Heavy Ion Reactions at Low Energies PDF
Preview Heavy Ion Reactions at Low Energies
Lecture 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 FoundingEditors WolfBeiglböck,Heidelberg,Germany JürgenEhlers,Potsdam,Germany KlausHepp,Zürich,Switzerland Hans-ArwedWeidenmüller,Heidelberg,Germany SeriesEditors MatthiasBartelmann,Heidelberg,Germany PeterHänggi,Augsburg,Germany MortenHjorth-Jensen,Oslo,Norway MaciejLewenstein,Barcelona,Spain AngelRubio,Hamburg,Germany ManfredSalmhofer,Heidelberg,Germany WolfgangSchleich,Ulm,Germany StefanTheisen,Potsdam,Germany DieterVollhardt,Augsburg,Germany JamesD.Wells,AnnArbor,MI,USA GaryP.Zank,Huntsville,AL,USA The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new devel- opmentsin physicsresearch and teaching-quicklyand informally,but with a high qualityand the explicitaim to summarizeand communicatecurrentknowledgein anaccessibleway.Bookspublishedinthisseriesareconceivedasbridgingmaterial between advanced graduate textbooks and the forefront of research and to serve threepurposes: (cid:129) to be a compact and modern up-to-date source of reference on a well-defined topic (cid:129) to serve as an accessible introduction to the field to postgraduate students and nonspecialistresearchersfromrelatedareas (cid:129) to be a source of advanced teaching material for specialized seminars, courses andschools Bothmonographsandmulti-authorvolumeswillbeconsideredforpublication. Edited volumesshouldhoweverconsist of a verylimited numberof contributions only.ProceedingswillnotbeconsideredforLNP. VolumespublishedinLNParedisseminatedbothinprintandinelectronicfor- mats,theelectronicarchivebeingavailableatspringerlink.com.Theseriescontent isindexed,abstractedandreferencedbymanyabstractingandinformationservices, bibliographicnetworks,subscriptionagencies,librarynetworks,andconsortia. Proposalsshouldbe sent to a memberof the EditorialBoard, ordirectly to the managingeditoratSpringer: DrLisaScalone SpringerNature PhysicsEditorialDepartment Tiergartenstrasse17 69121Heidelberg,Germany [email protected] Moreinformationaboutthisseriesathttp://www.springer.com/series/5304 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 TranslationfromtheRussianlanguageedition:ÂÇÈÓÐÞÈÓÈÃÍÙËËÔÕâÉÈÎÞÏËËÑÐÃÏËby ªÃÆÓÈÄÃÈÅ¥.«.,©V.I.Zagrebaev2016,ISBN978-5-9530-0435-0.PublishedbyJointInstitutefor NuclearResearch.AllRightsReserved. ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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 ©SpringerNatureSwitzerlandAG2019 1 V.Zagrebaev,HeavyIonReactionsatLowEnergies,LectureNotesinPhysics963, https://doi.org/10.1007/978-3-030-27217-3_1
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