Theoretical Studies of collisional processes and gases at ultracold and cold temperatures in research that is responsive to the experimental program. Scattering at low temperatures is sensitive to the interaction at large distances of the colliding species. We calculated the interactions at long-range of a pair of ytterbium atoms (P. Zhang and a. Dalgarno 2008) and between ground state hydrogen atoms and highly excited hydrogen atoms ( D. Vrinceanu and A. Dalgarno 2008). We studied the process of thermalization and clarified its meaning (P. Zhang et al. 2008), P. Zhang et al. 2009, Bovino et al. 2009). Several studies were completed of collisions at ultralow temperatures in the presence of electric and magnetic fields including their influence on chemical reactions (Tscherbul et al. 2008, Tscherbul 2008, Pavlovich et al. 2009).