  Aluminum monofluoride (AlF) is a suitable molecule for laser cooling and
trapping. Such experiments require an extensive spectroscopic characterization
of the electronic structure. Two of the theoretically predicted higher lying
triplet states of AlF, the counterparts of the well-characterized D$^1\Delta$
and E$^1\Pi$ states, had experimentally not been identified yet. We here report
on the characterization of the d$^3\Pi$ ($v=0-6$) and e$^3\Delta$ ($v=0-2$)
states, confirming the predicted energetic ordering of these states (J. Chem.
Phys. 88 (1988) 5715-5725), as well as of the f$^3\Sigma^+$ ($v=0-2$) state.
The transition intensity of the d$^3\Pi, v=3$ $-$ a$^3\Pi, v=3$ band is
negligibly small. This band gets its weak, unexpected rotational structure via
intensity borrowing from the nearby e$^3\Delta, v=2$ $-$ a$^3\Pi, v=3$ band,
made possible via spin-orbit and spin-rotation interaction between the d$^3\Pi$
and e$^3\Delta$ states. This interaction affects the equilibrium rotational
constants in both states; their deperturbed values yield equilibrium
internuclear distances that are consistent with the observations. We determine
the ionization potential of AlF to be 78492(1) cm$^{-1}$ by ionization from the
d$^3\Pi$ state.
