Independent N-electron method and high accuracy calculations of the groundstate energy of the nonrelativistic light atoms (3 <= N-e <= 10)

A new method based on the independent electron-pair approximation is develo ped 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 calculat ions can be separated into several parts, this new method gives very accura te results and does not require expensive computing facilities. As a test, the ground state energies (GSE) of the nonrelativistic atoms for 3 less tha n or equal to N-e less than or equal to 10 are calculated using this new me thod. The calculated results are found to be in close agreement with the mo st recent available version of the exact GSE which is derived from the expe rimental data after subtracting the contributions from the relativistic eff ect, QED radiative corrections, finite nucleon mass corrections, and the fi nite radius of the nuclear size. Those accurate results have not been repro duced for N-e greater than or equal to 5 by any direct theoretical calculat ions in literatures. Since this method is not restrained to nonrelativistic or Coulomb systems, it should become powerful to study other quantum inter acting systems.