The Physics of Warm Nuclei: With Analogies to Mesoscopic Systems (Oxford Studies in Nuclear Physics, Vol 25)

644 Pages·2008·4.84 MB·English

by  Helmut Hofmann

THE PHYSICS OF WARM NUCLEI
OXFORD STUDIES IN NUCLEAR PHYSICS
Generaleditor:P.E.Hodgson
1. J. L. Emmerson: Symmetry principles in particle physics
2. J. M. Irvine: Heavy nuclei, superheavy nuclei, and neutron stars
3. I. S. Towner: A shell-model description of light nuclei
4. P. E. Hodgson: Nuclear heavy ion reactions
5. R. D. Lawson: Theory of nuclear shell model
6. W. E. Frahn: Diffractive process in nuclear physics
7. S. S. M. Wong: Nuclear statistical spectroscopy
8. N. Ullah: Matrix ensembles in the many-nucleon problem
9. A. N. Antonov, P. E. Hodgson, I. Zh. Petkov: Nucleon momentum and density
distributions in nuclei
10. D. Bonatsos: Interacting boson models of nuclear structure
11.H.Ejiri,M.J.A.deVoigt:Gamma-rayandelectronspectroscopyinnuclearphysics
12. B. Castel, I. S. Towner: Modern theories of nuclear physics moments
13. R. F. Casten: Nuclear structure from a simple perspective
14. I. Zh. Petkov, M. V. Stitsov: Nuclear density function theory
15. I. Gadioli, P. E. Hodgson: Pre-equilibrium nuclear reactions
16. J. D. Walecka: Theoretical nuclear and subnuclear physics
17. D. N. Poenaru, W. Greiner: Handbook of nuclear properties
18. P. Fr¨obrich, R. Lipperheide: Theory of nuclear properties
19. F. Stancu: Group theory in subnuclear physics
20. S. Boffi, C. Giusti, F. D. Pacati, M. Radici: Electromagnetic response of
atomic nuclei
21. G. Ripka: Quarks bound by chiral fields
22. H. Ejiri, H. Toki (eds): Nucleon–hadron many-body systems
23. R. F. Casten: Nuclear structure from a simple perspective, second edition
24. M. N. Harakeh, A. van der Woude: Giant resonances: fundamental high-frequency
modes of nuclear excitation
25. H. Hofmann: The physics of warm nuclei: with analogies to mesoscopic systems
THE PHYSICS OF WARM NUCLEI
with analogies to mesoscopic systems
HELMUT HOFMANN
Department of Physics
Technical University of Munich
1
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PREFACE
EinBuch, dasnicht wert ist, wenigstens zweimal gelesen
zuwerden,istauchnichtwert,dassmaneseinmalliest.1
VonallenUnmo¨glichkeitenistes diegr¨oßte, einBuchzu
schreiben, das allen gef¨allt.2
Karl Julius Weber
A full comprehension of present-day nuclear physics is no longer possible solely
on the basis of a knowledge of quantum mechanics. In the past decades nuclear
physics has developed into a field which borrows methods and concepts from
diverse areas in physics. For an understanding of the nuclear force, for instance,
formulations in terms of quantum chromodynamics are in sight. To follow this
line requires the application of quantum relativistic field theory, together with
elements of elementary particle physics. In typical accelerator experiments with
heavyions,onthe otherhand,nuclearcompoundsarecreatedwithlargeexcita-
tionenergiesforwhichmethodsofstatisticalphysicsareindispensable.Itistrue
that a similar situation has already been faced in conventional reaction theory.
Different methods are necessary, however, to cope with the problem of collec-
tive motion. In many cases the latter is of a timescale much larger than that of
the residual degrees of freedom. This is the realm of non-equilibrium statistical
mechanics with transport equations at one’s disposal.
In this book we concentrate on examples which fall in this latter category.
The notion“warmnuclei”is meantto indicate thatonly verymoderatethermal
excitationswillbeconsidered.A“nucleartemperature”shouldnotonlybemuch
smallerthantheFermienergy,butwillbeassumedsmallenoughsothatsomeof
thosemany-bodyfeaturesarestillpresent,whichinasenserepresenttraditional
nuclearphysics.Takeshelleffectsasoneofthemostprominentexamples,known
todisappearatk T (cid:1)3MeV.Thestudyofthistransitionwillplayamajorrole
B
inourdiscussion,inparticularbecauseofitsintriguingimplicationsfortransport
properties.Wewill,however,refrainfromdescribinganyeffectswhichgobeyond
this regime. In fact for hotter systems the nucleons’ dynamics may no longer
be associated with that in a deformed mean field. At still larger energies sub-
nucleonicdegreesoffreedommaybeexcited,forwhichfieldtheoreticalconcepts
are involved, and which are beyond the scope of this book.
It should be evident that concepts of statistical mechanics cannot be taken
over to nuclear physics without serious forethought. This holds true both for
