Encyclopedia of Nuclear Physics - download.e-bookshelf.de · Hans Geissel, Mark Huyse, Gottfried M¨unzenberg, and Piet Van Duppen 6 Superheavy Nuclei 213 Sigurd Hofmann 7Nuclear

Encyclopedia of Nuclear Physicsand its Applications

Edited by

Reinhard Stock

Related Titles

Martin, B.R.

Nuclear and Particle Physics - AnIntroduction

2006

ISBN: 978-0-470-03547-4

Lilley, J.

Nuclear Physics –Principles &Applications

2001

ISBN: 978-0-471-97935-7

Lieser, K.H.

Nuclear and RadiochemistryFundamentals and Applications

2nd Edition

2001

ISBN: 978-3-527-30317-5

Stacey, W.M.

Fusion Plasma Physics

2005

ISBN: 978-3-527-40586-2

Turner, J.E.

Atoms, Radiation, and RadiationProtection

3rd Edition

2007

ISBN: 978-3-527-40606-7

Glaser, M., Kochsiek, M. (eds.)

Handbook of Metrology

2010

ISBN: 978-3-527-40666-1

Stacey, W.M.

Nuclear Reactor Physics

2nd Edition

2007

ISBN: 978-3-527-40679-1

Stock, R. (ed.)

Encyclopedia of Applied HighEnergy and Particle Physics

2009

ISBN: 978-3-527-40691-3

Bohr, H.G. (ed.)

Handbook of Molecular BiophysicsMethods and Applications

2009Print ISBN: 978-3-527-40702-6

Andrews, D.L. (ed.)

Encyclopedia of AppliedSpectroscopy

2009

ISBN: 978-3-527-40773-6

Krucken, R., Dilling, J.

Experimental Methods for ExoticNuclei

2014

ISBN: 978-3-527-41038-5

Encyclopedia of Nuclear Physicsand its Applications

Edited byReinhard Stock

Editor

Reinhard StockUniversitat [email protected]

CoverOuter vessel of fusion experimentWendelstein 7-X (Copyright: IPP,Wolfgang Filser).

All books published by Wiley-VCH are care-fully produced. Nevertheless, authors, editors,and publisher do not warrant the informa-tion contained in these books, includingthis book, to be free of errors. Readers areadvised to keep in mind that statements,data, illustrations, procedural details or otheritems may inadvertently be inaccurate.

Library of Congress Card No.:applied for

British Library Cataloguing-in-Publication DataA catalogue record for this book is availablefrom the British Library.

Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists thispublication in the Deutsche Nationalbibli-ografie; detailed bibliographic data are avail-able on the Internet at 〈http://dnb.d-nb.de〉.

© 2013 WILEY-VCH Verlag GmbH & Co.KGaA, Boschstr. 12, 69469 Weinheim,Germany

All rights reserved (including those of trans-lation into other languages). No part of thisbook may be reproduced in any form – byphotoprinting, microfilm, or any othermeans – nor transmitted or translated intoa machine language without written permis-sion from the publishers. Registered names,trademarks, etc. used in this book, evenwhen not specifically marked as such, are notto be considered unprotected by law.

Print ISBN: 978-3-527-40742-2ePDF ISBN: 978-3-527-64927-3ePub ISBN: 978-3-527-64926-6Mobi ISBN: 978-3-527-64925-9oBook ISBN: 978-3-527-64924-2

Cover Design Adam Design, WeinheimComposition Laserwords Private Ltd.,Chennai, IndiaPrinting and Binding Markono Print MediaPte Ltd, Singapore

Printed in SingaporePrinted on acid-free paper

mailto:[email protected]

http://dnb.d-nb.de

http://dnb.d-nb.de

http://dnb.d-nb.de

V

Contents

Preface IXList of Contributors XI

Part A: Fundamental Nuclear Research 1

1 Nuclear Structure 3Jan Jolie

2 Nuclear Reactions 45Carlos A. Bertulani

3 Electrostatic Accelerators 93David C. Weisser

4 Linear Accelerators 123Robert Jameson, Joseph Bisognano, and Pierre Lapostolle

5 Exotic Nuclear Beam Facilities 159Hans Geissel, Mark Huyse, Gottfried Munzenberg, and Piet Van Duppen

6 Superheavy Nuclei 213Sigurd Hofmann

7 Nuclear γ-Spectroscopy and the γ-Spheres 247Mark Riley and John Simpson

8 γ Optics and Nuclear Photonics 271Dietrich Habs

9 The Proton 299Allen Caldwell

10 Physics of the Neutron 321Klaus Schreckenbach

Encyclopedia of Nuclear Physics and its Applications, First Edition. Edited by Reinhard Stock.© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

