  It was recently shown that, for central spin-1/2 and central spin-1, the XX
central spin model is integrable in the presence of a magnetic field oriented
perpendicular to the XY plane in which the coupling exists. In the spin-1/2
case, it was also shown, through an appropriate limit of the non-skew symmetric
XXZ Richardson-Gaudin models, that it remained integrable even when the
magnetic field is tilted to contain an in-plane component. Although the model
has not yet been shown to explicitly belong to a known class of Richardson-
Gaudin models, we show, in this work, that the spin-1 case also remains
integrable in a titled magnetic field. We do so by writing explicitly the
complete set of conserved charges, then showing that these operators obey
polynomial relations. It is finally demonstrated numerically that dark states,
for which the central spin is completely unentangled with the bath, can emerge
at strong enough coupling just as they do in the central spin-1/2 model in an
arbitrarily oriented magnetic field.
