  The surface integral method for estimating ionic-covalent interactions in
diatomic systems been successful in producing cross sections for mutual
neutralisation (MN) in reasonable agreement with experimental results for
branching fractions between final states in systems such as O$^+$/O$^-$ and
N$^+$/O$^-$. However, for simpler cases of MN involving H$^-$ or D$^-$, such as
Li$^+$/D$^-$ and Na$^+$/D$^-$, it has not produced results that are in
agreement with experiments and other theoretical calculations; in particular,
for Li$^+$/D$^-$ calculations predict the wrong ordering of importance of final
channels, including the incorrect most populated channel. The reason for this
anomaly is investigated and a leading constant to the asymptotic H$^-$
wavefunction is found that is different by roughly a factor $1/\sqrt{2}$ to
that which has been used in previous calculations with the surface integral
method involving H$^-$ or D$^-$. With this correction, far better agreement
with both experimental results and with calculations with full quantum and LCAO
methods is obtained. Further, it is shown that the surface integral method and
LCAO methods have the same asymptotic behaviour, in contrast to previous
claims. This result suggests the surface integral method, which is
comparatively easy to calculate, has greater potential for estimating MN
processes than earlier comparisons had suggested.
