On the Production of Penetrating Showers in Lead and Carbon

Abstract

surface of Fermi distribution, E~Eo. The normal modes in the superconducting state are assumed to consist in part of wave groups which extend over distances of the order of 10" 6 cm and which have average wave vectors which connect electron states with energies near JSo. This implies a correlation between the displacements of ions from their equilibrium positions which extends over distances of this order. It will be shown below that it is reasonable to expect that coherence over distances of ^lO" 6 cm will give a lower energy for the electrons than coherence over larger or smaller distances. Interaction with these modes gives rise to new states which are linear combinations of the \pk with E near EG and which have energies which differ from the old by ~AE. If the interactions are such as to depress the levels just below EQ and raise those just above, there will be a net decrease in electron energy if kT~AE or less. We therefore assume that kTc^AE. The normal modes of the superconducting state have a lower zero-point energy than those of the normal state.It is presumed that the motion of the electrons is sufficiently rapid so that the wave functions are those appropriate to a fixed position of the ions at any moment and that they follow the motion of the ions adiabatically. 4 Superconductivity follows as in the earlier theory. 5 Electrons in the superconducting states near the Fermi surface have a small effective mass. These states are linear combinations of yph with small net current, but which are easily modified by an external field to give a large current. That superconductivity follows from the model is also suggested by Slater's theory. 6 The wave functions of the electrons in the superconducting state extend over the region of coherence of the lattice vibrations. Slater showed that wave functions extending over '-'137 atom diameters may be expected to give a large diamagnetism and lead to superconductivity.To get a rough estimate of the nature of the normal modes and of the interaction energies involved, we consider a volume V which contains only a small number p of states with energies within AE~kT c of Eo. The usual normal modes for a volume of this size will presumably be similar to the normal modes of the superconducting state. It is necessary to take the volume small because the amplitude of the zero-point motion varies as F -*, but if the volume is taken too small one cannot confine the wave functions of the electrons to the region of coherence without an increase of Fermi energy. If N(E)AE is the number of states/cm 3 in AE, we takeThe decrease in electron energy per unit volume at T=0 is of the order V~p/IN(E)&E].(1) The energy changes, AE } resulting from the interactions are of the order of the matrix element AEHM**|AV« !/^*'*£WT|AV,where U, the interaction potential for a mode which connects k and k', is proportional to the displacement of the ions. We can estimate the magnitude from conductivity theory. For a mode with zero-point energy \JIV -$K% in the volume V:The resistivity p is taken at a...

A Search for Penetrating Showers from Hydrogen at Sea Level Using a Cloud Chamber

“…If we consider the possibility that track a is a M-meson and b a knock-on electron, the relation between the angle, 0, between a and b and the momentum of b is where Z is the charge of the atom struck, a the fine 22 According to recent counter experiments of Amaldi, Castagnoli, Gigli, and Sciuti, however, the cross section for this type of event is 6X10" 30 …”

“…This is in agreement with recent results. 4 ' 30 In the case of 23 percent of the penetrating showers found under lead, 7-rays formed at least one electron shower in the lead plate in the center of the chamber, and in the case of 11 percent, at least two. In carbon the corresponding figures are 42 percent and 31 percent.…”

“…1) 30.5 cm in diameter and was operated with an air gap of 28 cm during part of the experiment and of 33 cm during the remainder. It was oil cooled and was capable of producing a field of 9270 oersteds with the smaller gap and of 8500 with the larger, without a temperature rise sufficient to disturb the operation of the cloud chamber.…”