The Oklo bound on the time variation of the fine-s

arXiv:hep-ph/9606486v128Jun1996IHES/P/96/40IASSNS-HEP-96/62TheOkloboundonthetimevariationofthefine-structureconstantrevisitedThibaultDamoura,b,c,FreemanDysonbaInstitutdesHautesEtudesScientifiques,F-91440Bures-sur-Yvette,FrancebSchoolofNaturalSciences,InstituteforAdvancedStudy,OldenLane,Princeton,NJ08540,U.S.A.cDARC,ObservatoiredeParis–CNRS,F-92195Meudon,France.June27,1996AbstractIthasbeenpointedoutbyShlyakhterthatdatafromthenaturalfissionreactorswhichoperatedabouttwobillionyearsagoatOklo(Gabon)hadthepotentialofprovidinganextremelytightboundonthevariabilityofthefine-structureconstantα.Werevisitthederiva-tionofsuchaboundby:(i)reanalyzingalargeselectionofpublishedrare-earthdatafromOklo,(ii)criticallytakingintoaccounttheverylargeuncertaintyofthetemperatureatwhichthereactorsoperated,and(iii)connectinginanewway(usingisotopeshiftmeasurements)theOklo-derivedconstraintonapossibleshiftofthermalneutron-captureresonanceswithaboundonthetimevariationofα.Ourfinal(95%C.L.)resultsare:−0.9×10−7(αOklo−αnow)/α1.2×10−7and−6.7×10−17yr−1˙αaveraged/α5.0×10−17yr−1.11IntroductionSinceDirac[1]firstsuggesteditasapossibility,thetimevariationofthefundamentalconstantshasremainedasubjectoffascinationwhichmotivatednumeroustheoreticalandexperimentalresearches.Forgeneraldiscussionsandreferencestotheliteraturesee,e.g.,[2,3,4,5].Superstringtheorieshaverenewedthemotivationforavariationofthe“constants”bysuggestingthatmostofthedimensionlesscouplingconstantsofphysics,suchasthefinestructureconstantα=1/137.0359895(61),arefunctionsofthevacuumexpectationvaluesofsomescalarfields(see,e.g.,[6]).Recently,amechanismforfixingthevacuumexpectationvaluesofsuchmasslessstringyscalarfields(dilatonormoduli)hasbeenproposed[7].Thismechanismpredictsthatthetimevariationofthecouplingconstants,atthepresentcosmologicalepoch,shouldbemuchsmallerthantheHubbletimescale,butmaybenotunmeasurablyso.Inthismodel,thetimevariationsofallthecouplingconstantsarecorrelated,andtheonesofmostobservationalsignificancearethefinestructureconstantαandthegravitationalcouplingconstantG.Inthepresentpaper,werevisitthecurrentbestboundsonthevariationofα.Oneoftheearlyideasforsettingaboundonthevariationofαwastoconsiderthefine-structuresplittingsinastronomicalspectra[8].Withthismethod,BahcallandSchmidt[9]concludedthatαhadvariedbyatmostafraction3×10−3ofitselfduringthelast2×109years.Arecentupdateofthismethodhasgiventheresult△α/α=(0.2±0.7)×10−4atredshifts2.8≤z≤3.1,i.e.thebound|˙α/α|1.6×10−14yr−1(2σlevel)onthetimederivativeofαaveragedoverthelast∼1010yr[10].SeealsoRef.[11]whichobtains−4.6×10−14yr−1˙α/α4.2×10−14yr−1fromfine-structuresplittings,and,denotingx≡α2gp(me/mp),−2.2×10−15yr−1˙x/x4.2×10−15yr−1bycomparingredshiftsobtainedfromhyperfine(21cm)andopticaldata.Oneofusobtainedtheupperlimit|˙α/α|5×10−15yr−1fromananalysisoftheabundanceratiosofRheniumandOsmiumisotopesinironmeteoritesandmolybdeniteores[2].Themostrecentdirectlaboratorytestofthevariationofαhasobtained|˙α/α|3.7×10−14yr−1bycomparinghyperfinetransitionsinHydrogenandMercuryatoms[12].Formorereferencesonthevariationofconstantssee[2,3,4,5].Ontheotherhand,themuchmorestringentbound|˙α/α|10−17yr−1hasbeenclaimedbyShlyakhter[13,14,15]tobederivable(atthethreestan-darddeviationslevel)fromananalysisofdatafromtheOklophenomenon.2TheOklophenomenondenotesanaturalfissionreactor(moderatedbywa-ter)thatoperatedabouttwobillionyearsagointheorebodyoftheOklouraniummineinGabon,WestAfrica.ThisphenomenonwasdiscoveredbytheFrenchCommissariat`al’EnergieAtomique(CEA)in1972.Theresultsofathorough,multi-disciplinaryinvestigationofthisphenomenonhavebeenpresentedintwoconferenceproceedings[16,17].Seealso[18]and[19]forsummariesofthefirstphaseofinvestigation.InviewoftheimportanceofShlyakhter’sclaim,ofthelackofpublicationofadetailedanalysis1,andofourdissatisfactionwithsomeimportantas-pectsoftheanalysispresentedintwopreprints[14,15],wedecidedtorevisittheOkloboundonα.Themainconclusionsofourworkarethefollowing:(i)weconfirmthebasicclaimofShlyakhterthattheOklodataisanextremelysensitiveprobeofthetimevariationofα;(ii)aftertakingintoaccountvar-ioussourcesofuncertainty(notablytemperatureeffects)intheanalysisofdata,andconnectinginaimprovedwaytherawresultsofthisanalysistoapossiblevariationofα,wederivewhatwethinkisasecure(95%C.L.)boundonthechangeofα:−0.9×10−7αOklo−αnowα1.2×10−7.(1)Intermsofanaveragedrateofvariation,thisreads−6.7×10−17yr−1˙αα5.0×10−17yr−1.(2)2Extractingtheneutroncapturecrosssec-tionofSamarium149fromOklodataTheproofofthepastexistenceofaspontaneouschainreactionintheOklooreconsistsessentiallyof:(i)asubstantialdepletionoftheUraniumisotopicratio2U235/U238withrespecttothecurrentstandardvalueinterrestrialsamples;and(ii)acorrelatedpeculiardistributionofsomerare-earthiso-topes.Therare-earthisotopesareabundantlyproducedinthefissionof1TheverybriefaccountpublishedinNature[13]omitsmostoftheanalysisthatispresentedinthetwopreprints[14,15].2Fortypographicalconvenience,weindicateatomicmassnumbersasright,ratherthanleft,superscripts.3U235andtheobservedisotopicdistributionisbeautifullyconsistentwithcal-culation