  We present a new theoretical framework for modelling 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 sizes of up to 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 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 gas 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.
