Models of the Atomic Nucleus: Unification Through a Lattice of Nucleons PDF
Preview Models of the Atomic Nucleus: Unification Through a Lattice of Nucleons
Models of the Atomic Nucleus Second Edition Norman D. Cook Models of the Atomic Nucleus Unification Through a Lattice of Nucleons Second Edition 123 Prof.NormanD.Cook KansaiUniversity Dept.Informatics 569Takatsuki,Osaka Japan [email protected] Additionalmaterialtothisbookcanbedownloadedfromhttp://extras.springer.com. ISBN978-3-642-14736-4 e-ISBN978-3-642-14737-1 DOI10.1007/978-3-642-14737-1 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2010936431 ©Springer-VerlagBerlinHeidelberg2006,2010 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply, even in the absence of a specific statement, that such names are exempt from the relevant protectivelawsandregulationsandthereforefreeforgeneraluse. Coverdesign:WMXDesignGmbH,Heidelberg Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface to the Second Edition Alreadybythe1970s,sometheoristshaddeclaredthatnuclearstructurephysicswas a“closedchapter”inscience,butsincethenithasrepeatedlybeenfoundnecessary tore-openthisclosedchaptertoaddressoldproblemsandtoexplainnewphenom- ena.Thepresentvolumeshowswhyadeclarationthatthereisnothingmoretolearn about nuclear structure is premature – and outlines the path toward unification of thediversemodelsstillinusebynucleartheorists. InpreparingtheSecondEditionofModelsoftheAtomicNucleusIhaveexpanded on twotopics mentioned only briefly in the FirstEdition. One isa more extensive discussion of the foundations of the independent-particle model, as established by Eugene Wigner in 1937. Despite first appearances, that discussion is not primar- ilyhistorical,butratherisanexplanationofWigner’searlydiscoveryofthelattice symmetries of the nucleus. For historical reasons, the geometry of the lattice was notemphasizedinthe1930sand1940s,butthesymmetriesinherenttothefcclat- ticeleddirectlytotheestablishmentoftheindependent-particlemodelasthecentral paradigmofnucleartheory–andeventuallytotheshellmodelanditsmodernvari- ants. As discussed in Chap. 10, the coordinate-space geometry of the lattice, as distinctfromanabstract“quantumspace”interpretation,hasclearimplicationsfor nuclearstructuretheory–andisindeedthemotivationforwritingthismonograph. The bottom-line is that the lattice symmetries are truly at the heart of conven- tional nuclear physics – originally stated in Wigner’s work from 1937, developed byFriedrichEverlinginthe1950sandKlausLezuointhe1970s–andpermeating everyaspectofnucleartheorysincethen.Inotherwords,Iarguethatitisincorrect to consider the fcc lattice as yet-another nuclear model with only limited applica- tions,orasanunorthodox“alternative”view.Rather,thelatticeisastrongcandidate forunifyingthemanypreviousandseemingly-contradictorymodelsofnuclearthe- oryemployedsincethe1950s.Anditisstrongbecauseitisbuilt,fromtheground up,onWigner’sdescriptionofthequantummechanicsofthenucleus. Tostatetheargumentmoreexplicitly,thesymmetriesofthefcclatticeareidenti- caltothoseoftheindependent-particlemodelandtheindependent-particlemodelis orthodoxnucleartheory.FollowingWigner’slead,itiseasytoshowthattheconven- tionaldescriptionoftheenergystatesofnucleonshasastraightforwardgeometryin v vi PrefacetotheSecondEdition theformofaspecific3Dlattice.Inthisregard,theunificationofnuclearstructure theory through the fcc lattice model is not as revolutionary as it may first appear tobe. Unfortunately,theunarticulated“picture”inthebackofthemindofnearlyevery nuclearphysicistalivetodayisoneofprotonsandneutronsbuzzingaroundinside ofthetinynuclearvolume–notunliketherandommovementsofelectronsinover- lappingelectronorbitals(“Zitterbewegung”).Theideathattheshellsandsubshells of the nucleus have a geometrical basis quite unlike electron clouds is therefore seen as “counter-intuitive.” For this reason, much of the following text is devoted toshowingwhy,onthecontrary,agaseous-phasepictureofthenucleusshouldbe consideredcounter-intuitive,andhowalatticemodelcanreproducetheexactsame sequenceandoccupancyofnucleonsfoundintheindependent-particlemodelona geometricalbasis. ThesecondmajorchangeintheSecondEditionisamoredetailedexamination ofthepredictionsofthelatticewithregardtofission.Thisincludesanintroduction tothenuclearstructureaspectsofso-calledlow-energynuclearreactions(LENR), alsoknownascondensed-matter nuclearscience(CMNS)andchemically-assisted nuclear reactions (CANR). This branch of nuclear physics is the progeny of the controversial “cold fusion” phenomena, first reported in 1989, but now widely understoodtohaveasolidempiricalfoundation.Idonotdelveintothehistoryand politicsofcoldfusion–bothofwhichhavebeendiscussedindetailbyothers,but have concentrated on the experimental results that have provided indication of the fissionofPalladiumincertaintypesofhigh-pressureelectrolysisexperiments.Many