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# Few-body methods and nuclear reactions

Starting from the microscopic interaction of a particular system, few-body methods are used to solve the Schroedinger equation in order to study the peculiarities of the dynamics when more than two particles are interacting. In the case of nuclear physics the characteristics and origin of nuclear forces have long be debated. At the end of the nineties a number of realistic potentials have appeared with the characteristic to describe the nucleon-nucleon world data with a χ2/per datum close to one. New ideas have also appeared using effective interactions based on the symmetries of QCD, and providing a link to the fundamental theory of the strong interaction in a systematic way. Great efforts have been done, and are at present done, by the few-body community to analyze the capability of all these interactions to describe the few-body nuclear dynamics, trying to minimize the error in the solution of the quantum mechanical problem, which could taint the comparison with experimental data and invalidate conclusions.

The intention of the course is to discuss different methods used to describe few-nucleon systems including a brief introduction to the theory the nuclear interaction (nucleon-nucleon and three-nucleon forces). Though in nuclear physics even the case A = 2 is not trivial (realistic forces couple different orbital angular momentum states), the main part of the course will focus on the A = 3 and 4 nucleon systems. The Faddeev and Faddeev-Yakubovsky equations as well as methods using expansion basis will be illustrated and solved in particular cases. The intense numerical treatment needed for the solution will be explained giving several examples. A particular attention will be given to the description of observables using the numerical solution of the equations for bound or scattering states. In the last part of the course the methods will be extended to describe few-body reactions with external probes. During the lessons all the arguments will be complemented with exercises and examples devoted to allow the students to attack these problems by themselves. Possible extensions of the methods to larger systems and/or non-nuclear systems will be also discussed.