Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Few-electron atomic ions in non-relativistic QED: the Ground state
  energy   Following detailed analysis of relativistic, QED and mass corrections for
helium-like and lithium-like ions with static nuclei for $Z \leq 20$ the domain
of applicability of Non-Relativistic QED (NRQED) is localized for ground state
energy. It is demonstrated that for both helium-like and lithium-like ions with
$Z \leq 20$ the finite nuclear mass effects do not change 4-5 significant
digits (s.d.), and the leading relativistic and QED effects leave unchanged 3-4
s.d. in the ground state energy. It is shown that the non-relativistic ground
state energy can be interpolated with accuracy not less than 13 s.d. for $Z
\leq 12$, and not less than 12 s.d. for $Z \leq 50$ for helium-like as well as
for $Z \leq 20$ for lithium-like ions by a compact meromorphic function in
${\lambda}=\sqrt{Z-{Z_B}}$ ($Z_B$ is the 2nd critical charge, see {TLO:2016}),
$P_9(\lambda)/Q_5(\lambda)$. It is found that the Majorana formula - a second
degree polynomial in $Z$ with two free parameters - and a fourth degree
polynomial in ${\lambda}$ (a generalization of the Majorana formula) reproduce
the ground state energy of the helium-like and lithium-like ions for $Z \leq
20$ in the domain of applicability of NRQED, thus, at least, 3 s.d. It is noted
that $\gtrsim 99.9\%$ of the ground state energy is given by the variational
energy for properly optimized trial function of the form of (anti)-symmetrized
product of three (six) screened Coulomb orbitals for two-(three) electron
system with 3 (7) free parameters for $Z \leq 20$, respectively. It may imply
that these trial functions are, in fact, {\it exact} wavefunctions in
non-relativistic QED, thus, the NRQED effective potential can be derived. It is
shown that the sum of relativistic and QED effects in leading approximation - 3
s.d. - for both 2 and 3 electron systems is interpolated by 4th degree
polynomial in $Z$ for $Z \leq 20$.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom