Measurement of the collisional frequency shift in a /sup 87/Rb fountain

We describe the operation of a laser cooled /sup 87/Rb frequency standard and present a measurement of the /sup 87/Rb ground state hyperfine frequency with a relative accuracy of 2.2/spl times/10/sup -15/, by comparison with Cs fountains primary standards. The measured frequency is 6834682610.904333(17) Hz. We present in detail our measurements of the cavity pulling effect and frequency shift induced by cold collisions. We compare it with the most recent predictions of collision theories. The collisional frequency shift is at least 30 times smaller than for /sup 133/Cs. This opens the way towards accuracies in the 10/sup -16/ range together with an excellent frequency stability for cold atom microwave standards. In addition, the comparisons between our Cs and Rb fountains lead to a test of the fine structure constant /spl alpha/ variations with time at the level of 7/spl times/10/sup -15/ per year.