VI Contents

11 Neutrino Astrophysics 353Wick C. Haxton

12 Nuclear Astrophysics 395Hendrik Schatz

13 Relativistic Nucleus–Nucleus Collisions 427Christoph Blume

Part B: Applied Nuclear Physics 451

14 Neutron Stars 453Jurgen Schaffner-Bielich

15 Supernovae and Their Nucleosynthesis 475Friedrich-Karl Thielemann and Matthias Liebendorfer

16 Accelerator Mass Spectrometry and its Applications 503Ragnar Hellborg, Goran Skog, and Kristina Stenstrom

17 Nuclear Medicine 535Ulli Koster, Ferid Haddad, Nicolas Chouin, Francois Davodeau, Jean-FrancoisChatal, Jacques Barbet, and Francoise Kraeber-Bodere

18 Cancer Therapy with Ion Beams 577Gerhard Kraft

Part C: Nuclear Power 597

19 The Physics of Nuclear Power from Fission and Fusion 599Weston M. Stacey

20 Fundamentals of Controlled Nuclear Fission and Essential Characteristics ofPressurized-Water Reactors 631Hartmut Lauer

21 Generation IV Nuclear Reactors 663Thomas Schulenberg

22 Transmutation of High-Level Nuclear Waste by Means of Accelerator DrivenSystem (ADS) 689Hamid Aıt Abderrahim, Didier De Bruyn, Gert Van den Eynde, and SidneyMichiels

23 Fusion Energy by Magnetic Confinement 705Friedrich Wagner

Contents VII

24 Heavy Ion Inertial Fusion 743Rudolf Bock and Ingo Hofmann

Index 761

IX

Preface

With this volume, WILEY-VCH continues a series of reeditions of the ‘‘WileyEncyclopedia of Applied Physics’’ that was edited by Professor G. L. Trigg in theearly 1980s. It united more than 600 monographic articles that embraced physics inthe widest conceivable way, from ‘‘Accelerators’’ via ‘‘Oceanography’’ to ‘‘Xerography.’’The individual articles were addressed at a broad scientific/technical readership, writtenin a didactical style combined with a focus on new and exciting developments.

About 25 years have elapsed since this monumental undertaking, and the fieldsof physics have undergone substantial evolution. In this volume, we revisit NuclearPhysics, an extremely broad field of multifaceted fundamental research, and a wealth ofapplication.

Nuclear Physics phenomena present a universal testing ground for processesand structures that are related to the three fundamental forces/interactions: strong,electromagnetic, and weak. In a certain sense, it could play the role of a paradigmaticrealization of the entire Standard Model of fundamental interaction, if it was notfor the fact that the strong force manifestations in nuclei and nuclear interactionsrepresent the remotest realizations of the elementary strong force that is described bythe quantum chromodynamics (QCD) theory – in the sense that nuclear forces are astrictly nonperturbative QCD effect of higher order that is essentially inaccessible toanalytic or even numerical methods. This is why we do not have, even today, a ‘‘nuclearstructure QCD approach.’’ This QCD approach exists, however, in the consideration ofnucleon structure. The many-nucleon patterns of nuclear properties and reactions canbe confronted with effective nucleon–nucleon forces that have been familiar for manydecades but can now be, at least qualitatively, understood as a QCD analogy to, forexample, van der Waals-like forces. At the limit of ultrarelativistic accelerator energies,nuclear collisions come under explicit governance of QCD, creating the primordial stateof matter consisting of quarks and gluons: the so-called quark–gluon plasma. This isone of the present day fundamental research themes of the field, which, furthermore,features some of the most intricate many-body problems known to science.

Applications of Nuclear Physics could fill many such books as this. The selectionof topics presented here is guided loosely by their importance in the intuitive viewof the scientifically and technically interested public. We have selected topics ranging


X Preface

from genuinely fundamental interdisciplinary science (such as nuclear and neutrinoastrophysics, neutron stars and supernovae) via nuclear medicine and matter analysisfinally to the techniques of nuclear power generation and its future. We have omittednuclear weapons, not for the sake of political correctness (we build them, so we should inprinciple also understand them) but for the reason that classification forbids reasonablemonographic public presentation. In any case, the presentation chosen here cannot beall-encompassing. However, to accomplish a certain level of comprehensiveness, we haveincluded a number of updated articles from the previous volume edited in the same style(Encyclopedia of Applied High Energy and Particle Physics, Wiley-VCH 2009), with aclosely related dedication.

I wish to thank all the authors for their outstanding devotion. Special thanks go toDr. A. Mueller of IN2P3 for his very essential help with the entire section on nuclearpower, which resulted in a unique spectrum of presentations.

Special thanks go to my editors at WILEY, Mrs. Vera Palmer and Anja Tschortner, fortheir unbending encouragement and patience.

