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By Clyde A. Morrison

From December 1985 via March 1986 the textual content of this ebook shaped the root of an in-hours direction taught by means of the writer at Harry Diamond Laborato­ ries. significant suggestions in revising and organizing the 1st draft was once given through John Bruno. the unique draft of those notes used to be in keeping with a set of lectures introduced on the Universidade Federal de Pernambuco, Recife, Brazil, among 2 November 1981 and a pair of December 1981. The stopover at to Recife was once a reaction to an invi tation of Professor Gilberto F. de Sa of the Physics division. within the instruction of those notes I made many requests of my coworkers for prior resul ts and memories of our early paintings. between these consul ted have been Donald Wortman, Nick Karayianis, and Richard Leavitt. extra, a couple of .suggestions from my Brazilian colleagues helped make the lectures extra transparent. specific between those have been Professor Oscar Malta and Professor Alfredo A. da Gama either one of whom I desire to thank for his or her support. Encouragement and tips with investment for far of this paintings got here from Leon Esterowitz of the Naval study Laboratory and Rudolph Buser and Albert Pinto of the heart for evening imaginative and prescient and Electro-Optics.

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Bevins, N. Metropolis, and J. K. Wooten, Jr. (1969), The 3-j and 6-j Symbols, MIT Press, Cambridge, MA. 33 Schiff, L. I. , McGraw-Hill, New York, NY. Sobelman, 1. 1. (1979), Atomic Spectra and Radiative Transitions, SpringerVerlag, New York, NY. Watanabe, H. (1966), Operator Methods in Ligand Field Theory, Prentice-Hall, Englewood Cliffs, NJ. Wybourne, B. G. (1965), Spectroscopic Properties of Rare Earths, Wiley, New York, NY. 34 4. 1 Discussion Because of the power of the Wigner-Ekhart theorem, it occurred to Racah to cast the various operators representing the interactions in terms of uni versal quanti ti es that could be tabulated for a frequently used manyparticle system.

Reduced. 8). I a = 1.

E. (1957), Elementary Theory of Angular Momentum, Wiley, New York, NY. Pages 103-106 discuss the unit vectors ea. Pages 120-124 discuss the derivation of the gradient formula. Chapter VII has many applications of Racah algebra in electromagnetic theory and multipole t'ields. Chapter VIII covers static multipolar interactions. Rose, M. E. (1955), Multipole Fields, Wiley, New York, NY. Practically the entire book is applications of Racah algebra. The Clebsch-Gordan coefficients are expressed in terms of 3F 2' and the Racah coefficients are expressed in terms of 4F3' where the pFq are hypergeometric functions.

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