The electromagnetic processes of annihilation of $(e^+ e^-)$ pairs, produced
in high-energy nucleus-nucleus collisions, into heavy lepton pairs are
theoretically studied in the one-photon approximation, using the technique of
helicity amplitudes . For the process $e^+e^- \rightarrow \mu^+\mu^-$, it is
shown that -- in the case of the unpolarized electron and positron -- the final
muons are also unpolarized but their spins are strongly correlated. For the
final $(\mu^+ \mu^-)$ system, the structure of triplet states is analyzed and
explicit expressions for the components of the spin density matrix and
correlation tensor are derived. It is demonstrated that here the spin correlations
of muons have the purely quantum character, since one of the Bell-type
incoherence inequalities for the correlation tensor components is always violated.
In doing so, it is established that the qualitative character of the muon spin
correlations does not change when involving the additional contribution of the
weak interaction of lepton neutral currents through the virtual $Z^0$ boson.
On the other hand, the theoretical investigation of spin structure for the two-photon
process $\gamma \gamma \rightarrow e^+e^-$ ( where the photon pairs, in
particular, may be emitted in relativistic heavy-ion and hadron-nucleus collisions )
is performed as well. Here -- quite similarly to the process
$e^+e^- \rightarrow \mu^+\mu^-$ -- in the case of unpolarized photons the final
electron and positron remain unpolarized, but their spins prove to be strongly
correlated. Explicit expressions for the components of the correlation tensor
and for the relative fractions of singlet and triplet states of the final $(e^+ e^-)$
system are derived. Again, one of the Bell-type incoherence inequalities for the
correlation tensor components is always violated and, thus, spin correlations of
the electron and positron have the strongly pronounced quantum character.
Analogous considerations can be wholly applied as well, respectively, to the
annihilation process $e^+ e^- \rightarrow \tau^+ \tau^-$ and to the two-photon
processes $\gamma \gamma \rightarrow \mu^+ \mu^-$, $\gamma \gamma \rightarrow \tau^+ \tau^-$, which become possible at considerably higher energies.
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