Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions

[摘要] ENGLISH ABSTRACT: In this dissertation we present, for the first time, a relativistic distorted wave impulse approximationformalism to describe quasielastic proton-nucleus scattering. We start from a full many-body descriptionof the transition matrix element and show systematically how to derive the equivalent two-bodyform. This procedure allows for a clear and unambiguous method to introduce relativistic distortedwaves. It is shown that the polarized double differential cross section may be written as the contractionof two tensors namely, the hadronic tensor (describing the projectile and ejectile), and the polarizationtensor describing the target nucleus. The basic nucleon-nucleon (NN) interaction is described by theSPVAT or IA1 representation of the NN scattering matrix. Analytical expressions are derived for thepolarization tensor using a Fermi gas model for the target nucleus. The nuclear distortion effects onthe projectile and ejectile are described using the relativistic eikonal formalism. The expression for thedouble differential cross section is a nine dimensional oscillatory integral and an efficient procedure isdeveloped to calculate this quantity. Comparison of Gaussian, Monte Carlo and quasi-Monte Carlonumerical integration schemes reveal that for this work, Gaussian quadrature is best suited for thisproblem. Traditional Gaussian quadrature is used to generate single variable functions whereby thesefunctions are used in combination with modern software such as MATLAB to complete the computationof the full multidimensional integral in a reasonable amount of time. Even though the calculationof the cross section for a single value of the energy transfer is still time consuming, the computationaltime can be decreased by spreading the calculational burden across a number of nodes in a clustercomputing system. A test calculation is performed whereby a proton with incident laboratory energyof 400 MeV is scattered off a 40Ca target nucleus at θcm = 40◦. For this reaction we calculate theunpolarized double differential cross section, as well as a complete set of spin observables namely Ay,Dℓ′,ℓ, Ds′s, Dnn,Ds′ℓ and Dℓ′s. We find that the distortions lead to a reduction of the unpolarizeddouble differential cross section. On the other hand the spin observables are complex entities whichshow no uniformity in behaviour. However, the differences between the distorted wave spin observablesand that of the plane wave observables are minor and we conclude that distortions have little effect onspin observables.

[发布机构] Stellenbosch University