Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-atomic three- and four-body systems with muonium   Properties of some few-body systems which include one positively charged muon
$\mu^{+}$ and two electrons $e^{-}$ are discussed. In particular, we consider
the negatively charged muonium ion Mu$^{-}$ (or $\mu^{+} e^{-}_{2}$) and
four-body MuPs (or $\mu^{+} e^{-}_{2} e^{+}$) systems each of which has only
one stable bound (ground) state. The problem of annihilation of the
electron-positron pair(s) in the MuPs system is investigated. The hyperfine
structure splitting of the ground state in the MuPs system evaluated with our
expectation value of the muon-positron delta-function is $\Delta \approx$
23.05758 $MHz$. Another group of interesting four-body neutral systems
investigated in this study includes the $p^{+} \mu^{+} e^{-}_2, d^{+} \mu^{+}
e^{-}_2$ and $t^{+} \mu^{+} e^{-}_2$ `quasi-molecules'. These quasi-molecules
are formed in large numbers when positively charged muons slow down in liquid
hydrogen, or in liquid deuterium and/or tritium. The properties of these
systems are unique, since they occupy an intermediate position between actual
two-center molecules and one-center atoms.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th