oftheexperimentalandtheoreticalissuesconcerningtheinductionofLENRarestill unresolved,buttheso-calledtransmutationresultsareamongthemostunambiguous empirical findings indicative of nuclear effects in “tabletop” experimental set-ups. The Second Edition discusses both the experimental findings and their simulation usingthefcclatticemodel. Similartothetheoreticalresultsobtainedfromthelatticemodelinexplainingthe fission of Uranium, predictions concerning the fission fragments from Palladium are concrete indication that the geometry of the nuclear lattice can be used to explainexperimentaldatathattheothernuclearstructuremodelscannot.Myhope is therefore that any nuclear physicist with lingering doubts about the “finality” and“completeness” ofconventional nuclearstructuretheorywillexamine thetwo fission sections, and give some thought to the lattice “reconstruction” of nuclear theory that led to Wigner’s Nobel Prize in 1963. The bottom-line is that – despite theconceptualdifficultiesofquantummechanicsingeneral,nuclearstructureitself is surprisingly straight-forward when viewed within the framework of a lattice of nucleons–andcomprehensibleonitsowntermswithoutinvokinganyofthevari- ouscontroversialquantummechanicaltricksoftime-reversal,partialchargeorthe selectiveallowanceoftheimpossibleundertheuncertaintyflag. My main argument, in other words, is that nuclear structure can be understood onageometricalbasisthatthetraditionaltextbookssimplydonotconvey.Although both the lattice and the conventional independent-particle model description of nucleon states are based fundamentally on the Schrödinger wave-equation, it is PrefacetotheSecondEdition vii onlythroughthelatticethatthegeometricalsymmetriesbecomeself-evident.Solid geometryisitselfperhapsnot“easy,”buttheNuclearVisualizationSoftwareallows for the 3D manipulation of specific nuclei and the visualization of their various quantummechanicalpropertieswithintheframeworkofthelatticemodel,oranyof theothermodelsofnuclearstructuretheory. The first Edition of this book was completed during a Sabbatical Leave of AbsencefromKansaiUniversity(September2004toSeptember2005). Finally, I would like to thank Valerio Dallacasa, Paolo Palazzi, Friedrich Everling,TraceyRunciman,PaoloDiSiaandDennisLettsfortheirtimeandeffort incontributingtotheSecondEdition. Osaka,November2010 NormanD.Cook Preface to the First Edition Models of the Atomic Nucleus is a largely non-technical introduction to nuclear theory–anattempttoexplainoneofthemostimportantobjectsinnaturalscience inawaythatmakesnuclearphysicsascomprehensibleaschemistryorcellbiology. Unlikemostotherscientificfields,thepopularizationofnuclearphysicshasnotgen- erallybeensuccessfulbecausemanyfundamentalissuesremaincontroversialand, even after more than 70 years of study, a “unified theory” of nuclear structure has not yet been established. Nevertheless, despite some widely-acknowledged unfin- ished business, the theme developed in this book is that each of the many models in use in nuclear theory provides a partial perspective on the nucleus that can be integratedintoacoherentwholewithintheframeworkofalatticeofnucleons.The proposed unification itself is not uncontroversial, but, at the very least, the lattice representationofnuclearstructureillustrateshowacomplexphysicalobjectsuchas thenucleuscanbeunderstoodassimultaneouslyexhibitingthepropertiesofagas, aliquid,amolecularclusterandasolid. The book is divided into three parts. Part I (Chaps. 1, 2, 3 and 4) introduces the main topics that must be addressed in any discussion of nuclear physics. My intentionhasbeentopresentabrief,buteven-handedsummaryofthebasicmodels thathavebeendevisedtoexplainnuclearphenomenaandtoreviewthetheoretical ideas that have occupied the minds of theorists for many decades. These chapters are historical and are intended to convey what the major insights and conceptual challengesofnuclearphysicshavebeenthusfar. Part II (Chaps. 5, 6, 7, 8 and 9) is a more detailed look at four topics that have notfoundsatisfactoryresolutionwithinanyofthecurrentmodelsofthenucleus– arguably the most basic nuclear properties that theory must eventually explain. Theseincludetopicsconcerningthesize,shapeanddensityofnuclei,andtherelated problemofthedistancethatnucleonstravelinthenucleusbeforetheyinteractwith other nucleons (the so-called “mean-free-path” problem). Other issues discussed here are the nuclear force, the non-existence of the so-called super-heavy nuclei, andthephenomenaofnuclearfission.Inthispartofthebook,noattemptismadeto resolveproblems;onthecontrary,Imerelypointto:(i)theirexistence,(ii)thelong history of related debate, and (iii) the lack of any widely acknowledged solutions. Anattemptatresolvingtheseproblemsonthebasisofalatticemodelistheburden ix
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