Mean Number Of Electrons Research Articles

ELECTRON SHOWER CURVES IN LEAD FOR ENERGIES OF 3 TO 40 Bev

Electron–photon showers in lead have been studied in a multiplate cloud chamber at energies up to 40 Bev. The numbers of electrons under various thicknesses of lead have been determined by a photometric method combined with scintillator measurements. Experimental shower curves for several energies are given as well as the mean number of electrons at the shower maximum as a function of shower energy. The results are compared with standard shower theory under Approximation A with an assumed low-energy cutoff.

The mean square deviation of the number of electrons and quanta in the cascade theory

On the basis of the quantum mechanical cross-sections for radiation emission by electrons and pair creation by quanta when screening is complete, the fluctuation in the mean number of electrons and photons in any given energy interval in a cascade is calculated. The expression for the mean square deviation of this number is given explicitly in the form of a double integral which can be evaluated by the saddle point method.

Note on the complete stochastic treatment of electron cascades

The present note extends to the actual cascade process a result already established by Scott and Uhlenbeck for a model in which there is only one type of physical entity involved. It is shown that with the sole approximation of neglecting the angular divergence of showers complete information about the stochastic process of cascade generation can be calculated. Theqth order correlation functions are expressed as integrals involving the (q-1)th order correlation functions and the two independent elementary solutions of the cascade equations (8). The latter are the usual functions giving the mean number of electrons and photons in cascades excited respectively by a single electron or photon of some definite energy. If the latter are known exactly, then all the higher order correlation functions can be calculated by repeated integration. One thus obtains explicit expressions for the mean of theqth power of the number of electrons or photons in some finite energy interval, and from this again, through a use of equation (5), of the probability of finding N particles in this energy interval at a deptht in a cascade started by an electron or photon of some given energy.