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• W144996327 abstract "The Institute of Space and Astronautical Science, Yoshinodai, Sagamihara 229–8510, JapanAbstract. Moliere theory of multiple Coulomb scattering`has been far improved to take account ionization loss by useof Kamata-Nishimura formulation of the theory. The newformulation only introduce the scale factor to the traversedthickness for effects of ionization process, and is simply re-duced to the traditional Moliere-Bethe formulation by use`of our translation formula. Introducing Kamata-Nishimuraconstants and Kspecific to the traversed substance, wecan simplify the configuration of Moli ere theory, so that the`sequence to derive Moliere angular distributions has become`much easy. Based on the new formulation, we propose apractical and efficient method to obtain Moli `ere angular dis-tributions. The method is accurate enough to apply in MonteCarlo simulations as well as designings and analyses of ex-periments concerning charged particles.1 IntroductionReconstruction of Moli`ere’s multiple scattering theory (Moli ere,`1947, 1948; Bethe, 1953) by Kamata-Nishimura formulation(Kamata and Nishimura, 1958; Nishimura, 1967) is contin-uing. The new formulation is equivalent to the traditionalMoliere-Bethe formulation, both cutting off the higher terms`of Fourier component at the same order (Nakatsuka, 1999b).We have found various superior aspects of the new formula-tion: ionization loss is taken into account (Nakatsuka, 1999a);properties of substance are all reflected in the Kamata-Nishimuraconstants, and K(Kamata and Nishimura, 1958; Nishimura,1967; Nakatsuka, 2001a); mixed or compound substancescan easily be treated; the formulation is simple as a thor-ough extension of the Rossi-Greisen or the Fermi-Yang the-ory (Rossi and Greisen, 1941; Yang, 1951); the theory is eas-ily applicable to other problems; and so on.Although the Moliere theory has been improved by the`new formulation, a few problems still remain in actual ap-plications. In case we take account ionization loss, the scaleCorrespondence to: T. Nakatsuka (nakatuka@osu.ac.jp)factor is newly introduced (Nakatsuka, 1999a). It makesthe expansion parameter Bof the Moli`ere angular distribu-tion smaller. Namely, we should take the smaller value of Bat the times shallower thickness, compared with the fixedenergy condition. Under the moderate relativistic condition,evaluation of the scale factor requires heavy calculationsof numerical integration. In case we get the Moliere angular`distribution for charged particles propagating through mixedor compound substances, we have to carry out multiple se-quence of evaluations according to the number of mixed sub-stances to get the stochastic mean among substances (Nakat-suka, 2001a). These facts will bring serious inefficiencies toour frequent derivations of the distribution.In this paper, we derive simple methods to avoid thesecomplicated sequences, and propose a practical and efficientprocedure of getting Moliere angular distribution with ion-`ization applicable widely in simulations and analyses (Hecket al., 1998).2 Sequence to Obtain Exact Moliere Angular Distribu-`tion With IonizationFor derivations of Moli`ere angular distribution under the mod-erate relativistic condition with ionization, we found it isenough to introduce a scale factor for the traversed thick-ness (Nakatsuka, 2001b). If we assume ionization loss ofcharged particles of zwith a constant rate asE= E" @default.
• W144996327 created "2016-06-24" @default.
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• W144996327 date "2001-01-01" @default.
• W144996327 modified "2023-09-24" @default.
• W144996327 title "Practical and efficient derivations of Moli ` ere angular distribution with ionization" @default.
• W144996327 hasPublicationYear "2001" @default.
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