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THE FOUNDATIONS OF NEUTRON TRANSPORT THEORY RICHARD K. OSBORN College of Engineering, Unlvertlty of Michigan Ann Arbor, Michigan SIDNEY YIP Massachusetts tn,tltute of Tecflnology Cambridge, M....chu.etts Prepared under the auspice. of the Division of Technical Information United States Atomic Energy Commission GORDON AND BREACH, SCIENCE PUBLISHERS, INC . NEW YORK · LONDON· PARIS Copyright 0 HIM by Gord on and Breaeh, Science Pub lishers, Inc. 150 Fifth Avenue , New YOB. N.Y . 10011 U brary of Congr e.. Camlog Card Number 66-24001 Distributed In the United Kingd om by: Blackie It. Son, ltd. 5 Fltzkardlnge Street, London W .1, England Distributed In France by: Dunod Edlt eur Il2, rue Bonapart e, Pari. 6. France Di str ibuted In Canada by: The Ryerson Press 299 Oueen Street W e. t. Toron to 28, Ontario All Rights Reserved No part of thi s book may be repr oduced In any fo rm without permission In wri t ing from the publi sher T hIs copyright hal ~ ... Igned and Is held by the General Manager of t he UnltH Stilt•• Atomic Energy Comm ission. A il royalti es from the .. Ie of this book accrue to the United SUite. Go¥ernmenL Preface There arc at least three reasons why the authors felt that a m ODO-graph such as this might prove useful. Fo r th e past fifteen yean or so there have appeared many texts and trea tises which have presented extensive studies at aU levels of sophistication of the solutions of the neutron t ransport eq uation . However, the: origins and limitations of this equatio n have: been given little or no attention. But the fission reactor teebD.ology [like the fusion technology and many other areas of modem engi neering) is demanding a deepening awareness of the subtle relationship between microsco pic cause and macroscopic effect. Thus we felt that an initiation of an exploration into the foundation of the neut ron transport equation was a needed co mplement to the examinelion of its solutions . The: subject matte r summarized in this monogra ph was initially generated in bits and pieces within the context of various courses offered to the nuclearengineering studentsat the University of Michigan. Thus a second reason for the preparation of this materialin its present form was to provide an integrated treatment of an integral topic. For example. it is qu ite conventional to separate the discussion of the transport equation from the study of microscopic reacti on ra tes. Thi s is both natural and necessary from the pedagogical point of view. particularly at the introductory level. Nevertheless it seems important that at so me point the essential unity of these concepts be restored, and this unity manifests itself in the study of the origins of the transport equationnot its solutio ns. Thirdly. it is probably inevitable that the analytical tools available to the engineer at any given insta nt in time will eventually become inadequate to his tasks. Indeed this may be the case in th e reactor technology today with respect to th e matter of interp reting neutron 6uotuaticn measurements. Thus a potentially practical purpose may be served by this work in that it suggests a path way along which generalization of the usual description of the reactor may be sought dedu ctively rathe r than indu ctively. v vi r ue fOUNDA TIONS Of N EUTRON TRA NSPORT T Il EOR.Y This book is not intended to be a text book, nor is it a imed at partieular areas of specialization, It deals with a smal l, well-defined topic. which, however, has broad implications. It is thus anticipated that graduate students, teachers. and research workers in nuc lear engineering. ph ysics, and chemistry (many of the principles and techniques of an alysis ca rry over intact from a study of neu tron transport to the study of th e kinetic th eo