Independent N-Electron Method and High Accuracy Calculations of the Ground State Energy of the Nonrelativistic Light Atoms (3 ≤ N_e ≤ 10)

A new method based on the independent electron-pair approximation is developed to calculate the correlation energy and the basis size truncation error. The formalisms for the nondegenerate systems are described in this paper. Because all important terms are very efficiently selected and the calculations can be separated into several parts, this new method gives very accurate results and does not require expensive computing facilities. As a test, the ground state energies (GSE) of the nonrelativistic atoms for 3 ≤ N_e ≤ 10 are calculated using this new method. The calculated results arc found to be in close agreement with the most recent available version of the exact GSE which is derived from the experimental data after subtracting the contributions from the relativistic effect, QED radiative corrections, finite nucleon mass corrections, and the finite radius of the nuclear size. Those accurate results have not been reproduced for N_e ≥ 5 by any direct theoretical calculations in literatures. Since this method is not restrained to nonrelativistic or Coulomb systems, it should become powerful to study other quantum interacting systems.