  Contact $P$-wave interactions connected to the Larmor interaction of a
magnetic dipole and Thomas spin precession in the filed of an electric
quadrupole are described and their implications for spectroscopy of exotic
$\Omega^{-}$-atoms are studied. In order to evaluate the magnitude of the
contact $P$-wave interactions as compared to the conventional long-range
interactions and the sensitivity of spectroscopic data to the
$\Omega^{-}$-hyperon quadrupole moment, we consider $2P$ states of $\Omega
^{-}$ atoms formed with light stable nuclei with spins $I \geq 1/2$ and atomic
numbers $Z \leq 10$. The energy level splitting caused by the contact
interactions is 2-5 orders of magnitude smaller than the conventional
long-range interactions. Strong decay widths of $p\Omega ^{-}$ atoms due to
reactions $p\Omega^{-} \to \Lambda \Xi^{0}$ and $p\Omega^{-} \to \Sigma \Xi$,
induced by $t$-channel kaon exchanges, are calculated. $\Omega ^{-}$ atoms
formed with the light nuclei have strong widths 5-6 orders of magnitude higher
than splitting caused by the contact interactions. The low-$L$ pattern in the
energy spectra of intermediate- and high-$Z$ $\Omega ^{-}$ atoms thus cannot be
observed. The $\Omega ^{-}$ quadrupole moment can be measured by observing
$X$-rays from circular transitions between high-$L$ levels in $\Omega^{-}$
exotic atoms. The effect of strong interactions in $^{208}$Pb$\Omega ^{-}$
atoms is negligible starting from $L \sim 10$. The contact $P$-wave
interactions exist in ordinary atoms and $\mu$-meson atoms.
