From the Current Literature

POSITRONIUM

The possibility of the existence of a metastable atomic system consisting of an electron and a positron has been discussed by various authors[^1]. However, “positronium” was detected experimentally only after it had been shown theoretically that there must exist two types of positronium with sharply different properties[^2][^3].

According to this theory, the lifetime of parapositronium (the spins of the electron and positron are antiparallel) should be of the order of \(10^{-10}\) sec, and annihilation should occur with the emission of two quanta[^2][^4]. Of particular importance was the theoretical prediction of the metastability of orthopositronium (the spins of the electron and positron are parallel) and the proof that its decay can occur only with the emission of three quanta[^2][^3]. According to the calculation, the lifetime of orthopositronium should be of the order of \(10^{-7}\) sec[^5][^3], which is quite accessible to experimental measurement. The indicated features in the lifetime and mode of annihilation of orthopositronium served as the basis for experiments on the detection and study of the properties of this new atomic system.

Our journal has already reported on a successful experiment detecting three-quantum annihilation of positrons[^6]. These experiments, however, do not yet prove the existence of orthopositronium, since three-quantum annihilation can also occur for a free electron and positron that do not form a bound system between them.

The first convincing experimental proof of the existence of positronium (more precisely, orthopositronium) was given by Deutsch[^7]. The idea of his experiment is as follows. As theory shows, the spontaneous transition of positronium from the ortho- to the para-state is forbidden, despite the very small energy difference between these two states (\(\sim 8 \cdot 10^{-4}\) ev). This transition, however, can be induced from outside, for example in collisions of positronium with gas molecules. An especially large effect can be expected in collisions of positronium with molecules that have an unpaired electron (for example, NO or \(O_2\)), since resonant electron exchange will occur. Generally speaking, both transitions from the ortho- to the para-state and reverse transitions are possible. However, owing to the difference in lifetimes, transitions of orthopositronium into parapositronium will predominantly occur.

Let us recall briefly that a similar mechanism also occurs in the quenching of the phosphorescence of certain dyes by admixtures of \(O_2\) or NO. As is known, an excited dye molecule passes into a long-lived

triplet state, from which spontaneous transition to the ground singlet state is forbidden, but can be induced upon collision with a molecule having an unpaired electron (see, for example, 8).

“Quenching” of orthopositronium was detected as follows. The positron source—Na²²—emits simultaneously with the positron a γ quantum. Consequently, the number of delayed double coincidences caused by this radiation and by the γ radiation of annihilation should characterize the amount of orthopositronium, provided that the delay time is of the order of the lifetime of orthopositronium.

According to the above, the addition of NO to the main gas (N₂) should lead to a decrease in the number of delayed coincidences.

Fig. 1.

In the experiment a distinct effect was indeed observed: at a delay time of the order of \((1 \div 3)\cdot 10^{-7}\) sec, the addition of 3% NO led to a decrease in the number of coincidences by a factor of 2.5–3 (Fig. 1). Still stronger quenching was observed when freon gas \((\mathrm{CCl_2F_2})\) was chosen as the main gas. In oxygen the effect was weak, since this gas itself quenches orthopositronium. Scintillation counters served as the γ-radiation detectors in these experiments.

The correctness of the interpretation of the experiment described as proof of the existence of orthopositronium is confirmed by an experiment in which the distribution in energy of annihilation-radiation quanta was determined. The measurements were carried out on a scintillation γ-spectrometer with a NaI crystal. The distribution was determined for pure nitrogen and for \(\mathrm{N_2}+3\%\ \mathrm{NO}\). As might have been expected, in \(\mathrm{N_2}\) the number of quanta with energy 510 keV (the maximum in the distribution curve) is somewhat smaller than in \(\mathrm{N_2}+3\%\ \mathrm{NO}\) (Fig. 2); the number of quanta with lower energies is relatively greater in \(\mathrm{N_2}\) (in which, according to the idea, three-quantum annihilation takes place with the emission of softer quanta) than in \(\mathrm{N_2}+3\%\ \mathrm{NO}\).

The experiments described thus establish a connection between the quenching of delayed annihilation and the hardness of the annihilation γ-radiation and the nature of the gas.

In another series of experiments the connection was studied between the multiplicity of the radiation and its hardness and the nature of the gas⁹. Three scintillation counters were used, arranged symmetrically around a Na²² source. The distribution of pulses by magnitude in one of the counters was measured. When double coincidences were recorded, the maximum observed corresponded to an energy of 510 keV \((mc^2)\), i.e. to the energy of the quantum produced in two-photon annihilation. For triple coincidences the peak was observed at an energy of 340 keV \((\tfrac{1}{3}mc^2)\), and in this case 510-keV pulses were completely absent. The number of triple coincidences decreased sharply when one of the counters was moved out of the plane formed by the other two counters and the source. Particularly sharp

a decrease in the number of triple coincidences was observed in freon, which is in good agreement with the data obtained from quenching the delayed annihilation by NO molecules and makes it possible to assert that in both cases one and the same phenomenon was studied.