Frankfurt Reinhard StockDecember 2012

XI

List of Contributors

Hamid Aıt AbderrahimSCK CENBoeretang 2002400 MolBelgium

Jacques BarbetGIP Arronax1 rue Arronax44817 Saint-HerblainFrance

and

Nantes-Angers Cancer ResearchCenterUMR 892 INSERM andUMR 6299 CNRS8 quai Moncousu44007 NantesFrance

Carlos A. BertulaniTexas A&M University-CommerceDepartment of Physics and Astronomy2600 South Neal StreetCommerce, TX 75428USA

Joseph BisognanoUniversity of Wisconsin-MadisonEngineering Physics Department andSynchroton Radiation Center3731 Schneider DriveStoughton, WI 53589USA

Christoph BlumeGoethe-Universitat FrankfurtInstitut fur KernphysikMax-von-Laue-Str. 160438 Frankfurt am MainGermany

Rudolf BockGSI Helmholtzzentrum furSchwerionenforschung GmbHPlanckstraße 164291 DarmstadtGermany

Allen CaldwellMax Planck Institute for Physics(Werner Heisenberg Institute)Fohringer Ring 680805 MunichGermany


XII List of Contributors

Jean-Francois ChatalGIP Arronax1 rue Arronax44817 Saint-HerblainFrance

Nicolas ChouinLUNAM UniversiteOnirisAMaROC44307 NantesFrance

Francois DavodeauNantes-Angers Cancer Research CenterUMR 892 INSERM and UMR 6299CNRS8 quai Moncousu44007 NantesFrance

Didier De BruynSCK CENBoeretang 2002400 MolBelgium

Hans GeisselGSI Helmholtzzentrum furSchwerionenforschungPlanckstr. 164291 DarmstadtGermany

and

Justus-Liebig-UniversitatGießenPhysics DepartmentHeinrich-Buff Ring 1435392 GießenGermany

Dietrich HabsLudwig-Maximilians-UniversitatMunchenFakultat fur PhysikAm Coulomb-Wall 185748 GarchingGermany

and

Max-Planck-Institute ofQuantum OpticsHans-Kopfermann-Strasse 185748 GarchingGermany

Ferid HaddadGIP Arronax1 rue Arronax44817 Saint-HerblainFrance

and

SUBATECHUniversite de NantesEcole des Mines de NantesCNRS/IN2P34 rue A. Kastler44307 NantesFrance

Wick C. HaxtonUniversity of CaliforniaDepartment of PhysicsMC-7300Berkeley, CA 94720USA

and

Lawrence Berkeley National LaboratoryNuclear Science DivisionBerkeley, CA 94720USA

List of Contributors XIII

Ragnar HellborgLund UniversityDepartment of PhysicsDivision of Nuclear PhysicsSolvegatan 1422362 LundSweden

Ingo HofmannGSI Helmholtzzentrum furSchwerionenforschungPlanckstraße 164291 DarmstadtGermany

Sigurd HofmannGSI Helmholtzzentrum furSchwerionenforschungDepartment of Nuclear Structure,Astrophysics and ReactionsPlanckstraße 164291 DarmstadtGermany

Mark HuyseUniversity of Leuven (K.U.Leuven)Instituut voor Kern-en StralingsfysicaDepartement Natuurkunde enSterrenkundeCelestijnenlaan 200 D3001 LeuvenBelgium

Robert JamesonGoethe University FrankfurtInstitute of Applied PhysicsMax-von-Laue-Str. 160438 Frankfurt am MainGermany

Jan JolieUniversity of CologneInstitute for Nuclear PhysicsZulpicher Straße 7750937 CologneGermany

Ulli KosterInstitut Laue-Langevin6 rue Jules Horowitz38042 GrenobleFrance

Francoise Kraeber-BodereNantes-Angers Cancer Research CenterUMR 892 INSERM and UMR 6299CNRS8 quai Moncousu44007 NantesFrance

and

Nuclear Medicine DepartmentUniversity Hospital-ICO-INSERM UMR892place Alexis Ricordeau44093 NantesFrance

Gerhard KraftGSI Helmholtzzentrum furSchwerionenforschungPlanckstraße 164291 DarmstadtGermany

Pierre Lapostolle†

Neuilly-sur-SeineFrance

Hartmut LauerRWE Power AGBiblis Nuclear Power Plantvice president rtd.BiblisGermany

XIV List of Contributors

Matthias LiebendorferUniversity of BaselDepartment of PhysicsKlingelbergstrasse 824056 BaselSwitzerland

Gottfried MunzenbergGSI Helmholtzzentrum furSchwerionenforschungPlanckstr. 164291 DarmstadtGermany

and

Manipal UniversityMARGMadhav NagarManipal 576104KarnatakaIndia

Sidney MichielsSCK CENBoeretang 2002400 MolBelgium

Mark RileyFlorida State UniversityDepartment of Physics214 Keen BuildingTallahassee, FL 32306-3016USA

Jurgen Schaffner-BielichJohann Wolfgang Goethe UniversitatInstitut fur Theoretische PhysikMax von Laue-Straße 160438 Frankfurt am MainGermany

Hendrik SchatzMichigan State UniversityNational Superconducting CyclotronLaboratory and Department of Physicsand Astronomy640 S. Shaw LaneEast Lansing, MI 48824-1321USA

Klaus SchreckenbachTechnische Universitat MunchenPhysik Department E21 and FRM IIJames-Franck-Strasse85747 GarchingGermany

Thomas SchulenbergKarlsruhe Institute of TechnologyInstitute for Nuclear andEnergy TechnologiesHermann-von-Helmholtz-Platz 176344 Eggenstein-LeopoldshafenGermany

John SimpsonSTFC Daresbury LaboratoryKeckwick LaneDaresburyWarrington WA4 4ADUK

Goran SkogLund UniversityDepartment of GeologySolvegatan 1222362 LundSweden

Weston M. StaceyNuclear and Radiological EngineeringGeorgia Institute of Technology770 State StreetAtlanta, GA 30332USA

List of Contributors XV

Kristina StenstromLund UniversityDepartment of PhysicsDivision of Nuclear PhysicsSolvegatan 1422362 LundSweden

Friedrich-Karl ThielemannUniversity of BaselDepartment of PhysicsKlingelbergstrasse 824056 BaselSwitzerland

Gert Van den EyndeSCK CENBoeretang 2002400 MolBelgium

Piet Van DuppenUniversity of Leuven (K.U.Leuven)Instituut voor Kern-en StralingsfysicaDepartement Natuurkunde enSterrenkundeCelestijnenlaan 200 D3001 LeuvenBelgium

Friedrich WagnerMax-Planck-Institut fur PlasmaphysikWendelsteinstr. 117489 GreifswaldGermany

and

St. Petersburg State PolytechnicalUniversity Research Laboratory forAdvanced Tokamak PhysicsPolytechnicheskaya 2919521 St. PetersburgRussia

David C. WeisserAustralian National UniversityDepartment of Nuclear PhysicsResearch School of Physics andEngineeringCanberra, ACT 0200Australia

1

Part AFundamental Nuclear Research


3

1

Nuclear Structure

Jan Jolie

1.1 Introduction 51.2 General Nuclear Properties 61.2.1 Properties of Stable Nuclei 61.2.2 Properties of Radioactive Nuclei 71.3 Nuclear Binding Energies and the Semiempirical Mass Formula 81.3.1 Nuclear Binding Energies 81.3.2 The Semiempirical Mass Formula 101.4 Nuclear Charge and Mass Distributions 121.4.1 General Comments 121.4.2 Nuclear Charge Distributions from Electron Scattering 131.4.3 Nuclear Charge Distributions from Atomic Transitions 141.4.4 Nuclear Mass Distributions 151.5 Electromagnetic Transitions and Static Moments 161.5.1 General Comments 161.5.2 Electromagnetic Transitions and Selection Rules 171.5.3 Static Moments 191.5.3.1 Magnetic Dipole Moments 191.5.3.2 Electric Quadrupole Moments 211.6 Excited States and Level Structures 221.6.1 The First Excited State in Even–Even Nuclei 221.6.2 Regions of Different Level Structures 231.6.3 Shell Structures 231.6.4 Collective Structures 251.6.4.1 Vibrational Levels 251.6.4.2 Rotational Levels 261.6.5 Odd-A Nuclei 281.6.5.1 Single-Particle Levels 281.6.5.2 Vibrational Levels 28


4 1 Nuclear Structure

1.6.5.3 Rotational Levels 281.6.6 Odd–Odd Nuclei 281.7 Nuclear Models 291.7.1 Introduction 291.7.2 The Spherical-Shell Model 301.7.3 The Deformed Shell Model 321.7.4 Collective Models of Even–Even Nuclei 331.7.5 Boson Models 35

Glossary 40References 41Further Readings 42

5

1.1Introduction

The study of nuclear structure todayencompasses a vast territory from the studyof simple, few-particle systems to systemswith close to 300 particles, from stablenuclei to the short-lived exotic nuclei, fromground-state properties to excitations ofsuch energy that the nucleus disintegratesinto substructures and individual con-stituents, from the strong force that holdthe atomic nucleus together to the effec-tive interactions that describe the collectivebehavior observed in many heavy nuclei.

After the discovery of different kinds ofradioactive decays, the discovery of thestructure of the atomic nucleus beginswith the fundamental paper by ErnestRutherford [1], in which he explainedthe large-angle alpha (α)-particle scatteringfrom gold that had been discovered earlierby Hans W. Geiger and Ernest Marsden.Indeed, Rutherford shows that the atomholds in its center a very tiny, positivelycharged nucleus that contains 99.98%of the atomic mass. In 1914, HenryMoseley [2, 3] showed that the nuclearcharge number Z equaled the atomicnumber. Using the first mass separators,Soddy [4] was able to show that onechemical element could contain atomicnuclei with different masses, forming

different isotopes. With the availability ofα-sources, due to the works of the Curies inParis, Rutherford [5] was able to performthe first nuclear reactions on nitrogen.The first attempt at understanding therelative stability of nuclear systems wasmade by Harkins and Majorsky [6]. Thismodel, like many others of the time,consisted of protons and electrons. In1924, Wolfgang Pauli [7] suggested thatthe optical hyperfine structure might beexplained if the nucleus had a magneticdipole moment, while later Giulio Racah[8] investigated the effect on the hyperfinestructure if the nuclear charge were notspherically symmetric – that is, if it had anelectric quadrupole moment.

All of these structure suggestionsoccurred before James Chadwick [9] discov-ered the neutron, which not only explainedcertain difficulties of previous models (e.g.,the problems of the confinement of theelectron or the spins of light nuclei), butopened the way to a very rapid expan-sion of our knowledge of the structure ofthe nucleus. Shortly after the discovery ofthe neutron, Heisenberg [10] proposed thatthe proton and neutron are two states of thenucleon classified by a new spin quantumnumber, the isospin. It may be difficultto believe today, 60 years after Chadwick’sdiscovery, just how rapidly our knowledgeof the nucleus increased in the mid-1930s.



Hans A. Bethe’s review articles [11, 12], oneof the earliest and certainly the best known,discuss many of the areas that not onlyform the basis of our current knowledgebut that are still being investigated, albeitwith much more sophisticated methods.

The organization here will begin withgeneral nuclear properties, such as size,charge, and mass for the stable nuclei,as well as half-lives and decay modes(α, β, γ, and fission) for unstable systems.Binding energies and the mass defectlead to a discussion of the stability ofsystems and the possibility of nuclearfusion and fission. Then follow detailsof the charge and current distributions,which, in turn, lead to an understanding ofstatic electromagnetic moments (magneticdipole and octupole, electric quadrupole,etc.) and transitions. Next follows thediscussion of single-particle and collectivelevels for the three classes of nuclei:even–even, odd-A, and odd–odd (i.e.,odd Z and odd N). With these mainlyexperimental details in hand, a discussionof various major nuclear models follows.These discussions attempt, in their ownway, to categorize and explain the mass ofexperimental data.

1.2General Nuclear Properties

1.2.1Properties of Stable Nuclei

The discovery of the neutron allowed eachnucleus to be assigned a number, A, themass number, which is the sum of thenumber of protons (Z) and neutrons (N)in the particular nucleus. The atomicnumber of chemistry is identical to theproton number Z. The mass number A isthe integer closest to the ratio between the

mass of a nucleus and the fundamentalmass unit. This mass unit, the unifiedatomic mass unit, has the value 1 u =1.660538921(73) ×10−27 kg = 931.494061(21) MeV c−2. It has been picked so thatthe atomic mass of a 12C6 atom is exactlyequal to 12 u. The notation here is AXN,where X is the chemical symbol for thegiven element, which fixes the number ofelectrons and hence the number of protonsZ. This commonly used notation containssome redundancy because A = Z + Nbut avoids the need for one to look upthe Z-value for each chemical element.From this last expression, one can seethat there may be several combinationsof Z and N to yield the same A. Thesenuclides are called isobars. An examplemight be the pair 196Pt118 and 196Au117.Furthermore, an examination of a table ofnuclides shows many examples of nucleiwith the same Z-value but different A-and N-values. Such nuclei are said tobe isotopes of the element. For example,oxygen (O) has three stable isotopes: 16O8,17O9, and 18O10. A group of nuclei thathave the same number of neutrons, N, butdifferent numbers of protons, Z (and, ofcourse, A), are called isotones. An examplemight be 38Ar20, 39K20, and 40Ca20. Someelements have but one stable isotope (e.g.,9Be5, 19F10, and 197Au118), others, two,three, or more. Tin (Z = 50) has the mostat 10. Finally, the element technetium hasno stable isotope at all. A final definitionof use for light nuclei is a mirror pair,which is a pair of nuclei with N and Zinterchanged. An example of such a pairwould be 23Na12 and 23Mg11.

The nuclear masses of stable isotopesare determined with a mass spectrometer,and we shall return to this fundamentalproperty when we discuss the nuclearbinding energy and the mass defect inSection 1.3. After mass, the next property

1.2 General Nuclear Properties 7

of interest is the size of a nucleus. Thesimplest assumption here is that the massand charge form a uniform sphere whosesize is determined by the radius. Whilenot all nuclei are spherical or of uniformdensity, the assumption of a uniformmass/charge density and spherical shapeis an adequate starting assumption (morecomplicated charge distributions arediscussed in Section 1.4 and beyond). Thenuclear radius and, therefore, the nuclearvolume or size is usually determined byelectron-scattering experiments; the radiusis given by the relation

R = r0A1/3 (1.1)

which, with r0 = 1.25 fm, gives an adequatefit over the entire range of nuclei nearstability. An expression such as Eq. (1.1)implies that nuclei have a density indepen-dent of A, that is, they are incompressible.A somewhat better fit to the nuclearsizes can be obtained from the Coulombenergy difference of mirror nuclei, whichcovers but a fifth of the total range ofA. This yields r0 = 1.22 fm. Even if thecharge and/or mass distribution is neitherspherical nor uniform, one can still definean equivalent radius as a size parameter.

Two important properties of a nuclide arethe spin J and the parity π , often expressedjointly as Jπ , of its ground state. These areusually listed in a table of isotopes and giveimportant information about the structureof the nuclide of interest. An examinationof such a table will show that the groundstate and parity of all even–even nucleiis 0+. The spin and parity assignmentsof the odd-A and odd–odd nuclei tell agreat deal about the nature of the principalparts of their ground-state wave functions.A final property of a given element is therelative abundance of its stable isotopes.These are determined again with a mass

spectrograph and listed in various tables ofthe nuclides.

