FROM CURRENT LITERATURE

NEW DATA ON NEUTRAL MESONS

As is known, neutral mesons (neutretto) have so far been introduced purely hypothetically as particles participating in the transfer of interaction between nuclear particles, in order to ensure the charge independence of nuclear forces. All attempts to observe such particles in the flux of cosmic rays, beginning with the work of Heitler and Arley, who advanced the neutretto hypothesis, have been unsuccessful.

In very recent times the solution of this problem has advanced considerably thanks to the investigation of the so-called electron-nuclear, or special, showers, whose characteristic feature is the presence in them, in addition to the usual electron-photon component and penetrating particles, also of products of nuclear disintegrations (Myssovsky–Zhdanov stars). As a result of investigations of these showers, begun for the first time in the Soviet Union in the Pamirs in 1944 under the direction of Skobeltsyn, Veksler, and Dobrotin, it was shown that the electron-photon component of such electron-nuclear showers is caused either by electrons or, what is apparently more reliable, by photons of high energies \(\sim 100\) MeV.

The probability of formation of electron-photon showers proved to be large; in other words, there was a high probability of formation of the particles that produce them, i.e. of photons or electrons of high energy, which could not be explained by any of the mechanisms known at that time.

Indeed, high-energy electrons producing electron-photon showers in electron-nuclear showers could not be ordinary high-energy \(\delta\)-electrons, since the probability of formation of the latter is negligibly small in comparison with the probability of formation of low-energy \(\delta\)-electrons, and therefore there would be too few high-energy \(\delta\)-electrons. In fact, no such relation was observed between electrons of low and high energies. Moreover, the experimentally observed number of nucleons and mesons could not have been responsible for such a large number of high-energy \(\delta\)-electrons as is observed in electron-nuclear showers.

Furthermore, the electrons (positrons) of interest to us likewise could not be electrons (positrons) from the decay of \(\mu\)-mesons, in view of the relatively long lifetime of the latter \((\tau = 2 \cdot 10^{-6}\ \text{sec.})\).

Finally, the electron-photon component of electron-nuclear showers likewise could not have been formed by high-energy photons arising in the ordinary bremsstrahlung of nucleons (or mesons), in view of the extremely small magnitude of the radiation from such heavy particles.

To explain the observed experimental facts, a whole series of new, less common mechanisms of production of electrons and photons in electron–nuclear showers was proposed. For example, a calculation was made of the bremsstrahlung emitted by nucleons in specific charge exchange occurring in the exchange interaction of nucleons; the total effective cross section turned out to be of the order of \(10^{-25}\)—\(10^{-26}\ \text{cm}^2\), i.e., close to the experimental value\({}^3\). However, experiments carried out recently show that this type of radiation does not play a major role in electron–nuclear showers.

The bremsstrahlung of particles possessing, in addition to electric charge, also an intrinsic magnetic moment exceeding the kinematic magnetic moment when damping is taken into account was also calculated; it turned out that, for example, for spin-\(1/2\) particles with a meson mass, in the presence of a small anomalous gyromagnetic moment one could also obtain the correct order of magnitude for the effective cross section\({}^3\).

However, as has now become clear, this process too is not the principal one.

One could also have supposed, as one of the possible explanations, the presence of nonlinear electromagnetic effects tending strongly to increase with increasing photon energy, but usually turning out to be insignificant\({}^*)\). Further, one could also have supposed the presence of a rapid transformation of a neutral (or charged) meson, decaying in the field of the nucleus into an electron–positron pair\({}^{16}\). However, it must be thought that the probability of such an effect, by analogy with the double \(\beta\)-decay of the neutron, is small\({}^4\).

It was also suggested that electrons of high energies are produced directly in the splitting of nuclei by primary nucleons.

However, the probability of such a process is too small.

The most successful explanation for the presence of a large number of photons in electron–nuclear showers, as has now become clear, proved to be the hypothesis of the existence of a neutral \(\pi^0\)-meson with a mass of the order of the mass of the charged \(\pi^\pm\)-meson, decaying extremely rapidly into two \(\gamma\)-quanta.

The lifetime of such a meson, at first assumed to be scalar, according to Oppenheimer’s calculation\({}^{5,6}\), turned out to be of the order of \(10^{-16}\) sec. In his calculation he used a scheme of processes in which, at the first stage, the neutral \(\pi^0\)-meson virtually created a nucleon–antinucleon pair which, after emitting a \(\gamma\)-quantum, annihilated; one of these nucleons annihilated with emission of a second \(\gamma\)-quantum. Subsequently, Steinberger carried out calculations for the lifetime of neutral \(\pi^0\)-mesons for various variants of the meson theory of nuclear forces (scalar, pseudoscalar) and the corresponding interactions of nucleons with the field of \(\pi^0\)-mesons.

For estimating \(\tau\) one may use the formula

\[ \tau \simeq A \cdot \tau_0 \cdot \beta \cdot \alpha^3 \left( \frac{M}{\mu_\pi} \right)^3, \]

where

\[ \tau_0 = \frac{h}{\mu_\pi c^2} \]

is the characteristic lifetime of a meson with mass \(\mu_\pi\).

