The results of a detailed rotational analysis involving the assignment of some 14 500 lines are reported. Observed bands have been ascribed to transitions between nine singlet states (including the ground state) and between seven triplet states. Singlet-triplet systems have not yet been observed, but the relative energies of the singlet and triplet states have been determined by the analysis of spin-forbidden perturbations. The ground state is π4σ2, X1Σ+, and the first excited states π4σπ*, a3Πr, A1Π. Above these lie two further non-Rydberg states, B1Σ+ and b3Σ+, which seem to arise from a configuration of the kind π4σσ*. The remaining eleven states seem to be Rydberg states, π4σ(nlλ) 3Λ, 1Λ, which converge on the 2Σ+ ground state of AlF+. However, no series have yet been recognized so that neither is the ionization potential of AlF well determined nor are there certain assignments of the Rydberg states, although suggestions are made. The triplet splittings in all but the a3Π state are very small (and in some systems there may be cancellation), so that the 3Σ+-3Σ+ transitions and a 3Π-3Σ+ system simulate, even at fairly high resolution, 1Σ-1Σ and 1Π-1Σ systems respectively. At high resolution lines of the 3Σ+-a3Π systems show small splittings, some of which are of the kind expected for nuclear magnetic hyperfine structure in transitions of the type case (bβ-S)-case (aβ); however some of the observations are not yet understood.
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