An Approximation Method for Solution of the Coupled Channels Inverse Scattering Problem At Fixed Energy

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ABSTRACT We present a method for the quantum mechanical inverse scattering problem at fixed energy for coupled channels in reactions with particles having internal degrees of freedom. The scattered particles can be excited by a local interaction between the relative motion and the internal dynamics which can be expanded in multipoles. The inverse scattering problem is solved by an extension of the modified Newton-Sabatier method, assuming a special ansatz for the integral kernel in the radial wave function. Application has been made for a hypothetical scattering of two nuclei interacting by a dipole-type interaction. Good agreement between the obtained potentials and the input data is found. 03.65.N, 24.10.E, 24.10.H, 25.70.

  • Second pages xxxii+499; Springer-Verlag., ISBN: 0-387-18731-6
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    ABSTRACT: Scattering amplitudes are extracted from (elastic scattering) differential cross sections under the constraint that the scattering function is unitary. A modification to the Newton iteration method has been used to solve the nonlinear equation that specifies the phase of the scattering amplitude in terms of the complete (0[degree] to 180[degree]) cross section. The approach is tested by using it to specify the scattering amplitude from simulated data and comparing the result with the amplitude found by using an exact iterated fixed point method of solution. The (modified) Newton method was then used to analyze the cross sections from neutron--[alpha]-particle scattering at low nuclear energies ([lt]24 MeV) and from 1000-eV electron-water molecule scattering.
    Physical Review A 12/1994; 50(5):4000-4006. · 3.04 Impact Factor


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