Heavy Nuclei in Primary Cosmic Radiation

A new paper by Bradt and Peters[^1] is a direct continuation of investigations[^2–^4] published in 1948. It contains results obtained during four balloon flights, during which photographic plates were raised to an altitude of about 30 km (air pressure about 16 g/cm²) at various latitudes.

Above all, the authors present data that make it possible to establish reliably the primary nature of the heavy nuclei under study. Among several hundred high-energy heavy nuclei, not a single one could be found that had originated inside the very stack of photographic plates, which usually contained up to 100 g/cm² of material. In all cases in which it was possible to determine the direction of motion of the particles, they fell into the photographic emulsion from the upper hemisphere, moving not only from top to bottom but also, to a considerable extent, concentrating around the vertical. Finally, the presence of nuclei with atomic number \(Z < 8\) also excludes the possibility that they originated through the interaction of primary protons with air.

To clarify the subsequent results, two principal methods of identifying heavy nuclei should be mentioned. For particles with atomic number \(Z > 6\), the number of \(\delta\)-electrons per unit length of track can be used; for \(\alpha\)-particles \((Z = 2)\), the method of counting grains proved sufficiently sensitive (for those plates that could be exposed once to charged relativistic particles); in the region \(2 < Z < 6\), determination of \(Z\) is not very reliable. It should also be noted that there is a noticeable number of electron–positron pairs produced with a very narrow angular divergence by high-energy photons; such cases often appear simply as tracks with bifurcations.

By counting the number of collisions of heavy nuclei in the glass of the photographic plates, accompanied by a decrease in the nuclear charge by at least 2 units, the following mean ranges \(L\) for various nuclei in glass were determined:

The ranges obtained exceed the values expected from the geometrical cross sections \(\sigma_0\); the actual cross sections are well described by the formula

\[ \sigma = \pi (R_1 + R_2 - 2\Delta R)^2, \]

where \(R_i = 1.45 \cdot 10^{-13} A_i^{1/3}\) cm is the geometrical radius of the corresponding nucleus, and \(\Delta R = 0.85 \times 10^{-13}\) cm gives the correction for the thickness of the “transparent edge” of the nucleus.

To determine the flux \(I(\vartheta)\) of various nuclei at the boundary of the atmosphere at different angles \(\vartheta\) with the vertical, the direct results—

of the track count were processed according to a formula of the type

\[ I(\theta)=\frac{\Delta N(\theta)}{\Delta\theta}\cdot P_l(\theta)\exp\left(\frac{p_g}{\lambda_g}+\frac{p_a}{\lambda_a\cos\theta}\right), \]

where \(\Delta N(\theta)\) is the counted number of tracks in the angular interval \(\Delta\theta\); \(P_l(\theta)\) is a geometrical factor taking into account the probabilities of observing a track of length \(l\); \(p_g, p_a\) are the thicknesses of the glass and of the air above the given layer of the photoemulsion; \(\lambda_g, \lambda_a\) are the mean free paths of nuclei in the same substances.

The corresponding calculations, first, established the fact of isotropic distribution of the primary particles with respect to angles \((I(\theta)=I_0)\) and, second, yielded the following absolute values of the fluxes \(I_0\) of various nuclei at the boundary of the atmosphere:

It is of interest to compare the data of the first row of the table (for \(\lambda=30^\circ\)) with the corresponding flux of primary protons, equal (according to Winkler’s measurements) to \(35.6\cdot 10^{-3}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\ \mathrm{sterad}^{-1}\). If one takes into account that for latitude \(30^\circ\) the mean free path for nuclear collisions is substantially smaller than the ionization range of the corresponding heavy nuclei, it turns out that all of them must contribute about half of the secondary radiation produced in the atmosphere at this latitude.

An analysis of all cases of ionization stopping of nuclei in the glass of photographic plates (these cases were distinguished from nuclear collisions by the increase in the relative number of \(\delta\)-electrons toward the end of the track) showed that the lower limit of the observed energies fully corresponds to the potential barrier of the earth’s magnetic field (at latitude \(55^\circ\) it is \(350\ \mathrm{Mev}\) per nucleon). It is thereby shown that the nuclei under study arrive at the boundary of the atmosphere already completely stripped of atomic electrons.

In the concluding section of their paper the authors attempt to interpret the data they obtained on the relative abundance of various nuclei in primary radiation (assuming an approximately identical integral energy spectrum for all nuclei, of the form \(E^{-1.6}\)) from the standpoint of various hypotheses on the origin of cosmic rays. If one takes into account the existing data on the effective cross sections for interaction between protons of high energy and nuclei of various substances and considers the conditions of equilibrium between heavy nuclei and the products of their interaction with interstellar gas (hydrogen), it turns out that the abundance of various nuclei observed experimentally agrees satisfactorily with the assumption that initially only heavy

nuclei, while all protons and \(\alpha\)-particles are only products of their fragmentation in interstellar space. A similar situation corresponds, in particular, to Shklovskii’s hypothesis on the origin of cosmic rays through the acceleration of particles of cosmic dust by the light pressure of supernovae.

G. B.

References

1. H. L. Bradt and B. Peters. Phys. Rev. 77, 54–70 (1950).
2. Freier, Lofgren, Ney, Oppenheimer, Bradt and Peters, Phys. Rev. 74, 213 (1948).
3. H. L. Bradt and B. Peters, Phys. Rev. 74, 1828 (1948).
4. Freier, Lofgren, Ney and Oppenheimer, Phys. Rev. 74, 1828 (1948).
5. L. Spitzer, Phys. Rev. 76, 853 (1949).