Inclusion of phonon exchange in a nuclear matrix e

arXiv:cond-mat/0606585v2[cond-mat.other]4Jan2007InclusionofphononexchangeinanuclearmatrixelementIrfanChaudhary∗andPeterHagelstein†ResearchLaboratoryofElectronicsMassachusettsInstituteofTechnologyCambridge,MA02139,USAAbstractPhononexchangewithnucleiinthecourseoffusionreactionsthatoccurinasolidhavenotbeenanalyzedpreviously.Thisproblemhasbecomeofinterestinconnectionwithclaimsofobservationsofanomaliesinmetaldeuterides.Ifthestrongforceinteractionweredependentonlyonposition(andnotspinorisospin),thenthecouplingwithphononscanbedevelopeddirectly.Sinceanuclearinteractioncanchangethelatticeconstituents,theinitialandfinalstatelatticescanbedifferent,andwemustincludethisintheformulation.Formorerealisticstrongforcemodelswithspinandisospindependence,wecanusecorrelatednuclearwavefunctionswhicharemadeupofproductsofspace,spinandisospincomponents.Inthiscase,thespinandisospinalgebracanbedoneanalytically,producingchannel-dependentpotentialsthatareonlyspacedependent.Theformulationthatresultscanbeusedforquantitativeestimatesofphononexchange.PACSnumbers:63.10.+a,63.20.-e,63.20.Kr,63.90.+t,25.10.+s,02.20.-a1I.INTRODUCTIONFewclaimshaveresultedinasmuchcontroversyastheclaimoftheobservationofanexcessheateffectofnuclearorigininmetaldeuteridesmadebyFleischmann,Pons,andHawkinsin1989.1ReviewsofworkonthisproblemwereconductedbytheDepartmentofEnergy(intheUnitedStates)in19892andin2004.3Theconclusionsofthe1989reviewwereverynegative.The2004reviewwasquitedifferentinhowitwascarriedout,whatmaterialwasreviewed,andintheresults.Onthespecificquestionoftheexistenceofanexcesspowereffect,whichwasthecentralissueofthereviewmaterialpresentedtoDoE,4thereweremorepositivecommentsthannegativecommentsvolunteeredfromthereviewers.5Thisissignificant,asDoEdidnotchargethereviewerstoconsiderthisquestionspecifically.Amongmanyothercommentsthatweremade,severalofthereviewerssuggestedthatmoreworkonthisproblembesubmittedtomainstreamjournals.Ourinterestinthispaperisnotfocusedonthequestionoftheexistenceofanexcessheateffect,althoughthisissuehasmotivatedourinvestigations.Weareinterestedinsteadintheoreticalissueswhichmustbebetterunderstoodinorderfortheorytobemorerelevanttotheproblem.Formostphysicists,thetheoreticalproblemwasadequatelyaddressedbyHuizenga,whoarguedthatthree“miracles”wererequiredforatheoreticalexplanation.6•Thefirst“miracle”involvesthequestionofreactionrate.Theexcessheateffectimpliesreactionratesontheorderof1012sec−1,tensofordersofmagnitudelargerthanthefastestfusionratespossibleinmolecularD2orHD.•Thesecond“miracle”concernsthebranchingratio.Fleischmanninitiallyspeculatedthat4Hewasbeingmadefromtwodeuterons.Sucharesultisseeminglymiraculousasthebranchingratioforthisreactionchannelislowerbyaboutsevenordersofmagnitudethantheprimaryn+3Heandp+treactionchannels.•Thethird“miracle”involvestherequirementthatthereactionenergybeexpressedthroughchannelsnotinvolvingenergeticreactionproducts.Ifonebelievesthattheseissuesareinsurmountable,thenonewouldrequirethatanyclaimofexcessheatofnuclearoriginmustbeaccompaniedbymeasurableenergeticreactionproducts.ThisviewwasadoptedbyHuizenga,andbythe1989ERABPanel.Thisviewisalsowidelyheldamongthephysicscommunityatthistime.A.MotivationHowever,otherviewsarepossible.Fleischmann’sinitialspeculationwasthatanewphysicalprocesswasinvolved,onethatbehavesdifferentlyfromwhatisdescribedinthetextbooks.Itseemsthatifwearetryingtounderstandwhetheranexcessheateffect2canexist,weshouldbeaskingwhethertherecanbeinteractionsbetweennucleiandacondensedmatterenvironment.Forexample,supposethatphononsareexchangedinthecourseofanuclearreactionthatoccursinalattice.Couldthisphononexchangeresultinamodificationoftheselectionrules?Andifphononexchangeoccurs,wouldthatnotconstituteanewchannelintowhichreactionenergymightgo?Nuclearphysicsreliesheavilyonthenotionofanequivalentvacuumreactioninordertounderstandquantitativelyfusionreactions.Huizenga’sthree“miracles”reflectsuchaview.Forexample,thesecond“miracle”isessentiallyastatementofenergy,linearmomentum,andangularmomentumconservation,allofwhichareconservedinvacuum.Isitobviousthatconservationlawsinacondensedmatterenvironmentalwaysproducethesamereactionpathwayswiththesamebranchingratios;and,ifso,canthisbeproven?Inthecaseofthethird“miracle,”thereactionenergymustbeexpressedasanenergeticproductinvacuum,sincenootherkindsofchannelsexist.Butisitobviousthatthismustalsobethecaseinacondensedmatterenvironment,wherelowenergychannelsdoexist?Onceagain,canthisbeproven?Inanyevent,allofthesequestionsoughttobecapableofbeingaddressedbytheory.Thecurrentlackofsuchatheoryinthemainstreamliteratureisunderscoredincommentsmadebysomereviewersinthe2004DoEreview.Forexample,areviewerwithexpertiseinmetaldeuteridesandphononswrote:“Tocreateacouplingbetweennuclearinteractionandphononsatsuchalowenergyregion(namely,theelectromagneticinteraction)isbeyondone’simaginationatthemoment.”Anotherreviewerwithexpertiseinnucleartheorywrote:“Iamconvincedthatsimpleorder-of-magnitudeestimatesofthiskindcouldquicklyruleoutanyoftheexoticmechanismsproposed...”Thisreviewerarguesthatthematrixelementfortheemiss