Suppression of inelastic collisions of polar $^1 \Sigma$ state molecules in an electrostatic field

Collisions of polar $^{1}\Sigma$ state molecules at ultralow energies are considered, within a model that accounts for long-range dipole-dipole interactions, plus rotation of the molecules. We predict a substantial suppression of dipole-driven inelastic collisions at high values of the applied electric field, namely, field values of several times $B_e/\mu$. Here $B_e$ is the rotational constant, and $\mu$ is the electric dipole moment of molecules. The sudden large drop in the inelastic cross section is attributed to the onset of degeneracy between molecular rotational levels, which dramatically alters the scattering Hamiltonian. As a result of the large ratio of elastic to inelastic collision rates, we predict that evaporative cooling may be feasible for $^{1}\Sigma$ state molecules in weak-field-seeking states, provided a large bias electric field is present.