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SLOW MESONS IN THE ATMOSPHERE
The literature has repeatedly discussed the question of the form of the energy spectrum with which cosmic-ray mesons are generated in the atmosphere, and of the number of mesons born in a single event. This is of considerable interest for elucidating the nature of the generation process, making it possible, in particular, to compare it with analogous properties of penetrating particles observed in processes of the electron–nuclear shower type. In turn, for experimental determination of the spectrum and multiplicity of meson generation, until recently various data on the intensity and spectrum of particles of the hard component were used, it being assumed that it consists mainly of $\mu$-mesons.
To clarify the character of the spectrum in the region of comparatively low energies, where the usually adopted power-law spectrum of mesons at the point of their generation is already clearly invalid, and also to analyze the distribution of generation processes over the depth of the atmosphere, Sands¹ specially investigated slow mesons at altitudes down to
10 km. In his experiments, mesons with ranges from 5 to 80 g/cm² were recorded by the method of delayed coincidences (i.e., by the presence of decay electrons emitted by stopped mesons), for which the differential range spectrum proves to be almost horizontal. The dependence of the number \(N\) of such mesons on the atmospheric depth \(x\) (for the given interval of recorded ranges) is presented in Table I, and the absolute intensity at sea level \((x = 1030\ \text{g/cm}^2)\) for various ranges \(R\) is given in Table II.
Table I
| \(x\) (in g/cm²) | 1030 | 610 | 390 | 310 | 250 |
|---|---|---|---|---|---|
| \(N(x)\) | 1 | \(5.3 \pm 0.6\) | \(13.5 \pm 1.1\) | \(20.5 \pm 2.6\) | \(30.5 \pm 3.9\) |
Table II
| \(R\) (in g/cm²) | 10 | 100 | 200 |
|---|---|---|---|
| \(N(R)\), (in cm\(^{-2}\) hr\(^{-1}\) sterad\(^{-1}\)) | \(0.0102 \pm 0.0006\) | \(0.0108 \pm 0.0006\) | \(0.0114 \pm 0.0006\) |
Using his data for three depths \(x_1 \simeq 300\), \(x_2 \simeq 600\), and \(x_3 \simeq 1000\) g/cm², as well as the known data on the intensity of the hard component at the same depths, Sands selects, with allowance for decay and ionization stopping, a function \(H(R_0, x_0)\) that would correctly describe the distribution of all mesons according to their initial ranges \(R_0\) and depths of origin \(x_0\). For this he takes a function of the form \(H(R_0, x_0) = G(R_0)e^{-x_0/L}\), where \(L = 125\) g/cm² is the “mean free path” of the component generating penetrating showers, and finds that of the simple functions the best fit to the experiment is provided by the spectrum \(G(R_0) = 1.5\,(R_0 + 210)^{-2.91}\). (\(G(R_0)\) gives the number of mesons generated in 1 g of matter per hour per range interval \(= \Delta R_0 + 1\) g/cm².)
The form of this spectrum, also checked by the author with the aid of the known spectra of the hard component at the three depths indicated above, is in general agreement with the range spectrum given in the work² for particles penetrating the showers (although the accuracy of determining both spectra is not very high). Knowledge of the normalization factor (1.5) also makes it possible to estimate the mean multiplicity of meson generation in the atmosphere by using the known data³ on the flux of the primary component of cosmic rays. This multiplicity, equal to 5.7, is close to the average number of mesons born in penetrating showers.
References
- M. Sands, Phys. Rev. 77, 180—193 (1950).
- W. D. Walker, Phys. Rev. 77, 686 (1950).
- B. Rossi, UFN 38, 222 (1949).
G. B.