Weighted Osillator Strengths and Lifetimes for the
Neutral Oxygen Spetrum, O I
I. V. L.Costa 1
, G. H.Cavalanti 2
, and A. G.Trigueiros 1;3
1
Institutode F
isia\GlebWataghin",
UniversidadeEstadual deCampinas, UNICAMP,
13083-970 Campinas,S~aoPaulo,Brazil,
2
InstitutodeF
isia,UniversidadeFederalFluminense,UFF
CampusdaPraia Vermelha-Gragoata, 24210-310Niteroi,RJ,Brazil,
3
InstitutodeQumia,UniversidadedoEstadodoRiodeJaneiro,UERJ,
20550-013Maraan~a,Riode Janeiro, RJ,Brazil
ismaeli.uniamp.br,gildoif.u.br,andagtrii.uniamp.br
Reeivedon15June,2000
Theweightedosillatorstrengths(gf)andthelifetimesforOIpresentedinthisworkwereobtained
inamultiongurationHartree-Fokrelativisti (HFR)approah. Inthisalulation,the
eletro-statiparameterswereoptimizedbyaleast-squaresproedure,inordertoimprovetheadjustment
to experimentalenergylevels. Thismethodproduesgf-valuesthat areinbetter agreement with
intensityobservationsandlifetimevaluesthatarelosertotheexperimentalones. Inthisworkwe
presentalltheexperimentallyknowneletridipoleatomitransitionsandenergylevelsfortheO
Ispetrum.
The data bases, inluding tables of wavelengths, energylevels, weighted osillator strenghts and
lifetime valuesfor the OIspetrum,are availableintheeletroni version ofthis paperonly[on
theworldwideweb,athttp://www.sbf.if.usp.br/bjp/Vol31/Num1/℄.
I Introdution
Theground stateongurationof the neutraloxygen,
OI,is1s 2
2s 2
2p 4
withtheterms 1
S, 3
Pand 1
D. The
ionizationpotentialforOIis109837.02m 1
(13.618
eV).
Edlen [1℄ has published a detailed analysis of the
spetrumofOI inwhihhe hasrevisedand extended
theearlierworkbyFowler[ 2℄;Frerihs[3;4℄,andMore
andRieke[5℄.
Moore [ 6℄summarized in the book AtomiEnergy
LevelsalltheenergylevelsforOIspetrum. Edlen[7℄
presentedalistofOIstandardlinesdeterminedbythe
Ritzombinationpriniple.
Edlen's [1℄ lassial paper on O I has been
re-vised and extended by Eriksson and Isberg [8;9℄,
Is-berg[10℄. Human et al. [11;12℄ presentedresultson
absortion spetra: Rydberg series from ground state
and metastablestates. Moore [13℄ presentedin anew
edition of the book Atomi Energy Levels all known
levels for the O I. Later, Moore [14℄ summarized all
theenergylevelsandwavelengthsfortheOIspetrum
inthebookAtomiEnergyLevelsandMultipletTable.
OIin thevauum ultra-violet,VUV,region.
Thepurpose of this workis to presentareview of
all known eletri dipole transitions of O I, their
os-illator strengths alulated from tted values of the
energyparametersandthelifetimes, alulatedbythe
samemethod,forallknownexperimentalenergylevels.
Theworkwepresentherewasstimulatedbythedesire
todetermineweightedosillatorstrengthsandlifetimes
for theOI spetrum. Bothparametersare important
inthestudyoflaboratoryandsolarspetra,asoxygen
is anastrophysially importantelement. Noextensive
soureofgfandlifetimevaluesurrentlyexistsforthis
spetrum.
II Calulation
The osillator strength f( 0
) is a physial quantity
related to line intensity I and transition probability
W(
0
),asgivenbySobelman[16℄:
W(
0
)= 2!
2
e 2
m 3
jf( 0
I /gW( 0
)/gjf( 0
)j=gf:
Herem=eletronmass,e=eletronharge,=
ini-tialquantumstate,!=(E() E( 0
))=h,E()initial
stateenergy,g=(2J +1)isthenumberofdegenerate
quantumstateswithangularmomentumJ (inthe
for-mulafortheinitialstate). Quantitieswithprimesrefer
to thenal state.