1.2.2Properties of Radioactive Nuclei

A nucleus that is unstable, that is, it candecay to a different or daughter nucleus,is characterized not only by its mass, size,spin, and parity but also by its lifetime τand decay mode or modes. (In fact, eachlevel of a nucleus is characterized by itsspin, parity, lifetime, and decay modes.)The law of radioactive decay is simply

N(t) = N(0)e−λt = N(0)e−t/τ (1.2)

where N(0) is the number of nuclei initiallypresent, λ is the decay constant, and itsreciprocal τ is the lifetime. Instead of thelifetime, often the half-life T1/2 is used.It is the time in which half of the nucleidecay. By setting N(T1/2) = N(0)/2 in Eq.(1.2), one obtains the relation

T1/2 = ln(2)τ = 0.693τ (1.3)

The decay mode of ground states can beα, β, or spontaneous fission. Excited statesmostly decay by γ-emission. More exoticdecays are observed in unstable nuclei farfrom stability where nuclei decay takesplace by emission of a proton or neutron.

In α-decay, the parent nucleus emitsan α-particle (a nucleus of 4He2), leavingthe daughter with two fewer neutrons andprotons:

AXN → A−4YN−2 + 4He2 (1.4)

The α-particle has zero spin, but it cancarry off angular momentum. In β-decaythe weak interaction converts neutronsinto protons (β−-decay) or protons intoneutrons (β+-decay). Which of the two


decays takes place depends strongly onthe masses of the initial and final nuclei.Because a neutron is heavier than aproton, the free neutron is unstable againstβ−-decay and has a lifetime of 878.5(10) s.The mass excess in β−-decay is releasedas kinetic energy of the final particles.In the case of the free neutron, the finalparticles are a proton, an electron, and anantineutrino, denoted by ν. All of theseparticles have spin 1/2 and can also carryoff angular momentum. In the case ofβ+-decay, the final particles are a boundproton, an antielectron or positron, anda neutrino. Finally, as an alternative toβ+-decay the initial nucleus can capturean inner electron. In this so-called electroncapture decay, only a neutrino, ν, is emittedby the final nucleus. In general, the decayscan be written as

β−-decay : AXN → AYN−1 + e−+ν (1.5a)

β+ -decay : AXN → AYN+1 + e++ ν

(1.5b)

β+-decay (ec) : AXN + e−→AYN−1 + ν

(1.5c)One very rare mode of decay is double

β-decay, in which a nucleus is unable toβ-decay to a Z + 1 daughter for energyreasons but can emit two electrons andmake a transition to a Z + 2 daughter. Anexample is 82Se48 → 82Kr46 with a half-lifeof (1.7 ± 0.3) × 1020 years. Double β-decayis observed under the emission of twoneutrinos. Neutrinoless double β-decay isintensively searched for in 76Ge because itis forbidden for massless neutrinos withdefinite helicities. Enriched Ge is henceused as it allows the use of a large singlecrystal as source and detector (for a reviewsee [13]).

In spontaneous fission, a very heavynucleus simply breaks into two heavypieces. For a given nuclide, the decay modeis not necessarily unique. If more thanone mode occurs, then the branching ratiois also a characteristic of the radioactivenucleus in question.

An interesting example of a multi-mode radioactive nucleus is 242Am147. Itsground state (Jπ = 1−, T1/2 = 16.01 h) candecay either by electron capture (17.3%of the time) to 242Pu148 or by β− decay(82.7% of the time) to 242Cm146. Onthe other hand, a low-lying excited stateat 0.04863 MeV (Jπ = 5−, T1/2 = 152 years)can decay either by emitting a γ-ray (99.52%of the time) and going to the ground stateor by emitting an α-particle (0.48% of thetime) and going to 238Np145. There is anexcited state at 2.3 MeV with a half-lifeof 14.0 ms that undergoes spontaneousfission [14]. The overall measured half-life of 242Am147 is then determined bythat of the 0.04863 MeV state. Such long-lived excited states are known as isomericstates. From this information on branch-ing ratios, one easily finds the severalpartial decay constants for 242Am147. Forthe ground state, λec = 2.080 × 10−6 s−1

and λβ− = 9.944 × 10−6 s−1, while for theexcited state at 0.04863 MeV, λγ = 1.439 ×10−10 s−1 and λα = 6.639 × 10−13 s−1 andfor the excited state at 2.3 MeV, λSF =49.5 s−1.

