We perform a theoretical analysis to interpret the spectra of purely
long-range helium dimers produced by photoassociation (PA) in an ultra-cold gas
of metastable helium atoms. The experimental spectrum obtained with the PA
laser tuned closed to the 23S1↔23P0 atomic line has been
reported in a previous Letter. Here, we first focus on the corrections to be
applied to the measured resonance frequencies in order to infer the molecular
binding energies. We then present a calculation of the vibrational spectra for
the purely long-range molecular states, using adiabatic potentials obtained
from perturbation theory. With retardation effects taken into account, the
agreement between experimental and theoretical determinations of the spectrum
for the 0u+ purely long-range potential well is very good. The results
yield a determination of the lifetime of the 23P atomic state