## Atomic core-ionization energies; approximately piecewise-linear and linear relationships

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**Atomic core-ionization energies; approximately piecewise-linear and linear relationships.** / Avery, James Emil; Avery, John Scales.

Research output: Contribution to journal › Journal article

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*Journal of Mathematical Chemistry*, vol. 46, no. 1, pp. 164-181. https://doi.org/10.1007/s10910-008-9450-z

#### APA

*Journal of Mathematical Chemistry*,

*46*(1), 164-181. https://doi.org/10.1007/s10910-008-9450-z

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TY - JOUR

T1 - Atomic core-ionization energies; approximately piecewise-linear and linear relationships

AU - Avery, James Emil

AU - Avery, John Scales

N1 - Paper id:: 10.1007/s10910-008-9450-z

PY - 2008/8/5

Y1 - 2008/8/5

N2 - 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.

AB - 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.

U2 - 10.1007/s10910-008-9450-z

DO - 10.1007/s10910-008-9450-z

M3 - Journal article

VL - 46

SP - 164

EP - 181

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 1

ER -

ID: 12129291