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In Part One they formulate in a general way the problem of analyzing and evaluating the aberrations of quadrupole magnet beam systems, and of characterizing the shapes and other properties of the beam envelopes in the neighborhood of foci. They consider all aberrations, including those due to misalignments and faulty construction, through third order in small parameters, for quadrupole beam systems. One result of this study is the development of analytic and numerical techniques for treating these aberrations, yielding useful expressions for the comparison of the aberrations of different beam systems. A second result of this study is a comprehensive digital computer program that determines the magnitude and nature of the aberrations of such beam systems. The code, using linear programming techniques, will adjust the parameters of a beam system to obtain specified optical properties and to reduce the magnitude of aberrations that limit the performance of that system. They examine numerically, in detail, the aberrations of two typical beam systems. In Part Two, they examine the problem of extracting the proton beam from a synchrotron of 'H' type magnet construction. They describe the optical studies that resulted in the design of an external beam from the Bevatron that is …

The basic assumption of the Serber model in the description of high- energy nuclear reactions is that the interactions of incident particles with complex nuclei can be described in terms of individual particle-particle collisions within the nucleus. Calculations were performed making use of the basic assumption of the Serber model, a more realistic nuclear model, recent cross-section data, and an exact statistical sampling technique. The sampling technique has not been used previously in calculations of this type. Calculations were performed for incident e (as Fe/sup 59 /sup +/, e (as Fe/sup 59 /sup -/, neutrons, and protons on nuclei from lithium to uranium. The energy range of the incident particles varied from about 50 to 350 Mev, i.e., the energy region in which pion production is not likely. Free-particle cross sections were used in determining the collisions within the nucleus, and statistical sampling techniques were used throughout, The problem was coded for the IBM-7090. Extensive comparisons with experiment were made and the results indicate that the calculation can be used to predict most of the cascade data for incident nucleons on complex nuclei, but only the gross features of the data are predictable for incident pions on nuclei. The effects …

Production of {Lambda} + K{sup 0}, {Sigma}{sup 0} + K{sup 0}, and {Sigma}{sup -} + K{sup +} by 1170-MeV/c {pi}{sup -} mesons has been studied in the Lawrence Radiation Laboratory 72-inch hydrogen bubble chamber, Cross sections, angular distributions, and polarizations are presented. The polarization of the {Sigma}{sup 0} is determined at four center-of-mass angles and found to be small everywhere. Based on published results for the reaction {pi}{sup +} + p {yields} {Sigma}{sup +}, K{sup +}, a comparison of the polarizations of {Sigma}{sup +}, {Sigma}{sup -}, and {Sigma}{sup 0} is made from the charge-independence triangle. A conclusion is reached that the {Sigma}{sup -} polarization should be large, and that the {Sigma}{sup -} and {Sigma}{sup +} polarizations should be opposite in sign.