A “STAR” FORMED BY A PROTON WITH AN ENERGY OF $3\cdot 10^{13}$ ELECTRON VOLTS

Recently, a case of multiple meson production in the collision of two nucleons has been described in the literature$^{1}$. The experiment was carried out with Ilford G-5 photographic plates with an emulsion thickness of 200 microns, which were raised to an altitude of over 30 km and exposed there for 16 hours. On one of them a star was obtained, shown in Fig. 1. The track of particle $A$—the primary proton—is longer than 10,000 microns. Particle $B$, after passing some distance in the emulsion, entered the glass. This track could not be identified; by its character, however, it resembles the track of a proton with an energy of 10 Mev. $C$ is a proton with an energy of 200 Mev.

The paths of the remaining 15 particles (all of them characterized by minimal, relativistic ionization) lie in a narrow cone with its axis in the direction of motion of the primary proton. Five of them are relatively far from the axis; ten tracks pass so close together that near

Measurement data (for Fig. 1)

$^*)$ $c$ is the speed of light, $\beta=\dfrac{v}{c}$; $\beta \simeq 1$. $E \simeq pc$.

from the initial point it is impossible to distinguish them from one another. In the lower half of Fig. 1, at a distance of 4800 microns from the point of collision of the nucleons, eight of these ten tracks can be distinguished separately. In addition, at the point marked by the arrow (β), another pair of charged particles arises. The tracks of both particles of the pair are almost parallel and merge in Fig. 1.

Fig. 2 shows the curve of the distribution of particle paths by angles. It is characteristic that the tracks of particles of very high energies lie in a narrow cone with an aperture of 0.003 radian, while eight particles of lower energies lie in a considerably wider cone with an aperture of 0.13 radian. The reason for this peculiar distribution is illustrated by Fig. 3. In the upper drawing the trajectories of particles formed in a proton–nucleon collision are shown in a reference system connected with their center of inertia.

In the lower drawing the paths of the particles are shown in a stationary sys-

Fig. 1. Microprojection of a star produced by a proton of ultra-high energy — \(3 \cdot 10^{13}\) eV.

Fig. 2. Angular distribution of particle tracks.

stem. Here they are distributed over two cones, the same as in Fig. 1. From the magnitude of the deviations in multiple scattering², the momentum of the particle was measured. The table gives the measured values of the momentum, multiplied by the velocity, or the lower bound of these values. In the collision proton–nucleon, besides charged particles, a neutral meson is also produced. In its decay, γ-quanta are produced. One of these γ-quanta gives the observed pair. From such a picture one can determine the energy of the initial neutral meson; it turned out to be equal to \(10^6\) MeV. The mean lifetime of the neutral meson does not exceed, according to the authors’ estimate, \(2\cdot 10^{-15}\) sec.

Fig. 3.

As is seen from the table, the energy of the primary proton that produced the star is equal to \(3\cdot 10^{13}\) eV. Free protons of such high energies have not yet been observed. The nucleus with which the proton collided is, possibly, a hydrogen or deuterium nucleus—that is, a nucleus of an element with a very small atomic weight. This supposition is also supported by the almost complete absence of slow particles in the given process.

Another supposition may also be made⁹: that the proton collided with a nucleon situated at the edge of an atomic nucleus and weakly bound to the rest of the nucleus. But both suppositions reduce to the same thing—in the star described we are dealing with the rare case of a collision of a proton of high energy not with the whole nucleus, but with a single nucleon. A similar star was also observed in⁷, but there the proton energy was ten times smaller—\(3\cdot 10^{12}\) eV. Several cases of multiple meson production were described in the literature earlier (see⁵). But these were, apparently, collisions of particles of high energies with heavy emulsion nuclei, and the production of mesons was complicated by secondary processes⁶. Secondary mesons and electrons, situated in a very broad cone, complicated the picture.

