but the errors are probably important only for very large distances from the source, where only a minor fraction of the energy is dissipated. Since a major effort is required to improve the results further, and since experimental studies show generally good agreement where comparisons have been made, it is felt that the data are of sufficient accuracy and usefulness to justify their publication. ' Figures in brackets indicate the literature references at the end of this Monograph.
1The remainder of this Monograph is divided into two parts, the first outHning the methods and data which were used to make the calculations and the second presenting and describing the tabular data. Section 3 describing the tabular data, has been made almost completely self-contained so that persons who need data but do not wish to follow the derivations may turn immediately to this latter section and find all the information they require.Since the basic theoretical methods used to calculate electron energy dissipation distributions have already been given in considerable detail in [1]. We only sketch the arguments and procedures here.The assumption that electrons lose their energy continuously established a relation between the residual range r of the electrons, measured along their path, and the average rate of energy loss, i.e., the stopping power {dEjdr):where 0<^E'CEo is the kinetic energy of an electron which has slowed down but not lost its energy completely.This equation is the basis for the tabulations of electron ranges [2].It is convenient to measure both distances and residual ranges in units of ro=r{Eo) . For an electron source located on the plane 2=0 which emits electrons of kinetic energy Eq in the direction perpendicular to this plane and towards increasing z, the distance of a point from the source plane will be conveniently identified by a dimensionless parameter x=z/ro-Similarly, we replace the residual range r by a dimensionless ratio t=rjro.We define the flux of electrons, I(t,d,x)2ir d{cos d)dt, as the number of electrons per second that cross a small spherical probe of unit cross sectional area at a distance x from the source, having residual ranges between t and t-\-dt and obliquities between 6 and 6-\-dd relative to the direction from the source to the probe.The electron flux must satisfy a transport equation, which has the following form in steady state conditions for the plane perpendicular source:where 6 is the angle between the electron directions {6' ,4>') and {6,) before or after a collision. This is basically a continuity equation. The terms on the left describe a rate of change in Iit,9,x) due to slowing down (first term) and due to spatial displacement (second term). The terms on the right describe a rate of change in the flux due to elastic collisions (first term) and due to generation of electrons by the source.The last term, describing a unit-electron source current, is the product of three Dirac delta functions which guarantee that the electrons are generated only at a;=0, t= 1 , and cos 6=1...
