  Dipolar relaxation happens when one or both colliding atoms flip their spins
exothermically inside a magnetic ($B$) field. This work reports precise
measurements of dipolar relaxation in a Bose-Einstein condensate of ground
state $^{87}$Rb atoms together with in-depth theoretical investigations.
Previous perturbative treatments fail to explain our observations except at
very small $B$-fields. By employing quantum defect theory based on analytic
solutions of asymptotic van der Waals interaction $-C_6/R^6$ ($R$ being
interatomic spacing), we significantly expand the applicable range of
perturbative treatment. We find the $B$-dependent dipolar relaxation lineshapes
are largely universal, determined by the coefficient $C_6$ and the associated
$s$-wave scattering lengths $a_{\rm sc}$ of the states before and after spin
flips. This universality, which applies generally to other atomic species as
well, implicates potential controls of dipolar relaxation and related cold
chemical reactions by tuning $a_{\rm sc}$.