In previous theoretical works³,⁴ the number of mesons generated by particles of energies as high as \(3\cdot 10^{13}\) eV was estimated at several hundreds. Therefore the small number of mesons in the star described is a very interesting experimental fact. The authors refer to the latest unpublished calculations of Fermi, and also to unpublished calculations of Oppenheimer, which agree with the data of the star described above. alto-

... Fermi’s paper was published \(^{8,9}\). Without setting out Fermi’s theory in detail (a translation of his paper is being prepared for publication), we shall indicate only the author’s idea. Fermi considers the collision of two high-energy nucleons and assumes that all the energy is then released in a small volume (\(V_0\)—in the center-of-inertia system), the order of whose dimensions is that of the \(\pi\)-meson cloud surrounding the nucleons. Accordingly, in calculating the probability of the formation of one or another number of particles and their angular distribution, Fermi uses not the apparatus of perturbation theory, but a diametrically different method—a statistical one, based on the assumption of a strong interaction of the particles and on the establishment of statistical equilibrium between them. The meson cloud that is formed is regarded as an equilibrium system obeying the usual laws of statistical physics and thermodynamics; even the concept of meson temperature is introduced. It is further assumed that the probability of obtaining one or another state (with one or another number of mesons and with the corresponding distribution of them over energies) is proportional to the probability that, in the indicated small volume \(V_0\), all the particles of the given state will be located simultaneously.

For comparatively small energies (the nonrelativistic case \(\beta \ll 1\)), when the Lorentz contraction of lengths

\[ l=\frac{l_0}{\sqrt{1-\beta^2}} \]

may be neglected, Fermi takes the volume \(V_0\) to be equal to the volume of a sphere

\[ V_0=\frac{4\pi}{3}R^3 \]

with radius

\[ R=\frac{\hbar}{\mu c}=1.4\cdot 10^{-13}\ \text{cm}. \]

At high energies, in the relativistic case, he introduces a correction for Lorentz contraction and gives the following expression for the volume:

\[ V=\left(\frac{2Mc^2}{W}\right)V_0, \tag{1} \]

where \(W\) is the total energy of both nucleons in the center-of-inertia system (including the rest energy as well). Thus, in this theory it is assumed that equilibrium in the system is established much sooner than the \(\pi\)-meson cloud has time to disperse appreciably from the volume \(V_0\).

Fermi’s theory gives the following expression for the number of particles born in a proton–nucleon collision:

\[ n=1.06\sqrt{\frac{W'}{Mc^2}}, \tag{2} \]

where \(W'\) is the energy of the proton in the stationary coordinate system, and \(M\) is its mass. If one takes into account that at high energies (\(W'\gg 4Mc^2\)) the formation is possible not only of mesons, but also of pairs of heavy particles—a nucleon–antinucleon pair (although the probability of such a process is very small), then for the total number of charged particles born in the collision we obtain the expression

\[ n=1.2\sqrt[4]{\frac{W'}{Mc^2}}, \tag{2a} \]

which differs from (2) only by a constant factor. Relations (2) and (2a) give, for star \(^{1}\) (\(W'=3\cdot 10^{13}\ \text{eV}\)), \(n=16\) and 14 (experiment gives \(n=15\)). In star \(^{7}\), respectively, \(n=9\) or 8 (experiment gives 7).

This agreement of the theory with experiment indicates the applicability of assumption (1). However, it should be borne in mind that \(n\) is proportional to the square root

of the fourth power of \(V\), so that a change of \(V\) by a factor of 2–3 has little effect on the value of \(n\). Fermi’s theory also gives formulas for the angular distribution of mesons, in agreement\(^9\) with the results of measurements for star\(^1\) and for star\(^7\).

M. Ginzburg

References

1. J. J. Lord, J. Fainberg, M. Schein, Phys. Rev. 80, 970 (1950).
2. P. H. Fowler, Phil. Mag. 41, 169 (1950).
3. Lewis, Oppenheimer, Wouthuysen, Phys. Rev. 73, 127 (1948).
4. W. Heisenberg, Nature 164, 65 (1949).
5. N. Birger, UFN 40, 491 (1950).
6. W. Heitler and L. Jánossy, Proc. Phys. Soc., London A62, 669 (1949).
7. Camerini, Fowler, Lock and Muirhead, Phil. Mag. 41, 413 (1950).
8. E. Fermi, Reports on Progress in Theoretical Physics, Tokyo, 5, 570 (1950).
9. E. Fermi, Phys. Rev. 81, 683 (1951).