Non-conventional optimization procedure for mass effects investigation in the ground state energies of 1s core-ionized helium-like atoms from helium to xenon

摘要

The non-relativistic energy magnitudes for the ground state of He and He isoelectronic series with atomic numbers Z=3-54 are calculated. Calculations are performed using explicitly correlated trial wave-functions of the generalized Hylleraas type. A variational procedure is developed that allows solution of the two-particle Schroedinger equation for a practically unlimited number of parameters in a series of trial wave-functions along the positive degrees of the Hylleraas coordinates. Nonconventional optimization methods are developed and, in particular, applied nonlinear programming is used to solve the problem. The contributions to the energy for various parameters is analyzed. Mass corrections and polarizations to the non-relativistic energy are studied. The obtained results are compared to existing experimental data and available theoretical data by other authors. One should note that until now, such data have been computed only for atomic numbers Z=2-12. The behavior of the ground state energy versus Z, and the effects of mass corrections and polarizations, contributing to these effects in the electron system energies, are investigated.