Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The collinear helium atom and two-electron ions   Collinear configurations of the helium-like atomic systems, relevant, e.g.,
for the quasifree mechanism of the double photoionization of helium, are
studied, parameterized by the single scalar parameter $-1\leq \lambda\leq1$
("collinear parameter") where $\lambda=0$ corresponds to the electron-nucleus
($\textbf{e-n}$) coalescence and $\lambda=1$ corresponds to the
electron-electron ($\textbf{e-e}$) coalescence. In general, $\lambda>0$
corresponds to the \textbf{n-e-e} configuration, and $\lambda<0$ to the
\textbf{e-n-e} configuration. Simple mathematical representations of the
expectation values of the Dirac delta function relevant for the collinear
configurations are derived and calculated from fully three-body dynamics
without approximation for the two-electron atomic wave functions with nuclear
charge $1\leq Z\leq5$. Simple formulas for calculating the expectation values
of the kinetic and potential energy operators in collinear configurations are
derived. Unusual physical properties of the \textbf{n-e-e} collinear
configurations found for certain ranges of $\lambda$ are presented. The first
few angular Fock coefficients for collinear configurations are derived as
functions of $\lambda$. Highly accurate model wave functions describing the
ground states of the two-electron atoms with collinear arrangement of the
particles are constructed. All results are illustrated by tables and figures.

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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin