## Angular Momentum Theory Applied to Interactions in SolidsFrom December 1985 through March 1986 the text of this book formed the basis of an in-hours course taught by the author at Harry Diamond Laborato ries. Considerable assistance in revising and organizing the first draft was given by John Bruno. The original draft of these notes was based on a collection of lectures delivered at the Universidade Federal de Pernambuco, Recife, Brazil, between 2 November 1981 and 2 December 1981. The visit to Recife was a response to an invi tation of Professor Gilberto F. de Sa of the Physics Department. In the preparation of these notes I made many requests of my coworkers for earlier resul ts and recollections of our early work. Among those consul ted were Donald Wortman, Nick Karayianis, and Richard Leavitt. Further, a number of .suggestions from my Brazilian colleagues helped make the lectures more clear. Particular among these were Professor Oscar Malta and Professor Alfredo A. da Gama both of whom I wish to thank for their help. Encouragement and assistance with funding for much of this work came from Leon Esterowitz of the Naval Research Laboratory and Rudolph Buser and Albert Pinto of the center for Night Vision and Electro-Optics. |

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### Contents

CLEBSCHGORDAN COEFFICIENTS | 19 |

UNIT SPHERICAL TENSORS | 35 |

RACAH ALGEBRA | 49 |

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### Common terms and phrases

6-j Symbols Atomic Bibliography and References C-G coefficients C. A. Morrison Calcium Tungstate calculated Cambridge CaWOj Chem commutation consider Crystal Field Crystal Field Theory crystal-field interaction crystal-field parameters dipole discussion ELECTRONIC CONFIGURATION energy levels Erbium experimental data Faucher Field Parameters free ion given in equation given in table gives Hamiltonian Harry Diamond Laboratories Hartree-Fock International Tables IONIZED RARE-EARTH IONS Judd Karayianis lattice sums Ligand Field Theory LiYFj McGraw-Hill multipolar multipole multipole moments Nd3+ Nielson and Koster notation obtain Optical Spectrum orbital Phys point charge point groups polarizability problem R. P. Leavitt Racah coefficients recouple reduced matrix reduced matrix elements relation result given Rose Rotenberg scheelite Slater integrals solid Spectra Spectroscopic Properties spherical harmonics spherical tensors spin spin-orbit interaction symmetry operations total angular momentum transition-metal ions Trivalent unit cell values vector wave functions Wigner-Eckart theorem Wiley Wortman Wybourne York