  This work stresses the importance of the choice of the set of reference
functions in the Generalized Multichannel Quantum Defect Theory to analyze the
location and the width of Feshbach resonance occurring in collisional
cross-sections. This is illustrated on the photoassociation of cold rubidium
atom pairs, which is also modeled using the Mapped Fourier Grid Hamiltonian
method combined with an optical potential. The specificity of the present
example lies in a high density of quasi-bound states (closed channel)
interacting with a dissociation continuum (open channel). We demonstrate that
the optimization of the reference functions leads to quantum defects with a
weak energy dependence across the relevant energy threshold. The main result of
our paper is that the agreement between the both theoretical approaches is
achieved only if optimized reference functions are used.
