  The effects of core polarization and tensor coupling on the magnetic moments
in $^{13}_\Lambda$C, $^{17}_\Lambda$O, and $^{41}_\Lambda$Ca
$\Lambda$-hypernuclei are studied in the Dirac equation with scalar, vector and
tensor potentials. It is found that the effect of core polarization on the
magnetic moments is suppressed by $\Lambda$ tensor coupling. The $\Lambda$
tensor potential reduces the spin-orbit splitting of $p_\Lambda$ states
considerably. However, almost the same magnetic moments are obtained using the
hyperon wave function obtained via the Dirac equation either with or without
the $\Lambda$ tensor potential in the electromagnetic current vertex. The
deviations of magnetic moments for $p_\Lambda$ states from the Schmidt values
are found to increase with nuclear mass number.

Nuclear Theory