Ultracold silver-atom collisions and the formation of silver dimers by photo- and magneto-association

We have performed three theoretical simulations relevant for describing collisions among laser-cooled silver atoms and for the formation of $Ag_2$ molecules from these colliding atoms. Firstly, we determined the relativistic electronic structure of $Ag_2$ molecules in ground and low-lying excited states. Secondly, we computed rotational and vibrational levels of the ground and excited electronic states as well as rovibrationally averaged electric transition dipole moments. Using this knowledge, we analyzed a simplified quantum-mechanical model of the one-photon photoassociation process to form electronically excited $Ag_2$ from microkelvin Ag atoms and make predictions for lineshapes and saturation effects as functions of laser frequency and intensity. Finally and thirdly, we performed coupled-channels calculations, numerical solutions of sets of coupled radial Schrödinger equations of ultracold ground-state Ag collisions in an external magnetic field. These calculations include the effects of two Born-Oppenheimer potentials as well as hyperfine Fermi-contact and Zeeman interactions. We discuss the expected range of 𝑠-wave scattering lengths as well as strengths and distribution of Fano-Feshbach resonances as a function of the magnetic-field strength for the $_{107}Ag$ and $_{109}Ag$ isotopes. We highlight the periodicity of the scattering length with small changes in the depths of the Born-Oppenheimer potentials. The Fano-Feshbach resonances can be used to magneto-associate ultracold Ag atoms into weakly bound ground-state $Ag_2$ dimers.