons, after being scattered many times on the walls of the lead cylinder, reach a paraffin block \(A\), in which they are slowed down and then annihilate. Since block \(A\), which has a thickness of several millimeters, consists of light elements, it only weakly absorbs the annihilation radiation of energy \(0.5\) MeV.

Counters \(C_1\) and \(C_2\), \(1.7\)–\(2\) cm in diameter and with an active length of \(7.5\) cm, are connected in the usual coincidence circuit with a resolving time of \(3\ \mu\)sec. A mechanical counter is placed at the output. The distance between the counters and the annihilator \(A\) is chosen so that the gamma radiation gives only a small \((<4\ \text{pulses/min})\) background of spurious double coincidences.

If the counters \(C_1\), \(C_2\), and the annihilator \(A\) are on one straight line, the circuit gives a large number of double coincidences. If, however, \(C_1\), \(C_2\), and \(A\) are not arranged on one straight line, the number of pulses decreases sharply. To convince the audience that in the second case the double coincidences are caused not by annihilation \(\gamma\)-quanta but by random coincidences, a source is placed in front of each counter (each of intensity \(1\ \mu\)C), and the circuit is first switched for single pulses, which gives a large count, and then for double coincidences. The two independent sources in the second case give random double coincidences, serving as a good illustration of what has been said.

A study of counters of the indicated dimensions makes it possible to measure the directions of emission of the quanta with an accuracy of up to \(1^\circ\) of solid angle.

Replacing the Geiger–Müller counters by crystal counters and a photomultiplier makes it possible to increase the counting efficiency and reduce the resolving time to \(0.3\ \mu\)sec, and consequently to increase the accuracy of measuring the angle of emission by reducing the working surface of the counters. It is then found that the annihilation quanta are not emitted at exactly an angle of \(180^\circ\). This deviation in the laboratory coordinate system is due to the motion of the center of inertia of the system of annihilating particles with a velocity of the order of the orbital velocity of atomic electrons.

P. R.

References

1. J. S. Levinger, Am. Jour. Phys. 20, 71 (1952).
2. Rich, Phys. Rev. 81, 140 (1951).