Burst Production by Mesotrons

Assuming that, under great absorbing thicknesses, cosmic-ray bursts are cascade showers from high energy soft secondaries produced in the shielding matter by mesotron-electron collisions and by mesotron bremsstrahlung, we have calculated the frequency of burst production as a function of burst size. For the mesotron of spin 1 and moment $\frac{e\hslash }{2\mu c}$, we have used the previously calculated knock-on formulae, supplemented by our own calculations of the bremsstrahlung; for the latter, the cross section has terms, significant for our work, in $E$, ${\ln }^2 E$, and $\ln E$. Up to energies close to ${10}^{11}$ ev, only slight modifications are introduced by omitting altogether those processes which cannot be treated by the Born approximation, and the minimum cross sections we used differ little from those given directly by the Born approximation. Using these cross sections, the cascade theory of showers, and a modified form of the Furry model to take into account the fluctuations, the frequency of burst production was calculated. The sea-level data of Schein and Gill give for the number of bursts of size greater than $S$, $N_S\sim S^{-\gamma }$, with $\gamma =1.8\mathrm{}$. Our calculations give for spin 1, $\gamma \sim 1.5$ and numerically too many by a factor of 20. Similar calculations for the mesotron of spin 0 give $\gamma \sim 1.8$ and the same in number as the observations within an uncertainty of about a factor 1.5. For spin ½ and moment $\frac{e\hslash }{2\mu c}$, the bursts are approximately twice as numerous as for spin 0. This evidence thus favors spin 0, or possibly spin ½, but tends to exclude spin 1.