On the theory of coincidence experiments on cosmic rays

Abstract

Assuming now th a t the mean energy loss due to ionization is constant, i.e. of coincidence experiments on cosmic rays 521 which is correct down to energies of the order of 100,000 eV, our Plon will be a (^-function Pi0Xl{E",l")AE" = A{E" ^E C)8{E"-ft") A E", (5) Vol. CLXVIII. A. X This shower u n it length has th e value 0-358 cm. for P b, 0-215 cm. for Au, 0-207 cm. for P t, 0-824 cm. for Sn, 1-02 cm. for Cu, 1-26 cm. for F e, 6-71 cm. for A1 an d 15-5 cm. for C in form of g rap h ite, d ensity 2-3 g./cm .3. (The value 7-8 for A1 as given b y B h ab h a an d H eitler was incorrect.

Physics of cascading shower generation and propagation in matter: principles of high-energy, ultrahigh-energy and compensating calorimetry

“…The theory of cascade showers originates from two independent papers by Bhabha and Heitler [35] and by Carlson and Oppenheimer [36]. Improvements and amplifications with regard to the physical and mathematical approximations have been made by several authors [22,[37][38][39].…”

“…where L S is the physical thickness of the active readout detectors, L i is the thickness of the absorber i, ( dE dx ) S is the mip average energy loss per unit of length in the active readout planes, and ( dE dx ) i is the mip average energy loss per unit of length in the absorber i (as given in [29,82]). In (37), F (S) represents the fraction of the energy lost by a minimumionizing particle depositing its energy by collision losses in similar (with respect to the sampling electromagnetic calorimeter structure) but indefinitely extended calorimeter, so that the mip is completely absorbed. The value of F (S) can be computed by considering a single passive sampler, which can be made of several absorbers, and a single readout active plane.…”

“…It provides a way to determine how much the energy-deposition processes for showering and mip particles differ from each other. From (37) and (39), we can write…”

A cloud-chamber investigation of penetrating showers

“…The relevant data are given in tables 1a and 1b , and from these data it will be shown th at there is only a small chance of confusing pe tetrating particles and electrons above 5 x 108 eV In the table are given the average number of particles (N) emerging from the lead plate when the incident particle is an electron of energy Ee. Data in column (ii) are taken from Arley (1938) and in column (iii) from the more accurate calcula tions of Bhabha & Chakrabarty (1943). As the differences between the two sets of data are not significant for present purposes, Arley's data will be used.…”

“…The detailed probabilities for N = 0 ,1 and 2, when the average is NA (column (ii) for different values of Ee are given in table 1 b . The values for the Polya distribution have been taken from Arley (1943), who has shown th at this distribution gives a more accurate picture of the growth of an electron cascade shower than the Poisson distribution because the former assumes a growth analogous to biological growth, in which one generation succeeds another, whereas the latter assumes shower particles to be independent. The number N includes all particles, primary as well as secondary.…”