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Contact $P$-wave interactions connected to the Larmor interaction of amagnetic dipole and Thomas spin precession in the filed of an electricquadrupole are described and their implications for spectroscopy of exotic$\Omega^{-}$-atoms are studied. In order to evaluate the magnitude of thecontact $P$-wave interactions as compared to the conventional long-rangeinteractions 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 atomicnumbers $Z \leq 10$. The energy level splitting caused by the contactinteractions is 2-5 orders of magnitude smaller than the conventionallong-range interactions. Strong decay widths of $p\Omega ^{-}$ atoms due toreactions $p\Omega^{-} \to \Lambda \Xi^{0}$ and $p\Omega^{-} \to \Sigma \Xi$,induced by $t$-channel kaon exchanges, are calculated. $\Omega ^{-}$ atomsformed with the light nuclei have strong widths 5-6 orders of magnitude higherthan splitting caused by the contact interactions. The low-$L$ pattern in theenergy spectra of intermediate- and high-$Z$ $\Omega ^{-}$ atoms thus cannot beobserved. 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 $P$-waveinteractions exist in ordinary atoms and $\mu$-meson atoms.

Decays, contact P-wave interactions and hyperfine structure in Omega- exotic atoms