We present a new theoretical framework for modeling the fusion process of Lennard�Jones (LJ) clusters.Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing paths up to the cluster size of 150 atoms. We demonstrate that in this way all known global minima structures of the (LJ)-clusters can be found. Our method provides an efficient tool for the calculation and analysis of atomic cluster structure. With its use we justify the magic number sequence for the clusters of noble gas atoms and compare it with experimental observations. We report the striking correspondence of the peaks in the dependence of the second derivative of the binding energy per atom on cluster size calculated for the chain of the (LJ)-clusters based on the icosahedral symmetry with the peaks in the abundance mass spectra experimentally measured for the clusters of noble gas atoms. Our method serves as an efficient alternative to the global optimization techniques based on the Monte-Carlo simulations and it can be applied for the solutions of a broad variety of problems in which atomic cluster structure is important.