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Register a new userA Small Parameter Method for Few-Body Problems
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Authors
V. D. Efros
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A procedure to solve few-body problems which is based on an expansion over a small parameter is developed. The parameter is the ratio of potential energy to kinetic energy in the subspace of states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to those in the finite subspace with K le K_0. The contribution from the subspace with K>K_0 is taken into account in a closed form, i.e. without an expansion over basis functions.
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A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with Kle K_0. Contributions from states with K>K_0 are taken into account in a closed form, i.e. without an expansion over basis functions. Estimates on efficiency of the approach are presented.
The method of integral transforms is reviewed. In the framework of this method reaction observables are obtained with the bound--state calculation techniques. New developments are reported.
A convenient framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. Unlike relativistic quantum field theory, one deals with a fixed, or at least restricted number of degrees of freedom while maintaining relativistic invariance. For systems of interacting particles this is achieved by means of the, so called, Bakamjian-Thomas construction, which is a systematic procedure for implementing interaction terms in the generators of the Poincare group such that their algebra is preserved. Doing relativistic quantum mechanics in this way one, however, faces a problem connected with the physical requirement of cluster separability as soon as one has more than two interacting particles. Cluster separability, or sometimes also termed macroscopic causality, is the property that if a system is subdivided into subsystems which are then separated by a sufficiently large spacelike distance, these subsystems should behave independently. In the present contribution we discuss the problem of cluster separability and sketch the procedure to resolve it.
A non-conventional approach to calculating reactions in quantum mechanics is presented. Reaction observables are obtained with bound state calculation techniques. The accuracy of the method to calculate few-nucleon response functions is discussed.
A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction channels in a dynamics calculation. These channels come into play at merely the kinematics level and only after a dynamics calculation is done. This calculation is of the bound--state type while continuum spectrum states never enter the game.
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