Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Potential energy surfaces in atomic structure: The role of Coulomb
  correlation in the ground state of helium   For the $S$ states of two-electron atoms, we introduce an exact and unique
factorization of the internal eigenfunction in terms of a marginal amplitude,
which depends functionally on the electron-nucleus distances $r_1$ and $r_2$,
and a conditional amplitude, which depends functionally on the interelectronic
distance $r_{12}$ and parametrically on $r_1$ and $r_2$. Applying the
variational principle, we derive pseudoeigenvalue equations for these two
amplitudes, which cast the internal Schr\"odinger equation in a form akin to
the Born-Oppenheimer separation of nuclear and electronic degrees of freedom in
molecules. The marginal equation involves an effective radial Hamiltonian,
which contains a nonadiabatic potential energy surface that takes into account
all interparticle correlations in an averaged way, and whose unique eigenvalue
is the internal energy. At each point $(r_1,r_2)$, such surface is, in turn,
the unique eigenvalue in the conditional equation. Employing the ground state
of He as prototype, we show that the nonadiabatic potential energy surface
affords a molecularlike interpretation of the structure of the atom, and aids
in the analysis of energetic and spatial aspects of the Coulomb correlation, in
particular correlation-induced symmetry breaking and quantum phase transition.

14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin