Table Of ContentLecture Notes in Physics 963
Valery Zagrebaev
Heavy Ion
Reactions
at Low
Energies
Andrey Denikin · Alexander Karpov
Neil Rowley Editors
Lecture Notes in Physics
Volume 963
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Valery Zagrebaev
Heavy Ion Reactions at Low
Energies
Andrey Denikin (cid:129) Alexander Karpov (cid:129) Neil Rowley
Editors
123
Author
ValeryZagrebaev
FlerovLaboratoryofNuclearReactions
JointInstituteforNuclearResearch
Dubna,Russia
Editors
AndreyDenikin AlexanderKarpov
NuclearPhysicsDepartment FlerovLabofNuclearReactions
DubnaStateUniversity JointInstituteforNuclearResearch
Dubna,Russia Dubna,Russia
NeilRowley
InstitutdePhysiqueNucléaire
UMR8608,CNRS-IN2P3andUniversitéde
OrsayCEDEX,France
Translatedby
AndreyDenikin
Dubna,Russia
AlexanderKarpov
Dubna,Russia
ISSN0075-8450 ISSN1616-6361 (electronic)
LectureNotesinPhysics
ISBN978-3-030-27216-6 ISBN978-3-030-27217-3 (eBook)
https://doi.org/10.1007/978-3-030-27217-3
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Foreword
More than a 100 years of advances in the field of nuclear physics have allowed
scientiststoframeageneralideaofthestructureofatomicnuclei,todeterminethe
maincharacteristicsofnuclearinteractions,toanswerquestionsontheoriginofthe
chemicalelementsintheUniverse,andtolearnhowtoproducenewelementsand
predicttheirproperties.Modernnuclearphysicshasprovidedawealthofpractical
experienceandmanytoolsthatenableustosolveawiderangeofappliedproblems
thathumanitycurrentlyfaces.Allthismakesitevenmoreintriguingthataftersuch
long-termresearchinthisfield,manyblankpagesremaintobefilled.
Overthepastfewdecades,newexperimentalmethodshavebeendevelopedthat
allowustorevealareasofnuclearphysicspreviouslyinaccessibletoinvestigation.
The boundaries of the known parts of the nuclear map have been considerably
extended.Wecannowobtainandinvestigatesystemsofnucleonswithveryexotic
properties, in particular neutron-rich nuclei located at the drip line, such as 7H,
8,10He,22C,and28O.Inaddition,anincreaseinexperimentalsensitivityhasmade
it possible to study, for example, nuclear reactions occurring at deep sub-barrier
energies, and a breakthrough in the studies of the heaviest nuclei has also been
made.Inthelast15years,sixnewsuperheavyelementshavebeensynthesized,and
convincingevidence for an “island of stability” in this region of mass—predicted
overhalfacenturyago—hasfinallybeenestablished.
The rapid developmentsin nuclear and elementaryparticle physicsover recent
yearsrequiretheinformationaccumulatedovera30-yearperiodtobesystematized
and presented comprehensively. Unfortunately, the scope of recently published
Russian academic literature on this subject is somewhat lacking. The author of
this tutorial—a scientist with an excellent international reputation—has managed
topartiallyfillthisgap.Thisbookoutlinesthemainexperimentalfactsonnuclear
reactionsinvolvingheavyionsatlowenergies.Itfocusesondiscussionsofnuclear
physics processes that are a subject of active, modern research, and it gives
pictorialexplanationsofthesephenomenaintheframeworkofup-to-datetheoretical
concepts.
Thebookisintendedforphysicsstudentswhohavecompletedastandardcourse
of quantum mechanics and have a basic idea of nuclear physics processes. It is
v
vi Foreword
designed to become a kind of lifeboat that at the end of the course will allow
studentstonavigatethemodernscientificliteratureandtounderstandthegoalsand
objectivesofcurrent,on-goingresearch.
