Adimensional theory of shielding in ultracold collisions of dipolar rotors

We investigate the electric field shielding of ultracold collisions of dipolar rotors, initially in their first rotational excited state, using an adimensional approach. We establish a map of good and bad candidates for efficient evaporative cooling based on this shielding mechanism, by presenting the ratio of elastic over quenching processes as a function of a rescaled rotational constant (B) over tilde B = B/s(E3) and a rescaled electric field (F) over tilde = dF/B. B, d, F, and s(E3) are respectively the rotational constant, the full electric dipole moment of the molecules, the applied electric field, and a characteristic dipole-dipole energy. We identify two groups of bi-alkali-metal dipolar molecules. The first group, including RbCs, NaK, KCs, LiK, NaRb, LiRb, NaCs, and LiCs, is favorable with a ratio over 1000 at collision energies equal to (or even higher than) their characteristic dipolar energy. The second group, including LiNa and KRb, is not favorable. More generally, for molecules well described by Hund's case b, our adimensional study provides the conditions of efficient evaporative cooling. The range of appropriate rescaled rotational constant and rescaled field is approximately (B) over tilde >= 10(8) and 3.25 <= (F) over tilde <= 3.8, with a maximum ratio reached for (F) over tilde similar or equal to 3.4 for a given (B) over tilde. We also discuss the importance of the electronic van der Waals interaction on the adimensional character of our study.