The fine-structure constants \(\beta = g^2/hc\) and \(\alpha = e^2/hc\) characterize the strength of the interaction: the first—of a nucleon of mass \(M\) with the field

\({}^*)\) According to a remark by D. Ivanenko.

of \(\pi^0\)-mesons (absorption of a \(\pi^0\)-meson), and the second—the interaction of a nucleon with the electromagnetic field (emission of two \(\gamma\)-quanta).

The numerical coefficient \(A\) turns out to be different for different variants of meson theory\(^{6,7}\).

Recently experiments have been carried out on the artificial production of neutral \(\pi^0\)-mesons in the slowing down of protons in nuclei\(^{8}\). Observation of the \(\gamma\)-quanta produced in the decay of the neutral meson made it possible to establish that the lifetime of neutral mesons is \(\tau \le 10^{-13}\) sec, and the threshold of their production is \(\sim 170\) MeV.

Especially convincing evidence for the existence of neutral mesons decaying into two \(\gamma\)-quanta is the work of Steinberger, Panofsky, and Steller\(^{9}\). In their work they used photons with an upper energy limit up to 330 MeV, directed through two collimators onto a target, which was Be and C. The arrangement of their apparatus is shown in Fig. 1.

Fig. 1.

For registering the photons emerging from the target, scintillation counters with a resolving power of \(10^{-7}\) sec were used, arranged in the form of two groups, three counters in each group. After the counter nearest to the target there was placed a converter (usually a Pb plate \(1/4\) inch thick), where the photons were converted into electrons and positrons, which then caused discharges of the subsequent counters. The registration scheme was such that only cases were recorded in which non-ionizing neutral particles passed through both groups of counters (right and left), but after passing through the converter were transformed into charged particles. Measurement of the number of coincidences when the thickness of the converter was changed, as well as replacement of the converters by other materials, shows that the decay photons have energies of the order of 100 MeV.

To measure the energy of the electrons formed in the converter, an absorber of Al was placed between the rear (from the target) counters; changing its thickness made it possible to determine the energy of the electrons emerging from the converter, which proved to be \(\sim 50\) MeV. The fact that the photons emerging from the target are indeed due to an effect of nuclear, and not electromagnetic, origin was demonstrated by the weak dependence of the effective cross section \(\sigma\) of their formation on the material of the target (with a lead converter it was only 6 times greater than with a beryllium one), whereas in the case of their electromagnetic origin (ordinary bremsstrahlung) the dependence of \(\sigma\) on the atomic number of the element \(Z\) is very strong (\(\sim Z^3\)).

For greater certainty, coincidence experiments were carried out at primary \(\gamma\)-quantum energies below \(175\) MeV, with the number of coincidences falling by a factor of 50; nevertheless, the same sharp threshold was observed, analogous to the threshold for the formation of charged mesons. This indicates that the mass of the neutral mesons is \(\mu_{\pi^0}\sim 300\) electron masses.

Next, experiments were carried out to determine the dependence of the number of coincidences on the angle \(\beta\) between the two groups of counters, at a fixed angle \(\alpha\) between the plane of the counters and the direction of the primary \(\gamma\)-rays. The results of these experiments are shown in Fig. 2. The maximum number of coincidences, as is seen from the graph, is observed near \(\beta=90^\circ\), which is not surprising in view of the fact that the \(\pi^0\)-meson decays in flight.

The angular distribution in fact gives the energy distribution of the neutral \(\pi^0\)-mesons. From the distribution curve one can also draw a conclusion about the velocity of the \(\pi^0\)-mesons, namely:

\[ \frac{v}{c}\sim 0.8. \]

It also follows from it the important conclusion that the number of decay photons is no more than two (since otherwise there would not be such a sharp falloff at small angles \(\beta\)). The angular distribution of neutral and charged \(\pi\)-mesons (depending on the angle \(\alpha\)) proved to be completely different.

Namely, whereas \(\pi^\pm\)-mesons are emitted in the moving coordinate system almost with equal probability in all directions, neutral \(\pi^0\)-mesons have a predominantly forward direction of emission.

Fig. 2.

For the total effective cross section for the formation of neutral \(\pi^0\)-mesons by \(\gamma\)-rays of energy \(330\) MeV for H, Be, and C, the following values were found, respectively:

\[ 1.3\cdot 10^{-28}\ \text{cm}^2,\quad 7.5\cdot 10^{-28}\ \text{cm}^2\quad \text{and}\quad 10\cdot 10^{-28}\ \text{cm}^2. \]

These figures show that the total cross section for the formation of neutral mesons increases approximately in proportion to the number of nucleons in the nucleus.

