Many-Body Contributions for the Compressibility of Helium Atomic Cluster He9

Lowdin scheme was applied to calculate the repulsive potentials and their multi-body expansions of compressed atomic cluster He9. The micro-pressure and their expansions were calculated. The results show that many-body effects are important for the compressibility of atomic cluster He9. At the same volume, the pressure calculated by two-body approximation is 10%～30% higher than the actual many-body system. If three-body corrections are considered, the results become 1.5%～10% lower. When the four-body effect was included, the approximation calculations fit real system quite well. The compression properties of atomic cluster He9 are similar to the experimental results of solid helium.