#### Abstract

The dependence on altitude of the intensity of slow mesons, mesons with ranges less than 100 g ${\mathrm{cm}}^{-2\mathrm{}}$, has been measured by the method of delayed coincidences for atmospheric depths down to 250 g ${\mathrm{cm}}^{-2\mathrm{}}$. The intensity at this depth is thirty times that at sea level, and the variation with the depth $x$ is approximately as $\mathrm{exp}(-\frac{x}{\alpha})$ where $\alpha $ is 220 g ${\mathrm{cm}}^{-2\mathrm{}}$. The differential range spectrum of mesons at sea level has been measured by the same method for ranges between 10 g ${\mathrm{cm}}^{-2\mathrm{}}$ and 200 g ${\mathrm{cm}}^{-2\mathrm{}}$. The spectrum is nearly flat in this interval, the value at the lower limit being 0.9 of that at the upper limit. The data which are available in the literature have been examined to obtain the differential range spectrum of mesons whose ranges are greater than 100 g ${\mathrm{cm}}^{-2\mathrm{}}$ and less than 3×${10}^{4}$ g ${\mathrm{cm}}^{-2\mathrm{}}$, and to obtain the variation with altitude of the intensity of fast mesons—mesons with ranges greater than 100 g ${\mathrm{cm}}^{-2\mathrm{}}$.

The experimental results can be explained with the assumption that the number of mesons produced in the depth interval $\mathrm{dx}$ at the depth $x$ with ranges in $\mathrm{dR}$ at $R$ varies as $G\left(R\right)\mathrm{dR}\mathrm{exp}(-\frac{x}{L})dx$. Using 125 g ${\mathrm{cm}}^{-2\mathrm{}}$ for $L$ we have arrived at a production spectrum $G\left(R\right)\mathrm{}$ which is compatible with the experiment data. In the computations, the exact energy-range relation and an empirical atmospheric pressure-altitude relation were used.

The spectrum obtained can be represented approximately by $G\left(R\right)={(R+\alpha )}^{-2.9\mathrm{}}$, where $\alpha =210\mathrm{}$ g ${\mathrm{cm}}^{-2\mathrm{}}$. The exact spectrum is of the same form for ranges larger than 100 g ${\mathrm{cm}}^{2}$ but falls about 40 percent lower for ranges of 100 g ${\mathrm{cm}}^{-2\mathrm{}}$ and less. The observed spectra which result from the derived production spectrum have been computed for several altitudes.

DOI: http://dx.doi.org/10.1103/PhysRev.77.180

- Received 5 October 1949
- Published in the issue dated January 1950

© 1950 The American Physical Society