Ionization in cold collisions of Rydberg atoms is possible via two mechanisms: associative and Penning ionization. Associative ionization is a short range process of low efficiency, because it requires close encounters enabling overlap of Rydberg atom wavefunctions (at internuclaer distances R << n*2). In contrast, Penning ionization is a long-range process (at R >> n*2), which is enabled by the dipole-dipole interaction (atomic units are used in this abstract)
where Di are the dipole moments of both atoms and n denotes the orientation of the internuclear axis.
We consider the formation of atomic ions in an Ager-type processes: one of the Rydbrg atoms undergoes a dipole transition from the initial state nl to a lower state n'l', while the other atom is excited form the initial state nl to the ionization continuum. Such ionization can take place if the energy released in the nl → n'l' transition is equal to (or larger than) the binding energy of electron in the nl state, which is given by the condition n*' < n* sqrt(2) (n* is the effective quantum number). Perturbation theory  allows one to express the autoionization width Γ(R) via the photoionization cross section σph of atom in the nl state and the reduced dipole matrix elements |Dnn'| of the nl → n'l' transitions
We have evaluated the ionization rates using semiclassical analytical formulae for both the photoionization cross sections and the dipole matrix elements derived in  for alkali atoms. The resulting is a function that oscillates around the power-law curve with CS = 0.3 and CP = 0.46 for nS and nP states, respectively. These results should help in understanding the ionization dynamics of cold Rydberg gases .