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 $\tilde{B} = B/s_{E_3}$ and a rescaled electric field $\tilde{F} = dF/B$. $B, d, F, s_{E_3}$ 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 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 (or even higher) to 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 $\tilde{B} \ge 10^8$ and $3.25 \le \tilde{F} \le 3.8$, with a maximum ratio reached for $\tilde{F} \simeq 3.4$ for a given $\tilde{B}$. We also discuss the importance of the electronic van der Waals interaction on the adimensional character of our study.