By Professor Ingvar Lindgren, Dr. John Morrison (auth.)

ISBN-10: 3540166491

ISBN-13: 9783540166498

ISBN-10: 3642616402

ISBN-13: 9783642616402

In the hot variation basically minor ameliorations were made. a few print ing error were corrected and some clarifications were made. lately the job in relativistic many-body concept has elevated con siderably, yet this box falls outdoors the scope of this ebook. a quick precis of the new advancements, notwithstanding, has been incorporated within the part on "relativistic results" in Chap. 14. moreover, just a very constrained variety of references were extra, with none systematic updating of the cloth. Goteborg, December 1985 l. Lindgren· J. Morrison Preface to the 1st version This booklet has constructed via a chain of lectures on atomic conception given those final 8 years at Chalmers collage of know-how and several other oth er learn facilities. those classes have been meant to make the elemental parts of atomic idea 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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2 Coupling of Tensor Operators Thus far, we have considered coupling of angular-momentum states. The spherical tensor operators can be combined in a similar fashion. :(2)

For numerical purposes it then has the value one. Similarly, for a directed line, jm jm .. 5) = (_l)l+m r5(j,j') r5(m, -m') . 5) that reversing the direction of an arrow introduces a phase factor of ( -1 )2m = (-1 )21, jm .. j'm' . jm = (_1)2J .. j'm' . ,·m j'm' . 7a) Similarly, jm ... j'm' jm j'm' . 6), which gives I Note that Brink and Satchler [1968] as well as Sandars [1971] used the opposite phase convention. As we shall see later, our convention will lead to a closer analogy between the angular-momentum diagrams and the Feynman-Iike diagrams introduced later to represent terms in the perturbation expansion.

General equations, which will enable us to evaluate these reduced matrix elements, will be given in Sect. 3. We evaluate these coefficients here by means of a simple argument. 44 2. 119) when operating within an SLJ manifold. The identity of the diagonal elements leads to L(L + 1) = J(J + 1) + S(S + 1) - 2as J(J + 1). 123) This result, which is usually derived in elementary courses by the nonrigorous vector model, is a direct consequence of the Wigner-Eckart theorem. 3. 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.

### Atomic Many-Body Theory by Professor Ingvar Lindgren, Dr. John Morrison (auth.)

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