Microscopic description of diffractive deuteron breakup by 3 He nuclei
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CLEI Theory
Microscopic Description of Diffractive Deuteron Breakup by 3 He Nuclei V. I. Kovalchuk* Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska vul., 01601 Kyiv, Ukraine Received September 9, 2015
Abstract—A microscopic formalism for describing observed cross sections for deuteron breakup by threenucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction 2 H(3 He, 3 Hep)n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by 3 He nuclei at the projectile energy of 89.4 MeV. The importance of employing, in calculations, a deuteron wave function that has a correct asymptotic behavior at large nucleon–nucleon distances was demonstrated. DOI: 10.1134/S1063778816020101
1. INTRODUCTION Investigations between collisions of light nuclei treated as composite particles are an important source of information about the microscopic structure of these nuclei and about mechanisms of nuclear reactions proceeding under specific kinematical conditions. While one can still describe reactions involving three or four particles on the basis of a rigorous theory (for example, by invoking, respectively, the formalism of Faddeev equations or the formalism of Faddeev–Yakubovsky equations), a description of the interaction between nuclear systems featuring a greater number of particles already requires employing approximate methods. The diffraction model of multiparticle collisions [1], which admits the inclusion of a microscopic description of nucleon-density distributions, nucleon– nucleon phase shifts, and the corresponding profile functions, can be considered as one such approach. This permits minimizing the number of adjustable parameters, whereby one can obtain a quantitative description of relevant experimental data and verify the model itself and its applicability boundaries for the kinematics of the reaction being considered. By and large, the application of this approach complicates somewhat the formalism used: for example, the integrands in the scattering amplitude develop a dependence on multiple integrals. As will be shown below, however, the ultimate expression for the reaction amplitude can be reduced to an algebraic expression— multiple sums involving elementary functions—if *
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Gaussian functions are used as integrands. Here, Gaussian functions can be used as basis functions in expansions of both wave functions for colliding nuclei (variational problem) and arbitrary profile functions. It is noteworthy that a similar procedure was extensively employed in the variational approach in describing bound states of light nuclei [2–4], in parametrizations of ground-state charge densities of nuclei [5, 6], and in the problems of scattering [7] and deuteron stripping [8]. This makes it possible to calculate analytically resp
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