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.
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