%0 Journal Article %1 Avery2009 %A Avery, James %A Avery, John %D 2009 %I Springer Netherlands %J Journal of Mathematical Chemistry %K atomic core energies ionization %N 1 %P 164-181 %R 10.1007/s10910-008-9450-z %T Atomic core-ionization energies; approximately piecewise-linear and linear relationships %U http://dx.doi.org/10.1007/s10910-008-9450-z %V 46 %X In the generalized Sturmian method, solutions to the many-particle Schrödinger equation are built up from isoenergetic sets of solutions to an approximate Schrödinger equation with a weighted potential $$\beta_V_0(x)$$. The weighting factors β ν are chosen in such a way as to make all of the members of the basis set correspond to the energy of the state being represented. In this paper we apply the method to core ionization in atoms and atomic ions, using a basis where $$V_0(x)$$ is chosen to be the nuclear attraction potential. We make use of a large- Z approximation, which leads to extremely simple closed-form expressions not only for energies, but also for values of the electronic potential at the nucleus. The method predicts approximately piecewise linear dependence of the core-ionization energies on the number of electrons N for isonuclear series, and an approximately linear dependence of Δ E − Z 2 /2 on the nuclear charge Z for isoelectronic series.

@article{Avery2009, abstract = {In the generalized Sturmian method, solutions to the many-particle Schrödinger equation are built up from isoenergetic sets of solutions to an approximate Schrödinger equation with a weighted potential $${\beta_\nu \mathsf{V}_0({\bf x})}$$. The weighting factors β ν are chosen in such a way as to make all of the members of the basis set correspond to the energy of the state being represented. In this paper we apply the method to core ionization in atoms and atomic ions, using a basis where $${\mathsf{V}_0({\bf x})}$$ is chosen to be the nuclear attraction potential. We make use of a large- Z approximation, which leads to extremely simple closed-form expressions not only for energies, but also for values of the electronic potential at the nucleus. The method predicts approximately piecewise linear dependence of the core-ionization energies on the number of electrons N for isonuclear series, and an approximately linear dependence of Δ E − Z 2 /2 on the nuclear charge Z for isoelectronic series.}, added-at = {2012-06-28T23:07:23.000+0200}, affiliation = {University of Copenhagen Department of Computer Science Copenhagen Denmark}, author = {Avery, James and Avery, John}, biburl = {https://www.bibsonomy.org/bibtex/242c4539c044630118f1b07af8f1a2860/cafo78}, description = {Journal of Mathematical Chemistry, Volume 46, Number 1 - SpringerLink}, doi = {10.1007/s10910-008-9450-z}, interhash = {0f96c5f1d4c6a698599a12dfd0d031d3}, intrahash = {42c4539c044630118f1b07af8f1a2860}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {atomic core energies ionization}, number = 1, pages = {164-181}, publisher = {Springer Netherlands}, timestamp = {2012-06-28T23:07:23.000+0200}, title = {Atomic core-ionization energies; approximately piecewise-linear and linear relationships}, url = {http://dx.doi.org/10.1007/s10910-008-9450-z}, volume = 46, year = 2009 }