Theory of Counter Experiments on Collision Electrons Ejected in Air by Mesotrons

It was found in the preceding paper that mesotrons are associated with particles present at several meters distance from the mesotron trajectories. At least part of these particles are collision electrons ejected by these mesotrons along their path in the air. The theoretical results obtained in the present paper show that: (a) Only mesotrons of momenta $p>\mathrm{}{p}_0\sim {10}^8 \frac{\mathrm{ev}}{c}$ can eject in air collision electrons sufficiently energetic to reach and to traverse a counter tube ($C$) placed at a distance $D$ (a few meters) from the mesotron trajectory. (b) The number $v$ of collision electrons arising from a single mesotron and which are able to discharge ($C$) is practically independent of the mesotron momentum $p$ if the influence of the spin of the mesotron is neglected and is given, in first approximation, by ${\nu }_0=\left(\frac{\mathrm{BS}}{\pi D}\right)\times {\theta }_{max}(D,E_1)$. In this formula, if the effective area of ($C$) is expressed in ${\mathrm{m}}^2$ and $D$ in meters, then $B={10}^{-2\mathrm{}}$ for standard air. ${\theta }_{max}$ is a function of $D$ and of the minimum energy $E_1$ necessary for an electron to penetrate the wall of the counter. For $E_1=2\mathrm{}$ Mev, for example, ${\theta }_{max}$ decreases from 0.50 for $D=2\mathrm{}$ m, to 0.30 for $D=10\mathrm{}$ m. (c) When the mesotron spin (0 or ½) is taken into account, $\nu$ is about equal to $\frac{1}{2}{\nu }_0$ for the lowest mesotron momenta, but approaches asymptotically ${\nu }_0$ as $p$ increases. (d) A fraction of these collision electrons can give, by their subsequent cascade multiplication in air, a certain contribution to the counting rate in ($C$), in excess of $\nu$. However, when averaged adequately over the mesotron spectrum, this shower effect appears as a small correction only.