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

L. MIHAILOV1,* , R. PAVLOV2,3, CH. VELCHEV2, L. PAVLOV2, M. DIMITROVA-IVANOVICH2, J. MARUANI3

Affiliation

  1. Institute of Solid State Physics, Bulgarian Academy of Sciences,72 Tsarigradsko Chaussee,1784 Sofia,Bulgaria
  2. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
  3. Laboratoire de Chimie Physique, CNRS and UPMC, 11 Rue Pierre et Marie Curie, 75005 Paris, France

Abstract

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. Non-conventional 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..

Keywords

Explicitly correlated wave-functions, Helium isoelectronic series, Mass-polarization, Mass-correlations.

Submitted at: Nov. 28, 2006
Accepted at: Feb. 15, 2007

Citation

L. MIHAILOV, R. PAVLOV, CH. VELCHEV, L. PAVLOV, M. DIMITROVA-IVANOVICH, J. MARUANI, Non-conventional optimization procedure for mass effects investigation in the ground state energies of 1s core-ionized helium-like atoms from helium to xenon, Journal of Optoelectronics and Advanced Materials Vol. 9, Iss. 2, pp. 390-393 (2007)