Scattering- and Binding Properties of Two 133Cs Atoms in Free Space and in an Ultracold, Low-Dense 133Cs Vapor

Abstract

The scattering- and bound-state properties of two ¹³³Cs atoms, in free space as well as in low-dense Cs vapor, are calculated for both electronic singlet and triplet states. In free space, standard scattering theory is used; specifically, the Lippmann–Schwinger t-matrix equation is solved by a matrix-inversion technique. The output is the phase shifts, from which the corresponding (total, viscosity, [complex] spin-exchange, and average) cross sections are computed. In the vapor, a generalized scattering theory is invoked, the key equation being the Galitskii–Migdal–Feynman T-matrix equation. This is solved by the same technique to obtain the cross sections in the medium. Likewise, the t- and T-matrix equations are solved for negative definite energy eigenvalues—again, by matrix inversion, albeit after symmetrizing the kernel in the integral equation involved—to determine the respective binding energies of the Cs₂ dimer in free space and in the vapor. Sharp resonance peaks, representing ‘quasi’ bound states, appear in the cross sections. In the triplet total and viscosity cross sections, quantum effects appear as undulations. The results obtained for the complex spin-exchange cross sections are particularly highlighted, because of their importance in the spectroscopy of the ¹³³Cs₂ dimer. So are the results for the binding energy of this dimer, which are important in the physics of ultracold molecules. In calculating this quantity, as many relative partial waves as necessary (ℓ = 0–7 and 0–8 in free space and the medium, respectively) are taken into account to guarantee ‘convergence’. The role of the medium is given special attention throughout. Most of the quantities considered here are calculated for the first time; but whenever available, comparison is made with previous results.