From Current Literature

New Data on the Neutral Meson

The existence of a neutral meson is required by the meson theory in order to explain the necessary nuclear forces, which, as is known, are largely determined by the interaction between nuclear particles (nucleons) of one sign and constitute part of the interaction between nucleons of different signs*).

However, until recently the neutral meson had not been discovered experimentally.

The two experimental works reviewed below, taken together and in connection with theoretical data, make a preliminary report of such a discovery meaningful.

In interpreting the results of these works, an essential role is played by one theoretical prediction, whose history is as follows.

In 1947 Oppenheimer² pointed out the circumstance that, according to theory, the neutral meson must be unstable and, among other possible variants, may decay into two γ-quanta.

In the first published calculations³ the two-body decay was considered as including three virtual processes:

a) The neutral meson creates in vacuum a nucleon–antinucleon pair.
b) One of the particles of the pair emits a γ-quantum.
c) The pair annihilates with emission of a second γ-quantum.

Thus, in the initial state there is a neutral meson; in the final state—two γ-quanta.

There is an innumerable multitude of intermediate states satisfying this scheme and differing from one another in the values of the particle momenta.

On integrating over these states one obtains divergent integrals, which must be made convergent (“cut off”) by one or another artificial method.

In this way the author obtained for the lifetime of the neutral pseudoscalar meson \(\tau = 1.10^{-16}\) sec.

In 1949 Steinberger⁴, applying the more regular methods for eliminating divergences⁵ that had been developed by that time, obtained somewhat different numerical results, given in Table I.

The two-photon decay of pseudoscalar and vector mesons (mesons with spin 0 and 1) is forbidden. The constant \(g^2\) may be regarded, in order of magnitude, as close to unity; \((kf)^2\) is greater than unity.

*) This is indicated by experiments on the scattering of fast neutrons by protons¹.

It should be noted that in both calculations the Dirac equation is applied to heavy particles*) and a cut-off of divergent expressions is performed, i.e. the domain of phenomena considered is one in which, until quite recently, the theory was regarded as inapplicable.

All the more interesting, therefore, is the fact that the neutral meson and its $\gamma$-instability apparently have been observed experimentally.

Using plates sensitive to relativistic particles, the authors$^{6,7}$ obtained, at an altitude of 30 km above sea level, a photograph of the collision of a primary $\alpha$-particle of cosmic radiation with a nucleus of the emulsion (Ag or Br).

Table I

The density of grains in the track of the $\alpha$-particle is 15% greater than in the track of minimum ionization; hence the energy of the $\alpha$-particle is $E_\alpha \sim 10^{12}$—$10^{13}$ ev.

The so-called “R-star” obtained by the authors contains, in all, 74 tracks; of these, 56 tracks are those of relativistic particles—evidently $\pi$-mesons (the mass of the $\pi$-meson $\sim 300\,m_e$).

These latter are grouped into two showers: a broad one (33 particles in a cone of $\pm 60^\circ$) and a narrow one (23 particles in a cone $\pm 15^\circ$), directed exactly along the flight direction of the $\alpha$-particle.

The narrow shower goes beyond the limits of the emulsion and, after passing through 2 cm of glass, continues in the emulsion of the next plate.

A remarkable circumstance here is that in the emulsion of the second plate the narrow shower contains 21 relativistic tracks more than were present in the first plate.

In addition, near the boundary of the narrow shower there are 5 more analogous tracks. It is believed that the new tracks (they differ from the meson tracks) belong to electron pairs.

This is also confirmed by the fact that in two cases the tracks can be traced from the point of their origin in the first plate. In this case the tracks are the traces of pairs with energies $10^{10}$ and $5\cdot 10^{10}$ ev (which can be estimated from the angle of divergence), and the $10^{10}$-ev pair, at a distance of 700 $\mu$ from the point of origin, multiplies, giving rise to still another pair**).

