Estimating bounds on collisional relaxation rates of spin-polarized 87Rb atoms at ultracold temperatures

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Abstract
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.