1.3Nuclear Binding Energies and theSemiempirical Mass Formula

1.3.1Nuclear Binding Energies

One of the more important properties ofany compound system, whether molecular,

1.3 Nuclear Binding Energies and the Semiempirical Mass Formula 9

atomic, or nuclear, is the amount of energyneeded to pull it apart, or, alternatively, theenergy released in assembling it from itconstituent parts. In the case of nuclei,these are protons and neutrons. Thebinding energy of a nucleus AXN can bedefined as

B(A, Z) = ZMH + NMn − MX(Z, A) (1.6)

where MH is the mass of a hydrogenatom, Mn the mass of a neutron, andMX(Z,A) the mass of a neutral atom ofisotope A. Because the binding energy ofatomic electrons is very much less thannuclear binding energies, they have beenneglected in Eq. (1.6). The usual units areatomic mass units, u. Another quantity thatcontains essentially the same informationas the binding energy is the mass excess orthe mass defect, = M(A) − A. (Anotheruseful quantity is the packing fractionP = [M(A) − A]/A =/A.) The most inter-esting experimental quantity B(A,Z)/Ais the binding energy per nucleon,which varies from somewhat more than1 MeV nucleon−1 (1.112 MeV nucleon−1)for deuterium (2H1) to a peak near 56Fe30 of8.790 MeV nucleon−1 and then falls slowlyuntil, at 235U143, it is 7.591 MeV nucleon−1.Except for the very light nuclei, thisquantity is roughly (within about 10%)8 MeV nucleon−1. A strongly bound lightnucleus is the α-particle, as for 4He2 thebinding energy is 7.074 MeV nucleon−1. Itis instructive to plot, for a given massnumber, the packing fraction as a func-tion of Z. These plots are quite accuratelyparabolas with the most β-stable nuclideat the bottom. The β− emitters will occuron one side of the parabola (the left orlower two side) and the β+ emitters on theother side. For odd-A nuclei, there is butone parabola, the β-unstable nuclei pro-ceeding down each side of the parabola

until the bottom or most stable nucleusis reached. For the even-A nuclei, thereare two parabolas, with the odd–odd onelying above the even–even parabola. Thefact that the odd–odd parabola is abovethe even–even one indicates that a pair-ing force exists that tends to increase thebinding energy of the even–even nuclei.See Figure 1.1 for the A = 100 mass chain.Other indications of the importance of thispairing force are the before-mentioned 0+

ground states of all even–even nuclei andthe fact that only four stable odd–oddnuclei exist: 2H1, 6Li3, 10B5, and 14N7.For even-A nuclei, the β-unstable nucleizig-zag between the odd–odd parabolaand the even–even parabola until arriv-ing at the most β-stable nuclide, usuallyan even–even one. If the masses for eachA are assembled into a three-dimensionalplot (with N running along one long axis,Z along a perpendicular axis, and M(A,Z)mutually perpendicular to these two), onefinds a ‘‘landscape’’ with a deep valley run-ning from one end to the other. This valleyis known as the valley of stability.

The immediate consequence of thebehavior of B(A,Z)/A is that a very largeamount of energy per nucleon is to begained from combining two neutrons andtwo protons to form a helium nucleus.This process is called fusion. The release ofenergy in the fission process follows fromthe fact that B(A,Z)/A for uranium is lessthan for nuclei with more or less half thenumber of protons. Finally, the fact that thebinding energy per nucleon peaks near ironis important to the understanding of thosestellar explosions known as supernovae. InFigure 1.2, the packing fraction, P =/A,is plotted against A for the most stablenuclei for a given mass number. Notethat P has a broad minimum near iron(A = 56) and rises slowly until lawrencium(A = 260). This shows most clearly the


38 40 42 44 46 48 50

Z

−0.95

−0.9

−0.85

−0.8

−0.75

−0.7

−0.65

Pac

king

frac

tion

(Δ/A

) M

eV

44Ru56

45Rh55

41Nb59

43Tc57

40Zr60

39Y61

42Mo5846Pd64

48Cd52

47Ag53

Even ZOdd Z

A = 100

Figure 1.1 The packing fraction /A plotted against thenuclear charge Z for nuclei with mass number A = 100.Note that the odd–odd nuclei lie above the even–evenones. The β− transitions are indicated by - • -, the β+

transitions by ---, while the double β-decay 10042 Mo58 →100

44Ru56 is denoted by • • •. Data from [14]. The double β-decayfrom [15].

energy gain from the fission of very heavyelements.

1.3.2The Semiempirical Mass Formula

The semiempirical mass formula may belooked upon as simply the expansion ofB(A,Z) in terms of the mass number.Because B(A,Z)/A is nearly constant, themost important term in this expansionmust be the term in A. From Eq. (1.1)relating the nuclear radius to A1/3, we seethat a term proportional to A is a volumeterm. However, this term overbinds the sys-tem because it assumes that each nucleon

is surrounded by the same number ofneighbors. Clearly, this is not true forsurface nucleons, and so a surface termproportional to A2/3 must be subtractedfrom the volume term. (One might iden-tify this with the surface tension found in aliquid drop.) Next, the repulsive Coulombforces between protons must be included.As this force is between pairs of protons,this term will be of the form Z{Z − l)/2, thenumber of pairs of Z protons, divided by acharacteristic nuclear length or A1/3. Twoother terms are necessary in this simplemodel. One term takes into account that,in general, Z ∼ A/2, clearly true for stablelight nuclei, and less so for heavier stable