It is of great interest to compare the quantitative predictions of the theory with experiment. According to Lifshitz’s calculations\(^5\), the lifetime of orthopositronium is \(\tau = 8.8 \cdot 10^{-8}\) sec, or

\[ \lambda = \frac{1}{\tau} = 1.13 \cdot 10^{-7}\ \text{sec}^{-1}. \]

According to Ore and Powell\(^3\), \(\lambda = 7.2 \cdot 10^{-6}\ \text{sec}^{-1}\). In the experiment, the decay rate of orthopositronium, \(\lambda\), was measured as a function of gas pressure by the method of quenching with NO impurities\(^10\). The results are shown in Fig. 3. As can be seen, in freon the annihilation rate, \(\lambda\), depends only very weakly on pressure, which once again illustrates the special stability of orthopositronium in this gas. Extrapolating the experimental straight line to zero pressure, one can obtain the value \(\lambda = 6.8 \cdot 10^{-6}\ \text{sec}^{-1}\), in good agreement with the theoretical value.

Fig. 2.

In an oxygen atmosphere the annihilation rate is directly proportional to the pressure. This fact is explained by the quenching of orthopositronium by oxygen; practically the entire annihilation radiation (at \(p > 0.5\) atm) is due to free positrons colliding with the gas electrons.

Fig. 3.

The fine structure of the positronium levels was also studied experimentally. According to theory\(^ {11,12}\), the splitting of the \(S\)-state of positronium (the energy difference of the \({}^3S_1\) and \({}^1S_0\) states) is composed of the energy of the magnetic interaction of the spins, equal to \(4.8 \cdot 10^{-4}\) eV, and of an additional splitting caused by exchange interaction and equal to \(3.7 \cdot 10^{-4}\) eV.

By studying the dependence of the probability of the ortho–para transition of positronium on the strength of the magnetic field, one can determine the total energy difference \(E\) of the ortho and para states of positronium.

The destruction of orthopositronium in freon was determined from the spectrum of the annihilation radiation, measured on a scintillation spectrometer\(^ {13}\). The form of the spectrum depends on the field strength, and from the change in the spectrum one can judge the intensity of the ortho–para transition. On the basis

conducted experiments yielded the value \(E = 9.4 \cdot 10^{-4}\) eV, in general agreement with the theoretical value \(E = 8.5 \cdot 10^{-4}\) eV.

The probability of the ortho–para transition of positronium in a magnetic field was also determined from the change in the number of double coincidences upon adding 3% NO to nitrogen[^14]. The value of \(E\) calculated on the basis of the data from this experiment likewise agrees satisfactorily with the theoretical value.

In conclusion, departing somewhat from the main topic, we note the following[^7]. In three-quantum annihilation the energy of some of the photons will be less than, but close to, 510 keV. These photons cause a shift toward lower energies of the maximum of the experimental distribution curve for the energies of the annihilation quanta. This shift may explain the apparent discrepancy between the mass of the electron and the mass of the positron, as determined by comparing the Compton wavelength (which depends on the electron mass) and the wavelength of the (assumed two-quantum) annihilation radiation[^6].

L. B.

References

1. E. Ruark, Phys. Rev. 68, 278 (1945); D. Ivanenko and A. Sokolov, Vestn. MGU 6, 3 (1947).
2. I. Pomeranchuk, DAN LX, 213 (1948).
3. A. Ore, J. Powell, Phys. Rev. 75, 1696 (1949).
4. D. Ivanenko and A. Sokolov, DAN LVIII, 1329 (1947).
5. E. Lifshitz, DAN X, 211 (1948).
6. UFN XLV, 470 (1951).
7. M. Deutsch, Phys. Rev. 82, 455 (1951).
8. A. Terenin, Photochemistry of Dyes, 1947, p. 140.
9. S. DeBenedetti, R. Siegel, Phys. Rev. 85, 371 (1952).
10. M. Deutsch, Phys. Rev. 83, 866 (1951).
11. V. Berestetskii, ZhETF 19, 1130 (1949).
12. R. Ferrell, Phys. Rev. 84, 858 (1951).
13. M. Deutsch, E. Dulit, Phys. Rev. 84, 601 (1951).
14. T. Pond, R. Dicke, Phys. Rev. 85, 489 (1952).