It is demonstrated that with increase of the cooled atoms density the intermediate between paired and multi-particles process start to play a predominant role even under conditions of small gas parameter ?=nf3 < < 1, where n is the trapped atom density and f is the scattering amplitude of the binary collision. The influence of the environment, i.e. background gas density effects, on the process of excitation transfer between atoms is illustrated through the example of the Rb isotropes. The condition on the trapped, cooled atoms density for observation of such effects is deduced.
