Theoretical study for the dependence of collisional shift and width on isotopic mass in a Hg clock transition perturbed by Rb atoms*

The usage of two-species atomic mixtures for the realization of an atomic clock needs an accurate knowledge of their mutual interactions. Understanding the interactions between the atoms forming the atomic mixture is crucial for the study of collisional effects in the clock transition. In this regard, we investigate the isotopic dependence of collisional line shape parameters: widths and shifts of Hg clock transition perturbed by the Rb atoms in the temperature range 1nK to 1K.  To carry out these calculations, we utilized the Born-Oppenheimer effective interaction potential by including the leading long-range van der Waals terms. We demonstrate the connection between the dependence of collisional line shape parameters on the reduced mass of the colliding partners as well as the variation of the scattering length in the ground and excited state of Hg-Rb system. Further, we compare the full quantum scattering calculations with a semi-classical approximation for collisional parameters. We found that the shape resonances in the ground and excited  scattering states lead to significant variations of collisional line shape parameters with the change of the reduced mass of colliding atoms. This study provide insights to ongoing experiments focused on the collisional processes in a trapped ultra-cold mixtures of Hg and Rb atoms [1].

[1.] M. Witkowski et al. Optics Express 25, 3165 (2017).