In this report we present solutions of the design problem in which a system of quadruple lenses is required to carry a particle beam from given focal lines in the x and y planes to other given focal lines. Particular attention will be given to the case of the anastigmatic lens system which takes a beam from one focal point to another focal point. Since the general problem is almost impossibly complicated a simplification is introduced by breaking the lens system into two parts. The first part of the lens system is required to bring the initial beam to the state where it is parallel to the z axis in both planes. The second part carries the initially parallel beam to the required final condition. Each part will involve two quadrupoles so that the complete system will consist of four quadruples; usually, however, the field gradients in the second and third quadrupoles can be made identical so that those quadrupoles can be combined into one and the system becomes a three quadrupole system. The configuration of the lens element will be as shown in the figures below. These figures indicate also the general character of the beam path in the …

Report issued by the Brookhaven National Laboratory discussing capture positron ratios. As stated on page 1, "the purpose of this report is to present aids for the simple determination of the relative probabilities of K-electron capture and positron emission for allowed and first-forbidden transitions" (p. 1). This report includes tables, and illustrations.