electronic structure of heavy elements

SearchAdvancedHelp

(0.003 seconds)

1—10 of 299 matching pages

1: 33.22 Particle Scattering and Atomic and Molecular Spectra

… ►

§33.22(i) Schrödinger Equation

… ►Positive-energy functions correspond to processes such as Rutherford scattering and Coulomb excitation of nuclei (Alder et al. (1956)), and atomic photo-ionization and electron-ion collisions (Bethe and Salpeter (1977)). … ►For $Z_1{Z}_2=-1$ and $m=m_{\mathrm{e}}$, the electron mass, the scaling factors in (33.22.5) reduce to the Bohr radius, $a_0=\mathrm{\hslash }/(m_{\mathrm{e}}c\alpha )$, and to a multiple of the Rydberg constant, … ►

§33.22(iv) Klein–Gordon and Dirac Equations

… ►The motion of a relativistic electron in a Coulomb field, which arises in the theory of the electronic structure of heavy elements (Johnson (2007)), is described by a Dirac equation. …

2: 18.39 Applications in the Physical Sciences

… ►In the case of a single electron, charge $-e$ and mass $m_e$, interacting with a fixed (infinite mass) nucleus of charge $+Ze$ at the co-ordinate origin, with the choice of SI units, $V(r)=-Z{e}^2/(4\pi {ϵ}_{0}r)$. … ►, $\mathrm{\hslash }=m_e=e^2=4\pi {ϵ}_0=1$, Mohr and Taylor (2005, Table XXX, p. 71), where the relationship of $a.u.$ to SI units is spelled out. … ►Physical scientists use the $n$ of Bohr as, to $0$th and $1$st order, it describes the structure and organization of the Periodic Table of the Chemical Elements of which the Hydrogen atom is only the first. … ►Interactions between electrons, in many electron atoms, breaks this degeneracy as a function of $l$, but $n$ still dominates. … ►A relativistic treatment becoming necessary as $Z$ becomes large as corrections to the non-relativistic Schrödinger picture are of approximate order ${\left(\alpha Z\right)}^2\sim {\left(Z/137\right)}^2$, $\alpha$ being the dimensionless fine structure constant $e^2/(4\pi {\epsilon }_0\mathrm{\hslash }c)$, where $c$ is the speed of light. …

3: Bille C. Carlson

… ►Both contributions concerned the electronic structure of molecules and solids. …

4: Bibliography H

… ►

Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Internat. J. Quantum Chem. 88 (6), pp. 701–734.

ⓘ

External Links:

Document

Referenced by:

§8.24(iii).

Encodings:

BibTeX

… ►

Molecular Electronic-Structure Theory. John Wiley & Sons, New York.

ⓘ

Notes:

Paperback Reprint of 2004 Edition

External Links:

ISBN 9871118531471

Referenced by:

§18.39(iii).

Encodings:

BibTeX

►

On an “equivalent quadrature” calculation of matrix elements of ${(z-p^2/2m)}^{-1}$ using an $L^2$ expansion technique. J. Comput. Phys. 13, pp. 536–550.

ⓘ

External Links:

Document, Link

Referenced by:

§18.39(iv).

Encodings:

BibTeX

… ►

Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.

ⓘ

External Links:

ISSN 0003-4916, Document, MathReview

Referenced by:

§33.10(ii), §33.13, §33.22(vii).

Encodings:

BibTeX

…

5: Gloria Wiersma

… ►Then she began working with the staff of the Physics Laboratory Office of Electronic Commerce in Scientific and Engineering Data, developing and refining the Laboratory website until her retirement in 2007. …

6: About the Project

… ►The results have been published in book form as the NIST Handbook of Mathematical Functions, by Cambridge University Press, and disseminated in the free electronic Digital Library of Mathematical Functions. … ► Olver, Editor-in-Chief and Mathematics Editor of the DLMF, the other Editors initiated an effort aimed at updating the organizational structure of the DLMF project. …

7: Bibliography K

… ►

Determinant structure of the rational solutions for the Painlevé II equation. J. Math. Phys. 37 (9), pp. 4693–4704.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.8(ii).

Encodings:

BibTeX

►

Determinant structure of the rational solutions for the Painlevé IV equation. J. Phys. A 31 (10), pp. 2431–2446.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.8(iv).

Encodings:

BibTeX

… ►

Optical Waveguides. Quantum Electronics - Principles and Applications, Academic Press, New York.

ⓘ

External Links:

ISBN 0-12-396760-0

Referenced by:

§10.73(i).

Encodings:

BibTeX

… ►

The structure relation for Askey-Wilson polynomials. J. Comput. Appl. Math. 207 (2), pp. 214–226.

ⓘ

External Links:

ISSN 0377-0427, Document, Link, MathReview Entry

Referenced by:

(18.9.18_5).

Encodings:

BibTeX

… ►

Askey-Wilson polynomial. Scholarpedia 7 (7), pp. 7761.

ⓘ

Notes:

Electronic only

External Links:

Document, FullText

Referenced by:

§18.28(i), §18.28(i).

Encodings:

BibTeX

…

8: Bibliography N

… ►

Inequalities involving Bessel functions of the first kind. JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).

ⓘ

External Links:

ISSN 1443-5756, FullText, MathReview, ZentralBlatt

Referenced by:

§10.14.

Encodings:

BibTeX

… ►

Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

ⓘ

Notes:

Also available electronically through Cambridge Books Online, ISBN 9780511599903.

External Links:

ISBN 9780521383189, Document

Referenced by:

§9.16, §9.16.

Encodings:

BibTeX

►

Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations. Institute of Physics Publishing, Bristol.

ⓘ

External Links:

ISBN 0-7503-0610-6, MathReview (Peter Giblin), ZentralBlatt

Referenced by:

§36.14(ii).

Encodings:

BibTeX

…

9: Preface

… ►The new DLMF (Digital Library of Mathematical Functions) will appear in a hardcover edition and as a free electronic publication on the World Wide Web. …

10: Bibliography E

… ►

The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§15.18.

Encodings:

BibTeX

… ►

The Euler-Maclaurin formula revisited. J. Austral. Math. Soc. Ser. B 40 (E), pp. E27–E76 (electronic).

ⓘ

External Links:

ISSN 0334-2700, FullText, MathReview (J. Németh), ZentralBlatt

Referenced by:

§2.10(i).

Encodings:

BibTeX

… ►

The Thirteen Books of Euclid’s Elements. Cambridge University Press, Cambridge.

ⓘ

Notes:

Translated from the text of Heiberg, with introduction and commentary by Thomas L. Heath. Reprint of the Cambridge Univeristy second edition by Dover Publications, Inc., New York, 1956.

External Links:

MathReview, ZentralBlatt

Referenced by:

§27.2(i).

Encodings:

BibTeX

…