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Register a new userMethod of integral transforms for few-body reactions
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Authors
V.D. Efros
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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.
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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.
Various electromagnetic few-body break-up reactions into the many-body continuum are calculated microscopically with the Lorentz integral transform (LIT) method. For three- and four-body nuclei the nuclear Hamiltonian includes two- and three- nucleon forces, while semirealistic interactions are used in case of six- and seven-body systems. Comparisons with experimental data are discussed. In addition various interesting aspects of the $^4$He photodisintegration are studied: investigation of a tetrahedrical symmetry of $^4$He and a test of non-local nuclear force models via the induced two-body currents.
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.
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.
We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary differential equation. We illustrate the utility of the approach by providing examples of the evaluation of transforms, without the use of tables. We also demonstrate how the method may be used to obtain a general representation of a function in the form of a series involving the Dirac-delta distribution and its derivatives, which has applications in quantum mechanics, semi-classical, and nuclear physics.
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