Multiconfiguration Dirac-Hartree-Fock calculations of transi

The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p

EPJmanuscriptNo.

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arXiv:physics/0701239v1 [physics.atom-ph] 22 Jan 2007

Multicon gurationDirac-Hartree-Fockcalculationsoftransitionratesandlifetimesoftheeightlowestexcitedlevelsofradium

JacekBiero´n1,PaulIndelicato2,andPerJ¨onsson3

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InstytutFizykiimieniaMarianaSmoluchowskiegoUniwersytetJagiello´nskiReymonta4,30-059Krak´ow,Polande-mail:Bieron@uj.edu.pl

´LaboratoireKastlerBrossel,EcoleNormaleSup´erieure

CNRS;Universit´eP.etM.Curie-Paris6

Case74;4,placeJussieu,75252ParisCEDEX05,Francee-mail:paul.indelicato@spectro.jussieu.frNature,Environment,SocietyMalm¨oUniversityS-20506Malm¨o,Sweden

e-mail:per.jonsson@ts.mah.se

Abstract.Themulticon gurationDirac-Hartree-Fock(MCDHF)modelhasbeenemployedtocalculatethetransitionratesbetweentheninelowestlevelsofradium.Thedominantrateswerethenusedtoevaluatetheradiativelifetimes.Thedecayofthemetastable7s7p3P0statethrough2-photonE1M1andhyper neinducedchannelsisalsostudied.

1Introduction

Recentadvancesintrappingandspectroscopyoffree,neutralatomsmakeitpossibletoextendthesearchfortimereversalviolatione ectsintothedomainofradioactiveelements[1].Inthelastdecadeseveralheavyatomswereconsideredascandidatesforexperimentalsearches[2].Thereareatleasttwoongoingatomictrapexperiments(inKernfysischVersnellerInstituutinNetherlandsandinArgonneNationalLabintheU.S.whoseaimistodetecttheelectricdipolemomentofradium.Theadvantageofradiumliesinoctupoledeforma-tionsofnucleiinseveralisotopessimpleelectronicstructure(groundstatecon guration[Kr]4d104f145s25p65d106s26p67s2yieldstheclosed-shellsingletstate1S0)aswellasincoin-cidentalproximityoftwoatomicstatesofoppositeparity,7s7p3P1and7s6d3D2,whichareseparatedbyaverysmallenergyinterval5cm 1.

ThedataonatomicspectrumofradiumcompiledinthetablesofMoore[8]camefromtheexperimentalinvestigationsofRasmussenwithsubsequentrevisionsbyRussellbothgobacktothe1930s.Thesedatacoveronly69classi edlines.Theisotopeshiftsandhyper nestructuresofradiumweremeasuredbythegroupofWendtinthe1980s.TheyhavestudiedbothatomicRaIandionicRaIIspectra,andobtainedtheisotopeshifts,magneticdipolehyper neconstantsAandelectricquadrupoleconstantsBofthe7s7p1P1,7s7p3P1,7s7p3P2,and7s7d3D3levelsofneutralradium,aswellasthemagneticdipolehyper neconstantsAofthe7s2S1/2,7p2P1/2,and7p2P3/2levelsofRa+ion,togetherwiththeelectricquadrupoleconstantBofthe7p2P3/2stateofRa+.Hyper nestructuresofsingly-ionisedradiumhavebeenalsothesubjectofseveraltheoreticalpapers

The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p

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Theexcitationenergiesofseveralstatesofneutralandsingly-ionisedradium(andbarium)werelatercalculatedintheframeworktherelativisticcoupled-clustertheorybythegroupofKaldor[23,24].Morerecentlytherehavebeenthreepapersfromourgroupinwhichwecalculatedthelifetimesofthe7s7p1P1and7s6d3D2states[25];thehyper nestructureconstantsofalllevelsbelongingtothetwolowestexcited-statecon gurations[26];andtheelectric eldgradientsgeneratedbytheelectroniccloudinthe7s7p1P1,7s7p3P1,and7s7p3P2states,whichinturn(combinedwiththemeasuredvaluesoftheelectricquadrupoleconstantsB)yieldedthenuclearelectricquadrupolemomentofradium-223isotope[27].Theexcitationenergiesandlifetimesofseveralstatesofradium(andbarium)werecalculatedrecentlyintheframeworkofthecombinedcon guration-interactionandmany-bodyperturbationtheorybyDzubaandGinges[28].

Inthepresentpaperwecalculatedthetransitionprobabilitiesbetweenthestatesarisingfromthethreelowestcon gurationsofradium:7s21S0,7s7p3P0,1,2,7s7p1P1,7s6d3D1,2,3,and7s6d1D2,aswellasthelifetimesofthesestates.Thepurposeofthepresentpaperisfourfold.Firstly,weintendedtoextendthetransitionratecalculationsonalllevelsarisingfromthethreelowestcon gurations(i.e.7s2,7s7p,and7s6d).Weincluded(1)transitionswhichcontributeappreciablytolifetimes;(2)transitionsinvolving7s6d3D2and7s7p3P1levelsbecausetheyareofinterestinEDMexperiments(themixinginducedbyT-oddinteractionsisstrongestbetweenthesetwolevels);(3)transitionswhichmaybeimportantfortrapping;(4)transitionswhicharestrongerthan1/s(asomewhatarbitrarythreshold).Secondly,newcomparisonofourresultsbecameavailablewhenthetwomostrecentpapers[28,5]appearedinprint.Theseinturnpermittedfurthertestsofthenewlydeveloped[29]parallelversionoftheGRASPpackage[30]andcalibrationthetheoreticalmodelforthecalculationsofthespectroscopicpropertiesofradium.Finally,wepresentasummaryoftheavailabletheoreticaldataonthespectroscopicpropertiesofeightlowestexcitedlevelsofradium,withthehopethattheymaybeofhelpfortheexperimentalgroups,thatarecurrentlyintheprocessofsettinguptheatomictrapsforthesearchofpermanentelectricdipolemoments.TheArgonnegrouphasalreadymeasured[5]thefrequencyandtherateofthe3P1 1S0transitioninthe22588Raisotope,anddeterminedthe

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lifetimeoftheP1level.ThelifetimeofthislevelhavebeenpreviouslycalculatedbyHafnerandSchwarz[31]andbyBruneau[32].

2Theory

Themodi edversion[29]oftheGRASPimplementation[30]ofthemulticon gurationDirac-Hartree-Fockmethod[33]wasusedinthepresentpaper.ThestartingpointistheDirac-CoulombHamiltonian

2N

1/rij,(1)cαi·pi+(βi 1)c+Vi+HDC=

i

i>j

whereVNisthemonopolepartoftheelectron-nucleusCoulombinteraction.Thewavefunction

foraparticularatomicstate(Ψ)isobtainedastheself-consistentsolutionoftheDirac-Fockequation[30]inabasisofsymmetryadaptedcon gurationstatefunctions(Φ)

Ψ(ΓPJM)=

NCF i

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