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

Research output: Contribution to journalJournal articleResearchpeer-review

#### Standard

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

In: Journal of Mathematical Chemistry, Vol. 46, No. 1, 05.08.2008, p. 164-181.

Research output: Contribution to journalJournal articleResearchpeer-review

#### Harvard

Avery, JE & Avery, JS 2008, 'Atomic core-ionization energies; approximately piecewise-linear and linear relationships', Journal of Mathematical Chemistry, vol. 46, no. 1, pp. 164-181. https://doi.org/10.1007/s10910-008-9450-z

#### APA

Avery, J. E., & Avery, J. S. (2008). Atomic core-ionization energies; approximately piecewise-linear and linear relationships. Journal of Mathematical Chemistry, 46(1), 164-181. https://doi.org/10.1007/s10910-008-9450-z

#### Vancouver

Avery JE, Avery JS. Atomic core-ionization energies; approximately piecewise-linear and linear relationships. Journal of Mathematical Chemistry. 2008 Aug 5;46(1):164-181. https://doi.org/10.1007/s10910-008-9450-z

#### Author

Avery, James Emil ; Avery, John Scales. / Atomic core-ionization energies; approximately piecewise-linear and linear relationships. In: Journal of Mathematical Chemistry. 2008 ; Vol. 46, No. 1. pp. 164-181.

#### Bibtex

@article{21d67ba038c911de87b8000ea68e967b,
title = "Atomic core-ionization energies; approximately piecewise-linear and linear relationships",
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.",
author = "Avery, {James Emil} and Avery, {John Scales}",
note = "Paper id:: 10.1007/s10910-008-9450-z",
year = "2008",
month = "8",
day = "5",
doi = "10.1007/s10910-008-9450-z",
language = "English",
volume = "46",
pages = "164--181",
journal = "Journal of Mathematical Chemistry",
issn = "0259-9791",
publisher = "Springer",
number = "1",

}

#### RIS

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