If one assumes that the pairs are born by $\gamma$-quanta arising, in turn, from the decay of neutral $\pi$-mesons, then for the number

*) The extension of the Dirac equation to heavy particles—the proton and neutron—encountered difficulties connected with the intrinsic magnetic moments of the proton and neutron.

**) In another case, on another plate, the authors observed the direct birth of an electron pair. Probably the same phenomenon is also present here.

OF CURRENT LITERATURE

for $\gamma$-quanta in the narrow shower one obtains the estimate $N_\gamma \sim 35$ (taking into account that at least 8 pairs decay into 0.26 radiation unit of glass and emulsion).

The number of neutral mesons then proves to be smaller than, or of the order of, the number of charged mesons; the upper limit of the energy of the neutral mesons is $2 \cdot 10^{10}$ eV (from the mean angle between neighboring electron tracks) and the lower limit is $5 \cdot 10^9$ eV (from the opening of the $2.5^\circ$ cone in which the $\gamma$-quanta are concentrated). Finally, the proper lifetime of the neutral meson is $\tau_0 \leqslant 3 \cdot 10^{-13}$ sec (from the law of radioactive decay, assuming that the $\gamma$-quantum immediately produces a pair; the lifetime in the laboratory system is obtained, which is then recalculated in the system of the meson moving with energy $1.5 \cdot 10^{10} — 2 \cdot 10^{10}$ eV).

The authors also discuss some other questions connected with the production of $\pi$-mesons, which we shall not touch upon here.

Somewhat earlier than the above-mentioned work there appeared a report$^{8,9}$ that an anomalous yield of hard $\gamma$-quanta was observed when nuclei were bombarded by fast protons with energies above 175 MeV.

Various targets (Be, Cu, and Ta) were bombarded by protons; proton energies 175, 230, 290, and 340 corresponded to observation angles: 2 and 178°; 20 and 160°; 41 and 139°; 47 and 133°, which was determined by the limitations imposed by the collimator slit cut in the three-meter concrete wall of the synchrocyclotron.

Passing through the collimator slit, the $\gamma$-radiation from the target fell on a tantalum radiator. The produced pairs were deflected by a magnetic field so that, at a definite energy, they produced a coincidence in two counters*).

The authors obtained relative yields of $\gamma$-quanta for the mentioned values of proton energies and observation angles and for various targets. In doing so it was necessary to take into account the dependence of the pair-scattering energy in the material of the radiator. This was achieved by a corresponding change in the thickness of the radiator, so that the efficiency of the $\gamma$-spectrometer remained constant.

The intensity of the proton beam was measured by the positron activity of a carbon target produced as a result of the $\mathrm{C}^{12}(p,p,n)\mathrm{C}^{11}$ reaction. Using the cross section of this reaction and knowing the efficiency of the $\gamma$ spectrometer, the authors obtained for the effective cross section for the production of photons in a carbon target by 345-MeV protons the value $\sigma = 10^{-27}\ \text{cm}^2$. (In the center-of-mass system—see below.)

A characteristic feature of the yield curves is that only for 175-MeV protons does the yield curve, in shape and in magnitude, roughly agree with the bremsstrahlung spectrum.

Somewhere between 175 and 230 MeV an increase in the yield of $\gamma$-rays occurs, continuing for all the remaining energies, so that at 340 MeV (carbon target) the yield is 100 times greater than that expected for bremsstrahlung and differs greatly from it in spectral form. They are graphically represented in Fig. 1.

The principal assumption, that the source of the $\gamma$-rays is neutral $\pi$-mesons produced in proton–nucleon collisions, agrees well both with the observed threshold (the same as for charged mesons) and with the spectral and angular distribution of the yield of $\gamma$-quanta.

Indeed, one can transform the obtained curves of the photon spectrum to the system connected with the center of mass of the colliding nucleo-

*) A device analogous to the $\gamma$-spectrometer described in$^{10}$.