1.3 Nuclear Binding Energies and the Semiempirical Mass Formula 11

−2

0

2

4

6

0 50 100 150 200 250

Mass number (A )

Pac

king

frac

tion

(Δ/A

) M

eV

Figure 1.2 The packing fraction /A plotted against themass number A for all nuclei from 2

1D1 to 260103Lr157. Data

from [14].

nuclei where more neutrons are neededto overcome the mutual repulsion of theprotons. This term is generally taken tobe of the form asym (N − Z)2/A. The otherterm takes into account the fact, noted inSection 1.3.1, that even–even nuclei aremore tightly bound than odd–odd nucleibecause all of the nucleons of the formerare paired off. This is done by adding aterm δ/2 that is positive for even–evensystems and negative for odd–odd sys-tems and zero for odd-A nuclei. Thus, thetwo parabolas for even A are separatedby δ. From Eq. (1.6), the semiempiri-cal Bethe–Weisacker mass formula thenbecomes M(A,Z) = ZMH + NMn − B(A,Z)with

B(A, Z) = avA − asA2/3 − acZ(Z − 1)A−1/3

− asym(N − Z)2A−1 + δ

2(1.7)

Originally, the constants were fixedby the measured binding energies andadjusted to give appropriate behavior withthe mass number [16]. Myers and Swiatecki[17] (see also [18]) have included otherterms to account for regions of nucleardeformation, as well as an exponentialterm of the form −aaAexp(−γA1/3), forwhich they provide no physical explanationbeyond the fact that it reduces thedeviation from experiment. Their modelevolved into the macroscopic-microscopicglobal mass formula, called the finite-range droplet model (see [19]) and theDZ-model proposed by Duflo and Zuker[20], and more microscopic models, calledHFB [21]. The many adjustable parametersof the available mass formulas are thenfitted to masses of 1760 atomic nuclei[22]. The formulas fit binding energiesquite well with errors below 1%, but still


have problems to predict masses far fromstability. As those are important for nuclearastrophysics, the measurement of massesof exotic nuclei is an important field today.

A number of consequences flow fromeven a superficial examination of Eq. (1.7).The fact that the binding energy pernucleon, B/A, is essentially constant with Aimplies that the nuclear density is constantand, thus, the nuclear force saturates.That is, nucleons interact only with asmall number of their neighbors. Thisis a consequence of the very short rangeof the strong force. If this were not so,then each nucleon would interact with allothers in the given nucleus (just as theprotons interact with all other protons),and the leading term in B(A,Z) would beproportional to the number of pairs ofnucleons, which is A(A − l)/2 or roughlyA2. This would imply that B/A would goas A. Thus, not only does the nuclear forcesaturate (the Coulomb force does not) butit is also of very short range (that of theCoulomb force is infinite) as the sizes ofnuclei are of the order of 3.0 fm (recallEq. (1.1)).

1.4Nuclear Charge and Mass Distributions

1.4.1General Comments

In his 1911 paper, Rutherford was able toconclude that the positive charge of theatom was concentrated within a sphere ofradius <10−14 m (10 fm). This result camefrom α-particle scattering. However, forenergetic enough α-particles, the scatteringresult will contain a component due tonuclear interactions of the α-particle, aswell as the Coulomb interaction. Forprobing the structure of nuclei, electrons

have the advantage that their scattering ispurely Coulombic; however, to determinedetails of the internal nuclear structure,electron energies must be well over100 MeV for their de Broglie wavelengthsto be less than nuclear dimensions.Well before the existence of such high-energy electron beams, nuclear structureeffects were extracted from informationprovided by optical hyperfine spectra. Inparticular, nuclear charge distributions(electric quadrupole moments) and currentdistributions (magnetic dipole moments)were deduced from very accurate opticalmeasurements (see the following section).A result involving the innermost electronsof heavy atoms is the isotope shift, which canbe observed in atomic X-rays. This arisesbecause the nuclear radii for two differentisotopes of the same atom will produceslightly different binding energies of theirK-shell electrons. Thus, the K X-rays ofthese isotopes will be very slightly differentin energy. As an example, the isotopic pair203T1122 and 205T1124 have an isotope shiftof about 0.05 eV. Another early method todetermine the charge radius is to take thedifference between the binding energies oftwo mirror nuclei (cf. Section 1.2.1). Thisleads to an expression that only involvesac and, thus, the nuclear radius. This isuseful for light nuclei for which mirrorpairs occur.

With the advent of copious beams ofnegative muons, much more accurateoptical-type hyperfine spectrum studiescould be made. The process is quite simple,and the advantages obvious. By stoppingnegative muons in a target, an exotic atomis formed in which the muon replacesan orbital electron and transitions to themuonic K-shell follow. These transitions ofthe muon to the ls1/2 state emit photons ofthe appropriate (but high) energies. (As themuon is more than 200 times as massive as

Documents

Encyclopedia of Nuclear Physics - download.e-bookshelf.de · Hans Geissel, Mark Huyse, Gottfried M¨unzenberg, and Piet Van Duppen 6 Superheavy Nuclei 213 Sigurd Hofmann 7Nuclear