  Two recent experimental observations at the ATOMKI Institute of the Hungarian
Academy of Sciences (regarding the angular emission pattern of
electron-positron pairs from nuclear transitions from excited states in 8Be and
4He) indicate the possible existence of a particle of a rest mass energy of
roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the
process, preceding the emission of the electron-positron pair. Based on the
symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the
X17 could either be a vector, or a pseudoscalar particle. Here, we calculate
the effective potentials generated by the X17, for hyperfine interactions in
simple atomic systems, for both the pseudoscalar as well as the vector X17
hypotheses. The effective Hamiltonians are obtained in a general form which is
applicable to both electronic as well as muonic bound systems. The effect of
virtual annihilation and its contribution to the hyperfine splitting also is
considered. Because of the short range of the X17-generated potentials, the
most promising pathway for the observation of the X17-mediated effects in bound
systems concerns hyperfine interactions, which, for $S$ states, are given by
modifications of short-range (Dirac-delta) potentials in coordinate space. For
the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between
the bound lepton and the nucleus exclusively leads to hyperfine effects, but
does not affect the Lamb shift. Effects due to the X17 are shown to be
drastically enhanced for muonic bound systems. Prospects for the detection of
hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium,
muonic hydrogen, muonium, true muonium ($\mu^+\mu^-$ bound system), and
positronium.
