Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calculations of long-range three-body interactions for
  He($n_0\,^{\lambda}S$)-He($n_0\,^{\lambda}S$)-He($n_0^{\prime}\,^{\lambda}L$)   We theoretically investigate long-range interactions between an excited $L$
state He atom and two identical $S$ state He atoms, for the cases of the three
atoms all in spin singlet states or all in spin triplet states, denoted by
He($n_0\,^{\lambda}S$)-He($n_0\,^{\lambda}S$)-He($n_0^{\prime}\,^{\lambda}L$),
with $n_0$ and $n_0'$ principal quantum numbers, $\lambda=1$ or 3 the spin
multiplicity, and $L$ the orbital angular momentum of a He atom. Using
degenerate perturbation theory for the energies up to second-order, we evaluate
the coefficients $C_3$ of the first order dipolar interactions and the
coefficients $C_6$ and $C_8$ of the second order additive and nonadditive
interactions. Both the dipolar and dispersion interaction coefficients, for
these three-body degenerate systems, show dependences on the geometrical
configurations of the three atoms. The nonadditive interactions start to appear
in second-order. To demonstrate the results and for applications, the obtained
coefficients $C_n$ are evaluated with highly accurate variationally-generated
nonrelativistic wave functions in Hylleraas coordinates for
He($1\,^{1}S$)-He($1\,^{1}S$)-He($2\,^{1}S$),
He${(1\,^{1}S)}$-He${(1\,^{1}S)}$-He${(2\,^{1}P)}$,
He${(2\,^{1}S)}$-He${(2\,^{1}S)}$-He${(2\,^{1}P)}$, and
He${(2\,^{3}S)}$-He${(2\,^{3}S)}$-He${(2\,^{3}P)}$. The calculations are given
for three like-nuclei for the cases of hypothetical infinite mass He nuclei,
and of real finite mass $^4{}$He or $^3{}$He nuclei. The special cases of the
three atoms in equilateral triangle configurations are explored in detail, and
for the cases where one of the atoms is in a $P$ state, we also present results
for the atoms in an isosceles right triangle configuration or in an equally
spaced co-linear configuration. The results can be applied to construct
potential energy surfaces for three helium atom systems.

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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat