Multiconfiguration Dirac-Hartree-Fock calculations of transi(3)

4.3The7s6d3D2and7s7p1P1states

Thesetwolevelsaredistinguishedbecausetheywerethesubjectofaseparatepaper[25].Inthepresentpaperwedulyquotethedataobtainedincore-valenceapproximation,andthereaderisreferredtotheabovementionedpaperforfurtherdiscussion.4.4Theremaining7s7p3P2,7s6d3D1,7s6d3D3,and7s6d1D2states

Theremaining7s7p3P2,7s6d3D1,7s6d3D3,and7s6d1D2states,togetherwiththestatesdiscussedinsections4.1,4.2,and4.3above,constitutefullsetofstatesarisingfromthethreelowestelectroniccon gurationsofradium.

Someoftheselevelsshouldalsobeconsideredmetastable,notonly7s7p3P0.The3D3 3D2transitionisthestrongest’direct’decaychannelforthe3D3state,butitisinfactveryweak(comparabletothatofthe3P0 1S0transition).Theratesofotherpossible’direct’decaychannelswouldbestillsmaller(e.g.M2transition3D3 3P1rateiscomparabletothatofthe3

D2 3P0transition),thereforethemultiphotonorhyper ne-inducedtransitionsmayalsoplayaroleinthe3D3lifetime.Similarconsiderationsmayinprincipleapplytothe3P2,1D2,and3

D2states(wedidnotpursuethisissue,though).

5Summaryandconclusions

Table1presentscalculatedtransitionrates,andthelifetimesarepresentedintable2.Coulombgaugevaluesofelectricmultipoletransitionsfromthetable1werenotusedtoobtainthelifetimes.Withtheexceptionofthe3P0level,thetransitionratesaregivenwith4signi cantdigitsandthelifetimeswith3signi cantdigits,butthatnotnecessarilyre ectstheiraccuracy.

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

Willbeinsertedbytheeditor7

Table1.Calculatedtransitionratesbetweenninelowestlevelsofradium[s 1].Transitionmultipo-laritiesaredenotedbyE1,E2,M1,M2;theBabushkinandCoulombgaugevaluesby(B)and(C),respectively.HFSmeanshyper ne-induced.Numbersinbracketsrepresentpowersof10.

3

P0 1S03

P1 1S0

P1 3P03

P1 3D1

3

3

P1 3D2P2 3P0

3

3

P2 3D1

3

P2 3D2

3

P2 3D3P1 1S0

1

1

P1 3D1

1

P1 3D2

1

P1 1D2

3

D1 3P0D2 1S0

3

D2 3P03

D2 3D13

D3 3D21

D2 1S0

1

3

D2 3P1

1

D2 3P2

HFS+E1M1E1(B)(C)M1E1(B)(C)E1(B)(C)E2(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E1(B)(C)E2(B)(C)M2M1M1E2(B)(C)E1(B)(C)E1(B)(C)2.935[-2]2.374[6]1.873[6]1.334[-2]8.794[1]4.025[3]1.775[-3]1.607[2]1.185[-2]1.243[-2]4.310[3]9.722[3]4.602[4]1.109[5]1.044[5]4.201[5]1.793[8]1.795[8]3.282[4]5.222[4]9.793[4]1.441[5]3.241[5]5.875[5]1.390[3]7.940[3]2.524[-1]1.630[-1]3.021[-13]5.082[-4]6.352[-3]2.710[1]2.271[1]6.960[2]1.224[3]5.930[0]7.535[0]

2.760[6]2.37(12)[6]

9.850[1]1.572[-3]

4.897[3]5.204[4]1.234[5]1.805[8]4.195[4]2.646[4]3.194[5]1.529[3]3.032[-1]

7.722[3]7.973[0]

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

8Willbeinsertedbytheeditor

Table2.Calculatedlifetimesofeightlowestexcitedstatesofradium,comparedwithdatafromotherauthors.3

P034(15)sa

3P1421ns362ns505ns420ns250ns422(20)ns

3P26.46µs5.55µs5.2µs1P15.56ns5.53ns5.5ns3D1719µs654µs617µs3D23.95s3.3s15s3D3157sb1D2

1.37ms

0.129ms

c

38ms

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

Willbeinsertedbytheeditor9

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