Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coulomb singularities in scattering wave functions of spin-orbit-coupled
  states   We report on our analysis of the Coulomb singularity problem in the frame of
the coupled channel scattering theory including spin-orbit interaction. We
assume that the coupling between the partial wave components involves orbital
angular momenta such that $\Delta l = 0, \pm 2$. In these conditions, the two
radial functions, components of a partial wave associated to two values of the
angular momentum $l$, satisfy a system of two second-order ordinary
differential equations. We examine the difficulties arising in the analysis of
the behavior of the regular solutions near the origin because of this coupling.
First, we demonstrate that for a singularity of the first kind in the
potential, one of the solutions is not amenable to a power series expansion.
The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic
divergence arises at the second iteration. To overcome this difficulty, we
introduce two auxilliary functions which, together with the two radial
functions, satisfy a system of four first-order differential equations. The
reduction of the order of the differential system enables us to use a
matrix-based approach, which generalizes the standard Frobenius method. We
illustrate our analysis with numerical calculations of coupled scattering wave
functions in a solid-state system.

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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom