  The recently-computed ExoMol line lists for isotopologues of AlH are used to
analyse the blue spectrum (4000-4500 {\AA}) of Proxima Cen (M5.5 V). Comparison
of the observed and computed spectra enables the identification of a large
number of 27AlH lines of the A1{\Pi} - X1{\Sigma}+ band system: the spectral
range covering 1-0, 0-0 and 1-1 bands is dominated by clearly resolved AlH
lines. We reveal the diffuse nature of transitions close to the dissociation
limit which appears in the form of increasingly wider(up to 5 {\AA}) and
shallower (up to the continuum confusion limit) AlH line profiles. The
predicted wavelengths of AlH diffuse lines are systematically displaced. The
effect broadening by pre-dissociation states on the line profiles is included
by increasing the radiative damping rate by up to 5 orders of magnitude. We
determine empirical values of damping rates for a number of the clean 0-0
Q-branch transitions by comparing the observed and synthetic stellar spectra.
We find excellent agreement between our damping rates and lifetimes available
in the literature. A comparison of 27Al1H ExoMol and REALH spectra shows that
the observed spectrum is better described by the ExoMol line list. A search for
26Al1H lines in the Proxima Cen spectrum does not reveal any notable features;
giving an upper limit of 27Al1H/26Al1H {>} 100.
