  We present a new theoretical framework for modelling the cluster growing
process. 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 sizes of more than 100 atoms. We demonstrate
that in this way all known global minimum structures of the Lennard-Jonnes (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 numbers sequence for the clusters of noble gases atoms and compare it
with experimental observations. We report the striking correspondence of the
peaks in the dependence on cluster size of the second derivative of the binding
energy per atom calculated for the chain of LJ-clusters based on the
icosahedral symmetry with the peaks in the abundance mass spectra
experimentally measured for the clusters of noble gases atoms. Our method
serves an efficient alternative to the global optimization techniques based on
the Monte-Carlo simulations and it can be applied for the solution of a broad
variety of problems in which atomic cluster structure is important.