In the equation above, the weighted osillator
strength, gf; isgivenbyCowan[17℄:
gf = 8 2 ma 2 0 3h S; (2)
where = jE() E( 0
)j=h, h =Plank's onstant,
=lightveloity,anda
0
=Bohrradius,andtheeletri
dipole linestrengthisdened by:
S= <J P 1 0 J 0 > 2 : (3)
This quantityis ameasure ofthe totalstrengthof
the spetralline, inludingall possibletransitions
be-tweenm, m'dierent J
z
eigenstates. Thetensor
op-erator P 1
(rstorder) in the redued matrix element
is thelassialdipolemomentforthe atomin unitsof
ea
0 :
To obtain gf, we need to alulate S rst, or its
squareroot: S 1=2 0 =<J P 1 0 J 0
>: (4)
In a multionguration alulation we haveto
ex-pand the wavefuntion j J >in terms of single
on-guration wavefuntions, j J >, for bothupperand
lowerlevels:
jJ>= X
y
J
jJ>: (5)
Therefore,weanhavethemultiongurational
ex-pressionforS 1=2 0 : S 1=2 0 = X X 0 y J <J P 1 0 J 0 >y 0 0 J 0 (6)
Theprobabilityperunit time ofanatom ina
spe-istateJ tomakeaspontaneoustransition toany
statewithlowerenergyis
P(J)= X A(J; 0 J 0 ) (7) where: A(J; 0 J 0
) is the Einstein spontaneous
emis-sion transition probability rate, for a transition from
theJ statetothe 0
J 0
state. Thesumisoverall 0
J 0
stateswithE( 0
J 0
)<E(J).
TheEinstein probabilityrateis relatedto gf with
thefollowingrelationgivenbyCowan[17℄:
gA= 8 2 e 2 2 gf: (8)
Sine the natural lifetime (J) is the inverse of the
probabilityP(J),then:
(J)= X A(J; 0 J 0 ) 1 (9)
Thenaturallifetime isappliableto anisolatedatom.
Interationwithmatterorradiationwillreduethe
life-timeofastate.
ThevaluesforgfandlifetimesgiveninTables1and
2respetivelywerealulatedaordingtothese
equa-tions.
In order to obtain better values for osillator
strengths, we alulated the redued matrix elements
P 1
by using optimized values of energy parameters
whih were adjusted from a least-squares alulation,
Cowan [17℄. In this adjustment, the ode tries to t
experimentalenergyvaluesbyvaryingtheeletrostati
parameters. Thisproedure improves valuesusedin
eq. (2)andy J andy 0 0 J 0
valuesusedineq. (6).
III Disussion
The theoretial preditions for the energy levels
of the ongurations were obtained by
diagonaliz-ing the energy matries with appropriate
Hartree-Fok relativisti (HFR) values for the energy
pa-rameters. For this purpose the omputer ode
developed by Cowan [17℄ was used. The
pro-gram allowed us to alulate energy levels,
wave-lengths, transition probabilities and lifetimes. For
the even-parity ongurations we have the
follow-ing piture: 1s 2 2s 2 2p 4 , 1s 2 2p 3 (3p+4p+5p+6p) and 1s 2 2p 3
(6f+7f). For the odd-parity ase we study the
1s 2 2s 2 2p 3 (3s+4s+5s+6s+7s+8s+9s+10s+11s+12s+13s +14s+15s+17s+19s+20s+21s+22s+23s+24s+25s+26s +27s+28s+29s+30s+31s),1s 2 2s 2 2p 3 (3d+4d+5d+6d+ 7d+8d+9d+10d+11d+12d+13d+14d+15d+16d+17d+ 18d+19d+20d+21d+22d+23d+24d+25d+26d+27d+ 28d+29d+30d),and 1s 2 2s2p 5
. The members 2p 3
16s
and 2p 3
18s of the Rydberg serie 2p 3
ns are unknown.
Theinterpretationoftheongurationlevelstrutures
was made by a least-squares t of the observed
lev-els. Theenergy levelvalueswere determinedfrom the
observedwavelengthsbyaniterativeoptimization
pro-edure using the program ELCALC, Radziemsky and
Kaufman[18℄,in whih theindividual wavelengthsare
weighted aordingtotheir unertainties. Theenergy
levels adjusted by this method were used to optimize
the eletrostati parameters by a least-squares
proe-dureandnallythese optimizedparameterswere used
again to alulate the gf- values and lifetimes. This
method produes gf-values that are in better
agree-mentwithlineintensityobservationsandlifetimesthat
areloserto theexperimental ones.
Wehavepresentedosillatorstrengthsandlifetimes
presentworkispartofanongoingprogram,whosegoal
isto obtainweightedosillator strengthsand lifetimes
for elements of astrophysial importane. The works
for Si III, Si V, Si VI,Si VII,Si IX and Si X spetra
havebeenonluded[ 19℄,[20℄,[21℄,[22℄, [23℄,and[24℄.
Inthis partiularworkon OI,theresultsare part
ofCostas'sresearhprojetinludedinhisBSdegree.
All tables are available only in the eletroni
version of the paper on the world wide web at
http://www.sbf.if.usp.br/bjp/Vol31/Num1/.
Aknowledgements
This work was nanially supported by the
Funda~ao de Amparo a Pesquisa do Estado de S~ao
Paulo (FAPESP), Brazil, and by Conselho Naional
de Desenvolvimento Cient
io e Tenologio (CNPq),
Brazil. Computations were arried out at the Prof.
JohnDavidRogersComputationalCenter,UNICAMP.
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