Jamming densities of random sequential adsorption on d -dimensional cubic lattices

The rate of convergence of the jamming densities to their asymptotic high-dimensional tree approximation is studied, for two types of random sequential adsorption (RSA) processes on a d-dimensional cubic lattice. The first RSA process has an exclusion shell around a particle of nearest neighbors in all d dimensions (N1 model). In the second process the exclusion shell consists of a d-dimensional hypercube with length k=2 around a particle (N2 model). For the N1 model the deviation of the jamming density ρr(d) from its asymptotic high d value ρasy(d)=ln(1+2d)2d vanishes as [ln(1+2d)2d]3.41. In addition, it has been shown that the coefficients an(d) of the short-time expansion of the occupation density of this model (at least up to n=6) are given for all d by a finite correction sum of order (n-2) in 1/d to their asymptotic high d limit. The convergence rate of the jamming densities of the N2 model to their high d limits ρasy(d)=dln33d is slow. For 2≤d≤4 the generalized Palasti approximation provides by far a better approximation. For higher d values the jamming densities converge monotonically to the above asymptotic limits, and their decay with d is clearly faster than the decay as (0.432332...)d predicted by the generalized Palasti approximation.