  NDE (Near-dissociation expansion) including LeRoy-Bernstein formulas are
improved by taking into account the multipole expansion coefficients and the
non asymptotic part of the potential curve. Applying these new simple
analytical formulas to photoassociation spectra of cold alkali atoms, we
improve the determination of the asymptotic coefficient, reaching a 1%
accuracy, for long-range relativistic potential curve of diatomic molecules.
