1,781 research outputs found
Crossover from percolation to diffusion
A problem of the crossover from percolation to diffusion transport is
considered. A general scaling theory is proposed. It introduces
phenomenologically four critical exponents which are connected by two
equations. One exponent is completely new. It describes the increase of the
diffusion below percolation threshold. As an example, an exact solution of one
dimensional lattice problem is given. In this case the new exponent .Comment: 10 pages, 1 figur
The HeH Reaction with Full Final--State Interaction
An {\it ab initio} calculation of the HeH longitudinal
response is presented. The use of the integral transform method with a Lorentz
kernel has allowed to take into account the full four--body final state
interaction (FSI). The semirealistic nucleon-nucleon potential MTI--III and the
Coulomb force are the only ingredients of the calculation. The reliability of
the direct knock--out hypothesis is discussed both in parallel and in non
parallel kinematics. In the former case it is found that lower missing momenta
and higher momentum transfers are preferable to minimize effects beyond the
plane wave impulse approximation (PWIA). Also for non parallel kinematics the
role of antisymmetrization and final state interaction become very important
with increasing missing momentum, raising doubts about the possibility of
extracting momentum distributions and spectroscopic factors. The comparison
with experimental results in parallel kinematics, where the Rosenbluth
separation has been possible, is discussed.Comment: 17 pages, 5 figure
A small parameter approach for few-body problems
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 K\le 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.Comment: 17 pages, 1 figur
Method to solve integral equations of the first kind with an approximate input
Techniques are proposed for solving integral equations of the first kind with
an input known not precisely. The requirement that the solution sought for
includes a given number of maxima and minima is imposed. It is shown that when
the deviation of the approximate input from the true one is sufficiently small
and some additional conditions are fulfilled the method leads to an approximate
solution that is necessarily close to the true solution. No regularization is
required in the present approach. Requirements on features of the solution at
integration limits are also imposed. The problem is treated with the help of an
ansatz proposed for the derivative of the solution. The ansatz is the most
general one compatible with the above mentioned requirements. The techniques
are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes
and Laplace integral transforms are performed, and very satisfactory results
are obtained. The method is useful, in particular, for the calculation of
quantum-mechanical reaction amplitudes and inclusive spectra of
perturbation-induced reactions in the framework of the integral transform
approach.Comment: 28 pages, 1 figure; the presentation is somewhat improved; to be
published in Phys. Rev.
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