Spherical Tensor Operators: Tables of Matrix Elements and Symmetries

334 Pages·1990·97.182 MB·English

by  J. A. Tuszynski

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TENSOR
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Tables „, Matrix Element J u r i es
J. A. Tuszynski .
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SPHERICAL
TENSOR
OPERATORS
Tables of Matrix Elements and Symmetries
This page is intentionally left blank
SPHERICAL
TENSOR
OPERATORS
Tables of Matrix Elements and Symmetries
J. A. Tuszynski
Department of Physics
University of Alberta
Edmonton, Alberta
Canada
World Scientific
Singapore • New Jersey • London • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
P O Box 128, Farrer Road, Singapore 9128
USA office: 687 Haitwell Street, Teaneck, NJ 07666
UK office: 73 Lynton Mead, Totteridge, London N20 8DH
Library of Congress Cataloging-in-Publication Data
Tuszynski, J. A.
Spherical tensor operators : tables of matrix elements and
symmetries / J.A. Tuszynski.
p. cm.
Includes bibliographical references.
ISBN 9810202830
1. Matrices—Tables. 2. Symmetry (Physics) — Tables.
3. Racah algebra. 4. Calculus of tensors. I. Title.
QC20.7.M3T87 1990 90-37532
539.7'25—dc20 CIP
Copyright © 1990 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced
in any form or by any means, electronic or mechanical, including photo
copying, recording or any information storage and retrieval system now
known or to be invented, without written permission from the Publisher.
Printed in Singapore by Loi Printing Pte Ltd.
TABLE OF CONTENTS
I. INTRODUCTION 1
1. Racah's Reduction Scheme 1
2. Irreducible Tensor Operators 1
3. Tesseral Harmonics and Point Groups 3
4. Double Tensor Operators 4
5. The Effective Many-Particle Hamiltonian 5
6. Reduced Matrix Elements 6
II. TABLES 11
1. Classification of the States of the pn, dn and P1 Configurations 11
2. Tensor Operators T * (J) up to Sixth Order 16
19
3. Spherical Harmonics up to Sixth Order
5. Inva^LpolaxTensor Operators sor the 27Noncubic I
21
6 The Value* of the rVv»ffiH<»nr<! hf f lr n fn2 Varinn<: 9 ?' and Rank
values me coet icients D K}; various o,
U
Combinatioof (k}= ^^21^22)^2
III. REFERENCES 31
24
IV. TABLES OF REDUCED MATRIX ELEMENTS 33
1. p2 Configuration 33
1. 3 Configuration 33
P
2. d2 Configuration 33
3. d2 Configuration 33
4. d3 Configuration 33
5. d4 Configuration 39
6. f2 Configuration 55
7. f2 Configuration 55
8. ^Configuration 59
19. f5 Coniiguration 113
10. f5 Configuration 113
11. ^Configuration 275
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