## Abstract

In the Generalized Sturmian Method, solutions to the many-particle

Schr\"odinger equation are built up from isoenergetic sets of

solutions to an approximate Schr\"odinger equation with a weighted

potential $\beta_\nu \op{V}_0(\xx)$. The weighting factors

$\beta_\nu$ 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 $\op{V}_0(\xx)$ 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 $\Delta E-Z^2/2$ on the

nuclear charge $Z$ for isoelectronic series.

Schr\"odinger equation are built up from isoenergetic sets of

solutions to an approximate Schr\"odinger equation with a weighted

potential $\beta_\nu \op{V}_0(\xx)$. The weighting factors

$\beta_\nu$ 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 $\op{V}_0(\xx)$ 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 $\Delta E-Z^2/2$ on the

nuclear charge $Z$ for isoelectronic series.

Original language | English |
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Journal | Journal of Mathematical Chemistry |

Volume | 46 |

Issue number | 1 |

Pages (from-to) | 164-181 |

Number of pages | 17 |

ISSN | 0259-9791 |

DOIs | |

Publication status | Published - 5 Aug 2008 |