1Abooknotworthyofbeingreadtwiceisnotworthyofbeingreadonce.
2Thegreatestofallimpossibilitiesistowriteabookwhichpleaseseveryone.
viii Preface
static and dynamic properties, as well as for those involving irreversible fea-
tures. Most of the problems are related to the fact that the nucleus is a small,
self-bound and thermally isolated system. For example, a temperature can be
definedonly withinsome inherentuncertainty,andwillnot stayconstantin any
dynamic process. This is so even in the reversible case as required by the con-
stancy of entropy. The latter feature is intimately related to the extension of
thequantaladiabaticitytheoremto statisticalmechanics,andthus tothe differ-
ence of the susceptibilities involved. Another problem is that collective degrees
of freedom are not given per se; they must be introduced obeying conditions of
self-consistencywiththoseofthenucleons.Thisfeatureisalreadyknownforthe
conventionalcase of zero thermal excitation, but it still plays an important role
atfiniteexcitations.Itispredominantlyherethatirreversiblefeaturescomeinto
play, which for nuclear physics are not unexpected. Indeed, they have already
shown up in traditional theories of nuclear reactions, like those for overlapping
resonances and in relation to the nuclear compound model.
Alargepartofthebookisdevotedtoexplaininganddevelopingsuchaspects
at the borders where microscopic and macroscopic physics meet. Some of them
may be applied to other finite Fermi systems, like metal clusters and quantum
dots or wires. In some cases one may simply dwell on analogies, like the ap-
pearance of nuclear dissipation and the absorption of electromagnetic waves in
metal clusters. However, as is known, many methods have been applied outside
of nuclear physics which were originally developed solely for that domain.
To cover such a wide field is not an easy task. The general reader must not
only be introduced to the basicsof nuclearphysics (andof mesoscopicsystems),
butalsotoelementarytopicsofthetheoreticaltoolsinvolved.Forthisreasonthe
book is split into different parts. The first part is meant to acquaint the reader
with methods aimed at an understanding of the essentials of collective motion
and transport problems used in nuclear physics. In the second and third parts
applications to nuclear reactions and mesoscopic systems are given. The fourth
part contains a thorough discussion of several theoretical methods and is kept
at a more general level, but with emphasis on the specific problems discussed
in the other parts. The overall level of the presentation is oriented at a general,
alertreader,notnecessarilyaspecialistinnuclearphysics.Infact,parts1and4
are meant to serve as self-contained introductions to the fields presented there.
Hardly more than a basic knowledge of quantum mechanics is required for an
easyunderstandingofsuchdiversefieldsasthetheoriesofreaction,transportor
linearresponse,aswellasofthemethodsofWignertransformationsorfunctional
integrals.
ACKNOWLEDGEMENTS
It is a great pleasure to acknowledge the credit due to the many scientists and
colleagueswithwhomIhadclosecontactovertheyearsinwhichmyunderstand-
ing of the topics of this book has grown steadily albeit sometimes very slowly.
First I should like to acknowledge the important contributions from my former
collaborators R. Alkofer, G.-L. Ingold, F.A. Ivanyuk, A.S. Jensen, D. Kiderlen,
A.G. Magner, R. Nix, C. Ngo, C. Rummel, R. Samhammer, P.J. Siemens, R.
Sollacher and S. Yamaji for the fruits of joint publications which have been in-
corporated within these pages. I should also like to express my deep obligation
and the great benefit I have had from discussions with Professors A. Bohr, R.
Balian, M. Brack, W. Brenig, K. Dietrich, R.J. Glauber, W. Go¨tze, D. Kusne-
zov, B.R. Mottelson,D. Pines,P. Ring, V.M. Strutinsky, N.G. van Kampen,M.
V´en´eroni,H.A. Weidenmu¨uller, V.G. Zelevinsky andS. Aaberg,in which I have
been informedabout pertinentmethods andideas thathave oftenpreventedme
fromchoosinginappropriatepaths.MyfinalthanksgotoProfessorJ.A.Wheeler
who was the first to suggest that I take up the endeavor of writing this book,
to Professor R.H. Lemmer who gave the final push to this project, to Professor
W.U. Schro¨der for his continued interest during the preparation period, and to
Dr. F.A. Ivanyuk for his invaluable help in the preparation of figures, as well
as Dr. R.R. Hilton for much advice not only about questions of proper English
style.