Estimating Bounds on Collisional Relaxation Rates of Spin-Polarized ⁸⁷Rb Atoms at Ultracold Temperatures

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized ⁸⁷Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized ⁸⁷Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb₂ and Cs₂. The corrections lead to a reduction in the relaxation rate for ⁸⁷Rb. Our primary concern is to analyze the sensitivity of the ⁸⁷Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a³Σ⁺_u state is already known, the major uncertainties are associated with the X¹Σ⁺_g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10^-15 cm³/s and 2.4 × 10^-15 cm³/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.