Discussion on the origin of magic numbers in clusters

The distribution of the sizes of clusters is not continuous, but rather has local maxima. The numbers of atoms of those maxima distribution is called magic numbers. Two methods of determining magic numbers are firstly introduced, followed by three different models which were developed to explain the origin of magic numbers. Close-packing better explain those clusters build up with regular shells; LJ potential was used to calculate the energy properties of clusters which partially meet with the occurrence of magic numbers; LJ-plus-AT or LJ-plus-EX give a more detailed analysis of interaction mechanism.