  As a physically motivated and computationally simple model for cold atomic
and molecular collisions, the multichannel quantum defect theory (MQDT) with
frame transformation (FT) formalism provides an analytical treatment of
scattering resonances in an arbitrary partial wave between alkali-metal atoms,
leading to the experimental observation of $p-$ and $d-$wave resonances.
However, the inconsistency of quantum defects for describing scattering
resonances shows up when compared with experiments. Here, with two
heteronuclear atoms in the ground state of an optical tweezer, the energy
dependence of quantum defects is obviously revealed by comparing the measured
s-wave scattering length with the prediction of MQDT-FT. By dividing the
quantum defects into energy sensitive and insensitive categories, the
inconsistency is ultimately removed while retaining the analytic structure of
MQDT-FT. This study represents a significant improvement in the analytical
MQDT-FT and demonstrates that a clean two-particle system is valuable to the
test of collisional physics.