Dubna,Russia AndreyDenikin
Dubna,Russia AlexanderKarpov
2015
Contents
1 Introduction .................................................................. 1
2 NuclearInteractionsandClassesofNuclearReaction .................. 9
2.1 Nucleon–NucleonandNucleon–NucleusInteractions,Nuclear
MeanField .............................................................. 9
2.2 Nucleus–NucleusInteraction:FoldingandPhenomenological
Potentials................................................................ 13
2.2.1 FoldingPotentials............................................... 14
2.2.2 Woods–SaxonPotential ........................................ 16
2.2.3 ProximityPotential............................................. 17
2.2.4 BassPotential................................................... 18
2.2.5 Comparison of Diabatic Potentials
fortheNucleus–NucleusInteraction........................... 19
2.2.6 DependenceofPotentialEnergyonNuclearOrientation..... 19
2.2.7 DependenceofPotentialEnergyonDynamical
Deformations.................................................... 21
2.3 ClassificationofNuclearReactions,ExperimentalProcedures,
CrossSections,andKinematics........................................ 22
3 ElasticScatteringofNucleonsandHeavyIons........................... 29
3.1 ScatteringinaCoulombField.......................................... 29
3.2 ElasticScatteringofProtonsandNeutrons:OpticalModel .......... 32
3.3 ElasticScatteringofLightIons......................................... 37
3.4 ApplicabilityofClassicalMechanicsandTrajectoryAnalyses ...... 39
3.5 NuclearRainbowandDiffractionScattering .......................... 42
3.6 ElasticScatteringofHeavyIons ....................................... 49
4 Quasi-Elastic Scattering of HeavyIons and Few-Nucleon
TransferReactions........................................................... 51
4.1 DirectProcessofLight-ParticleTransfer.............................. 52
4.2 Distorted-WaveDescriptionofDirectReactions...................... 53
4.3 Single-ParticleStatesandClusterStates,SpectroscopicFactors..... 55
vii
viii Contents
4.4 InelasticExcitationofVibrationalandRotationalStates ............. 57
4.5 Quasi-ElasticScatteringofHeavyIons................................ 60
4.6 ReactionsofFew-NucleonTransfer.................................... 65
5 Deep-InelasticScatteringofNuclei ........................................ 69
5.1 ExperimentalSystematics of Deep-Inelastic Scattering
andQuasi-Fission....................................................... 70
5.2 Potential Energyof Heavy Nuclear Systems, Diabatic
andAdiabaticDrivingPotentials....................................... 75
5.2.1 NucleonTransferandDrivingPotentials...................... 75
5.2.2 Macro-MicroscopicModelandtheAdiabaticPotential
Energy........................................................... 76
5.3 TransportEquationsforDeep-InelasticNuclearCollisions:
FrictionalForces ........................................................ 80
5.4 CalculationofDeep-InelasticCrossSections ......................... 85
5.5 AnalysisofDeep-InelasticScatteringandQuasi-Fission............. 87
5.6 Multi-NucleonTransfer Reactions: Synthesis of Heavy
Neutron-RichNuclei.................................................... 91
6 FusionofAtomicNuclei..................................................... 99
6.1 Detecting Fission Fragmentsand EvaporationResidues
fromtheCompoundNucleus........................................... 100
6.2 StatisticalModelfortheDecayofanExcitedNucleus ............... 102
6.3 FusionatAbove-BarrierEnergies...................................... 109
6.4 Sub-barrierFusion:Hill–WheelerFormula............................ 111
6.5 CoupledChannels:EmpiricalandQuantumDescription
ofFusion................................................................. 113
6.6 BarrierDistributionFunction........................................... 118
6.7 NeutronTransferintheProcessofSub-barrierFusion ............... 119
6.8 SynthesisofSuperheavyElementsinFusionReactions.............. 125
6.9 RadiativeCaptureofLightNuclei ..................................... 139
References......................................................................... 145
Chapter 1
Introduction
To begin with, let us briefly recall the basic properties of atomic nuclei, such as
binding energy,size, and shape (deformation).The mass of the nucleus is always
lessthanthesumofthemassesofitsconstituentnucleons.Thedifferencebetween
thesevaluesiscalledthenuclearbindingenergy:
E (Z,A)=Z·m c2+N ·m c2−M(Z,A)c2, (1.1)
bind p n
where Z and N are the numbers of protons and neutrons in the nucleus, m and
p
m are their masses, A = Z +N is total number of nucleons. In the low-energy
n
nuclearreactionsthatweconsiderhere,thenumberofprotonsandneutronsremains
unchanged.Thebindingenergiesofthenucleiintheinitialandfinalstatesoftenplay
akeyroleindeterminingtheprobabilityandbehaviorofaparticularreaction.For
example,thelawofenergyconservationinthebinaryreactiona+A→b+B (in
whichanucleusahitsafixedtargetA)iswrittenas:
M(a)c2 + M(A)c2 + E (a) = M(b)c2 + M(B)c2 + E (b)+E (B),
kin kin kin
anditisthenuclearbindingenergythatdeterminesthekineticenergyoftheparticles
formedinthereaction(hereitisassumedthatthenucleibandB areformedinthe
groundstate,otherwisetheirexcitationenergiesshouldbeaddedtotherightside):
E (b)+E (B)=E (a)+[E (b)+E (B)−E (a)−E (A)],
kin kin kin bind bind bind bind
and the quantity Q = E (b) + E (B) − E (a) − E (A) is called the
bind bind bind bind
reaction Q-value. Since kinetic energy cannot be negative, when Q < 0, this
reactionispossibleonlyforE (a) > |Q|(endothermicreaction).Reactionswith
kin
Q > 0 are called exothermic. An example of exothermic reactions (those with
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V.Zagrebaev,HeavyIonReactionsatLowEnergies,LectureNotesinPhysics963,
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