Mean Field Theory PDF
Preview Mean Field Theory
Mean Field Theory Other Related Titles from World Scientific The Finite Quantum Many-Body Problem: Selected Papers of Aage Bohr edited by Ricardo A Broglia ISBN: 978-981-120-813-3 Pear-Shaped Nuclei by Suresh C Pancholi ISBN: 978-981-121-759-3 Electron–Phonon Interaction and Lattice Dynamics in High Tc Superconductors edited by Han Zhan ISBN: 978-981-3271-13-5 Heavy Ion Collisions at Intermediate Energy: Theoretical Models by Subal Das Gupta, Swagata Mallik and Gargi Chaudhuri ISBN: 978-981-3277-93-9 KKaahhFFeeee -- 1111559933 -- MMeeaann FFiieelldd TThheeoorryy..iinndddd 11 2244//44//22002200 33::0077::3377 ppmm Mean Field Theory World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Control Number: 2020937350 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. MEAN FIELD THEORY Copyright © 2020 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 photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-121-177-5 (hardcover) ISBN 978-981-121-178-2 (ebook for institutions) ISBN 978-981-121-179-9 (ebook for individuals) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/11593#t=suppl Desk Editor: Ng Kah Fee Printed in Singapore KKaahhFFeeee -- 1111559933 -- MMeeaann FFiieelldd TThheeoorryy..iinndddd 22 2244//44//22002200 33::0077::3377 ppmm April15,2020 16:49 ws-book961x669 MeanFieldTheory 11593-main pagev TO Natasha Alexei Benjamin Aviva Ida v TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk April23,2020 10:8 ws-book961x669 MeanFieldTheory 11593-main pagevii Preface The conceptofmeanfieldhasledtothe developmentofapproximatequantumand semi-classicalapproacheswhichsuccessfullydescribethepropertiesofamany-body interactingsystem. Inthisbookwepresentrecentdevelopmentsinmeanfieldtheory and beyond. Although each section of the book is related to theoretical problems in nuclear physics, with comparison to experimental data when available, there is a logical extension of it to different aspects of other many-body physics, such as atoms, condensed matter, plasma and other. The book is intended for graduate studentsandactiveresearchers. Weassumebasicknowledgeofquantummechanics and nuclear physics. An extensive list of references to original papers, reviews and books is given, so that the reader can follow up on a subject of personal interest. A significant part of the book is based on over three decades of collaborative work by the authors which commenced when they visited the Niels Bohr Institute, Copenhagen, Denmark. We have benefited from collaborative work with numerous studentsandcolleagues,ascanbeseenfromthereferencesinthe text,particularly, inthefiguresandtables. Theplanforthisbookoriginatedmorethanadecadeago. Mybestfriendandco-author,Academician,ProfessorVladimirM.Kolomietz,died in June 2018, a personal loss to his family, me and our collaborators. I hope the completed book closely follows his vision. Special thanks are due to Dr. Andrey I. Sanzhur for his help in preparing the final version of the book for publication. Shalom Shlomo College Station, Texas December 2019 vii TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk April15,2020 16:49 ws-book961x669 MeanFieldTheory 11593-main pageix Contents Preface vii Introduction xv 1. Self-consistent mean field approximations 1 1.1 Variational principle . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Effective interparticle interaction . . . . . . . . . . . . . . . . . . . 6 1.2.1 Nuclear matter . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 Finite nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.3 Landau’s effective interaction . . . . . . . . . . . . . . . . . 13 1.3 Energy density functional . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Potential energy due to Skyrme forces . . . . . . . . . . . . 15 1.3.2 Spin-orbit potential energy . . . . . . . . . . . . . . . . . . 18 1.3.3 Coulomb energy . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.4 Energy density . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Hartree-Fock equations for Skyrme forces . . . . . . . . . . . . . . 22 1.4.1 Nuclear matter properties in terms of Skyrme force parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.2 Skyrme parameters in terms of nuclear matter properties . 26 1.4.3 Determining the Skyrme force parameters . . . . . . . . . . 28 2. Many-body problem in phase space 30 2.1 Weyl’s and Wigner’s representations . . . . . . . . . . . . . . . . . 30 2.1.1 Weyl representation . . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 Wigner representation . . . . . . . . . . . . . . . . . . . . . 31 2.1.3 Composition formula . . . . . . . . . . . . . . . . . . . . . 31 2.2 Wigner distribution function. . . . . . . . . . . . . . . . . . . . . . 32 2.3 Application of the Wigner transformation . . . . . . . . . . . . . . 38 2.3.1 Kinetic equations . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.2 Pauli blocking . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.3 Heavy-ion collisions . . . . . . . . . . . . . . . . . . . . . . 40 ix
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