By Professor Ingvar Lindgren, Dr. John Morrison (auth.)
ISBN-10: 3540166491
ISBN-13: 9783540166498
ISBN-10: 3642616402
ISBN-13: 9783642616402
In the recent variation simply minor adjustments were made. a few print ing mistakes were corrected and some clarifications were made. in recent times the task in relativistic many-body idea has elevated con siderably, yet this box falls open air the scope of this e-book. a quick precis of the new advancements, even if, has been incorporated within the part on "relativistic results" in Chap. 14. furthermore, just a very restricted variety of references were extra, with none systematic updating of the fabric. Goteborg, December 1985 l. Lindgren· J. Morrison Preface to the 1st version This booklet has constructed via a sequence of lectures on atomic thought given those final 8 years at Chalmers collage of expertise and several other oth er learn facilities. those classes have been meant to make the elemental parts of atomic conception to be had to experimentalists operating with the hyperfine constitution and the optical houses of atoms and to supply a few perception into fresh advancements within the theory.
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Extra resources for Atomic Many-Body Theory
Sample text
Reduced Matrix Elements of the C Tensor The Winger-Eckart theorem is a fundamental result, which we shall use frequently in the following to evaluate the matrix elements ofinteraction operators. As can be seen from the Zeeman effect considered above, in order to actually make use of this theorem, it is necessary to be able to evaluate reduced matrix elements. 1 00), which occurs often in atomic physics. Q represents the angular coordinates () and,p. (Q) y~,(Q) = 2: aim n(Q) . Y~, = - J2k + 4n 12: (_I)/-m 1m (lkl')
76) for the vector-coupling coefficients is quite unwieldy for manual work, it can easily be programmed for computers, and several standard routines are now available for calculating these coefficients. The general formula can also be used to derive some important symmetry properties. 79) So the coupling coefficients have a very simple symmetry with respect to the interchange ofjl andjz. This is natural, sinceh andj2 appear on the same footing as components from which the total angular momentum J is constructed.
In this book we shall use graphical methods extensively, and we shall follow mainly the works of Brink and Satehler and of Sandars. In the first section of this chapter we shall give all the basic rules which we need to represent angular momenta graphically. These rules will then be used to derive a graphical representation of the vector-coupling coefficient, of coupled states, and of the Winger-Eckart theorem. Rules for treating diagrams with two or more vertices are developed in the second section, and these results are then applied to a particular physical problem: the interaction of a single electron with all electrons of a closed shell.
Atomic Many-Body Theory by Professor Ingvar Lindgren, Dr. John Morrison (auth.)
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