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 |
|---|---|
| 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 |