Comparison of the ratios of the formation cross sections in C and H for neutral and for charged \(\pi^0\)-mesons\(^{10,11}\) shows the existence of noticeable differences, namely:

\[ \frac{\sigma_{\mathrm{H}\pi^0}}{\sigma_{\mathrm{C}\pi^0}}=0.12\pm 0.03 \quad \text{and} \quad \frac{\sigma_{\mathrm{H}\pi^+}}{\sigma_{\mathrm{C}\pi^+}}\simeq 0.55 \]

(whereas the order of magnitude of the effective cross sections for both is the same). This circumstance is apparently connected with the fact that \(\pi^+\)-mesons can be formed only with the participation of protons, whereas neutral ones—with the participation of any nucleons. The angular distribution of \(\pi^\pm\)-mesons shows, apparently—

therefore, that in their formation an essential role is played by the coupling of mesons with the spins of nucleons. If one chooses such a type of interaction that the correct angular distributions of $\pi^\pm$ and $\pi^0$ mesons are obtained, then the cross sections for their production turn out to be different, whereas experimentally they are approximately the same. For charged mesons, Brueckner found that only the pseudoscalar version of meson theory gives satisfactory agreement with experiment[^12]. If it is assumed that $\pi^0$ mesons are also pseudoscalar (for which there are some grounds), then it follows that the ratio of the production cross sections for $\pi^0$ and $\pi^+$ mesons by photons will be

\[ \sim \left(\frac{\mu_\pi}{M}\right)^4, \]

where $\mu_\pi$ is the meson mass, and $M$ is the nucleon mass[^12].

If, further, it is assumed that the emission of $\pi^0$ mesons takes place through the interaction of the magnetic field of the photon $\mathbf{H}$ with the magnetic moment of the nucleon $\mu$, then the matrix element for the transition from the initial state $A$ to the final state $B$ with formation of a neutral meson will be:

\[ (B|H|A) \sim \mu H \cdot M_{AB}, \]

where $M_{AB}$ is a matrix element which differs from the matrix element for the $\pi^\pm$ meson only by a factor of the order

\[ \left(\frac{\mu_\pi}{M}\right)^2 \]

(for the same type of interaction, occurring owing to the retardation effect). This term is small for $\pi^0$ mesons, in view of the fact that in the emission of a $\pi^0$ meson the magnetic moment of the corresponding nucleon remains essentially unchanged.

Therefore, according to the theory,

\[ \frac{\sigma_{\pi^0}}{\sigma_{\pi^+}} \sim \left(\frac{\mu_\pi}{M}\right)^2, \]

whereas empirically $\sigma_{\pi^+} \approx \sigma_{\pi^0}$.

However, Brueckner and Watson assert that agreement with experiment can be obtained if one sets $g^2/4\pi = 10$, taking into account recoil, which becomes significant in the case of the pseudoscalar variant[^12].

Nevertheless, the question of whether the neutral meson is scalar or pseudoscalar has still not been finally resolved. From the fact that the neutral meson decays into two $\gamma$ photons, it may be concluded, according to the selection rules, that the spin of the neutral meson must be zero. On the basis of the selection rules established earlier in the study of positronium[^13,^14], one can determine which variant of meson theory—scalar or pseudoscalar—should be chosen to describe neutral mesons.

Thus, if the $\gamma$ quanta from the decay of the $\pi^0$ meson turn out to be polarized parallel to one another, then the $\pi^0$ mesons are scalar; if perpendicular, they are pseudoscalar[^15]; the remaining variants are excluded by the selection rules. On the basis of such considerations, Yang proposed a specific scheme for carrying out an experiment to determine how the photons from the decay of the $\pi^0$ meson are polarized. (For this purpose it is proposed to register the pairs formed by each of the two decay photons; moreover, if the photons are polarized identically, then both pairs will arise in one plane; if, however, the photons are polarized in mutually perpendicular directions, then so will be the angle between the plane in which the electron and positron of the first pair scatter and the plane of the second pair.)

Thus, at the present time one may consider established the existence of a neutral $\pi^0$ meson with spin zero and, consequently, obeying Bose statistics, with a rest mass of about 300 electron masses (i.e. of the same order as the mass of the $\pi^\pm$ mesons), unstable and decaying with a lifetime $\tau \leq 10^{-13}$ sec into two photons.

Thus, the hypothesis of the theory of nuclear forces concerning the existence of the neutral meson receives new confirmation; in particular, the creation of classical mesodynamics is justified.

In the near future one should expect a refinement of the properties of this new elementary particle, in particular clarification of the question whether $\pi^0$-mesons are scalar or pseudoscalar.

N. N. Kolesnikov

Cited Literature

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7. I. Steinberger, Phys. Rev. 76, 1180 (1949).
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13. D. D. Ivanenko, A. A. Sokolov, DAN 53, 1329 (1947); Vestnik MGU No. 6, 3 (1947). A. A. Sokolov, A. I. Mukhtarov, Vestnik MGU No. 8, 63 (1948).
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15. C. N. Yang, Phys. Rev. 77, 242, 722 (1950).
16. A. A. Sokolov, Sow. Phys. 12, 472 (1937); S. Hayakana, Phys. Rev. 75, 1958 (1949).