FI G. 1: Two-body inelastic loss for fermionic polar molecules. (A) We extract the inelastic loss rate coe fficient β from a fit (solid lines) to the measured time evolution of the trapped molecular gas de nsity. The data shown here are for an induced dipole moment d = 0 . 08 Debye (open triangle s) and d = 0 . 19 Debye (filled circles), and an initial temperature T = 300 nK. (B) We plot β , divided by T , as a function of the induced dipole moment, d . A fit to a power-law dependence in the region d > 0 . 1 Debye yields a power of 6 . 1 ± 0 . 8. The dashed line shows a fit to a simple model based on the quantum threshold behavior for tunneling through a dipolar-interaction modified p -wave barrier (see text). The solid line shows the result of a more complete quantum scattering calculation including an absorbing potential at short range. Note that the full model (dashed line) deviates from the simple model prediction at our largest d where the scattering is no longer in the Wigner threshold regime. The calculated dependence of the induced dipole moment on the applied electric field is shown in the inset to (B). ture. Previous work at zero electric field (without long-range dipolar interactions) showed that the lifetime of the trapped $^{40}$K$^{87}$Rb molecules is limited by atom-exchange chemical reactions that proceed via p -wave scattering [21]. In our experiments, the typical transla- tional temperature of the molecular gas is 300 nK, while the energy height of the p -wave barrier for $^{40}$K$^{87}$Rb molecules corresponds to a temperature of approximately 24 µ K [22]. With the barrier height much larger than typical collision energies, scattering rates in the molecular cloud are determined by the tunneling rate through the centrifugal barrier and the molecular gas lifetime is relatively long (on the order of 1 s) [21]. In this paper, we investigate the effect of electric dipolar interactions on collisions and find a surprisingly large effect even for our relatively modest range of applied electric fields. 4 0.01 0.1 1 10 100 0 1 2 0.0 0.2 0.4 Molec u lar density (10 12 cm -3 ) (B) Dipole moment (Debye)  β  / T (10 -5 cm 3 s -1 K -1 ) Time (s)  0.19 Debye 0.08 Debye  (A) 0 1 2 3 4 5 0.0 0.1 0.2  Dipole moment (Debye)  E field (kV/cm)