... by the formula

\[ I(E,\theta)=\frac{(1-\beta^2)^{\frac12}}{1-\beta\cos\theta}\, I^*(E^*);\quad E^*=\frac{1-\beta\cos\theta}{(1-\beta^2)^{\frac12}}, \tag{1} \]

Here \(I(E,\theta)\) is the observed intensity of photons with energy \(E\), propagating at an angle \(\theta\); \(\beta\) is the velocity (in units of \(c\)) of motion of the center-of-mass system; the corresponding quantities with an asterisk refer to this system.

Fig. 1.

The fact that \(I^*\) does not depend on \(\theta^*\) expresses the condition that photons in the center-of-mass system propagate isotropically.

In the case of \(340\) MeV (\(\gamma=0.32\)) all the yield curves, being transformed by formula (1) and renormalized so that their maxima have identical ordinates, coincide within the limits of error (Fig. 2).

The shape of the curve and the position of the maximum correspond to the isotropic production, in the center-of-mass system, of neutral \(\pi\)-mesons (\(m_0c^2 \simeq 150\) MeV) with velocities \(\sim 0.8c\), and to their subsequent decay into two \(\gamma\)-quanta with energies \(\sim 80\) MeV \(\pm\) (Doppler shift).

* The nucleon in the nucleus is assumed to be moving toward the proton with a Fermi energy \(\sim 25\) MeV. It is precisely such collisions that give the main yield because of the strong increase of the cross section with energy.

The photon yield, as a function of the angle of observation, fits the same scheme, as is seen from Table II below.

Table II

Assuming that neutral mesons are produced in the same quantities as charged ones, one can estimate the lifetime of the neutral meson as

\[ \tau_0 \leq 10^{-11}\ \text{sec}. \]

Discussion of other conceivable \(\gamma\)-sources leads to their more or less complete exclusion.

Excited states of nuclei are incompatible with the Doppler effect, and also with the observed decrease of the cross section by a factor of \(10^9\) when the \(340\)-MeV proton is replaced by a \(390\)-MeV \(\alpha\)-particle.

Fig. 2.

Vertical axis: relative yield.
Horizontal axis: \(E_\gamma\), MeV.
Legend: \(\circ\) \(180^\circ\); \(\times\) \(0^\circ\); \(\bullet\) \(47^\circ\); \(\triangle\) \(133^\circ\).

Excited states of nucleons require isotropic emission of \(\gamma\)-quanta in the system bound to the nucleon, which, of course, cannot be directly reconciled with the isotropy observed in the center-of-mass system.

Finally, excited states of the meson can, in principle, give the same effect for short lifetimes; however, the observed po-

threshold lying below 200 MeV is in poor agreement with the mass of the excited meson \((\sim 150\ \text{MeV} + 80\ \text{MeV} = 230\ \text{MeV})\).

It should be noted that the authors regard their results as preliminary.

A discussion of the \(R\)-star and of the synchrocyclotron experiments is contained in Marshak’s letter\(^{11}\), published simultaneously with the letter on the \(R\)-star.

Among other comments, it is noted there that comparison of the experimental and calculated lifetimes of the neutral meson leads to the exclusion of the possibility of three-photon decay (a meson with spin one).

Yu. Khokhlov

References

1. Hardly, Leith et al., Bull. Am. Phys. Soc. 23, 15 (1948).
2. I. R. Oppenheimer, New York Meeting of Am. Phys. Soc. (1947).
3. R. L. Finkelstein, Phys. Rev. 72, 415 (1947).
4. I. Steinberger, Phys. Rev. 76, 1180 (1949).
5. I. Schwinger, Phys. Rev. 74, 1439 (1948); 75, 651 (1949).
6. H. L. Brandt et al., Phys. Rev. 76, 1735 (1949).
7. The same, Helv. Phys. Acta, v. XXIII, fasc. 1/2 (1950).
8. R. Bjorklund et al., New York Meeting of Am. Phys. Soc. (1949).
9. The same, Phys. Rev. 77, 213 (1950).
10. B. D. McDaniel et al., Phys. Rev. 72, 985 (1947).
11. R. E. Marschak, Phys. Rev. 76, 1737 (1949).