We use accurate quantum mechanical calculations to analyze the effects of parallel electric and magnetic fields on collision dynamics of OH(2Pi) molecules. It is demonstrated that spin relaxation in 3He-OH collisions at temperatures below 0.01 K can be effectively suppressed by moderate electric fields of order 10 kV/cm. We show that electric fields can be used to manipulate Feshbach resonances in collisions of cold molecules. Our results can be verified in experiments with OH molecules in Stark decelerated molecular beams and electromagnetic traps.
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