PHYSICAL REVIEW A VOLUME 18, N UMBER 3 SEPTEMBER 1978

gJ factor of metastable S2 atomic oxygen using a time-of-flight,atomic-beam magnetic-resonance method

Tuncay Incesu, ~ Ahsanul Huq, ~ and Howard A. ShugartDepartment of Physics and Materials and Molecular Research Division, Lawrence Berkeley Laboratory,

University of California, Berkeley, California 94720(Received 12 August 1977; revised manuscript received 22 May 1978)

A time-of-flight, atomic-beam magnetic-resonance method was used to compare the g~ factor of 2p'3s 'S2

atomic oxygen with the g~ factor of metastable 2 S, atomic helium in magnetic fields of 3209 and 4228 G.The metastable oxygen and helium atoms were produced in a pulsed radio-frequency discharge source andafter traversing the apparatus were detected by electron emission from a tungsten surface. By collecting dataonly in a given interval of the time-of-flight distr'ibution the 0('S) and He(3S) states were isolated from otherdischarge products. From 158 pairs of resonances taken with four relative field and hairpin orientations theatomic magnetic g factor is gJ('S2, "0) = p,~/J = —2.0020910(10).

I. INTRODUCTION

The present measurement stems from an unex-pected observation. When beam- source develop-ment studies were initiated to produce metast3bleN('S, &,) atoms from dissociation of N„a,velocity-selected Stern-Gerlach deflection experimentshowed two magnetic moment peaks at 4 p, p and2 p, p rather than the expected three peaks at 5 p, p,3 p„and

leap

The cause of this discrepancy w3straced to the presence of 0('S,) metastable atomsmade from 0, which entered the gas-handling sys-tem from the atmosphere by permeating a shortsection of plastic tubing. Although this interfer-ence was easily eliminated, the strength of the0( S,) signal and the intrinsic interest in atomicoxygen as a constituent of the atmosphere and asa test case for multielectron atomic theory com-pelled the precision measurement reported here.

The ground-state configuration of atomic oxygen(1s'2s'2@~) produces two metastable levels 'D, and'Sp above the 'P, ground state. These states haveenergies 1.97 and 4.18 eV and lifetimes =150 and=15 sec. , respectively. Another state 'S, is thelowest quintet state of the configuration1s'2s'2P'3s and lies 9.14 eV above the groundstete. ' Three independent lifetime measure-ments of 0('S,) yielded 185 +10,' 170 +25,' and180 + 5 p, sec, which are consistent with a theoreti-cal calculation of 192 p, sec. '

Throughout this paper all gJ values will bequoted using the convention g~ = ij, ~/J. This con-vention is consistent with that used for nuclei and,therefore, provides a uniform convention for thesign of a g factor. The negative sign for the freeelectron (g, =- 2) indicates the magnetic momentand angular momentum point in opposite directions.In 1949 Kiess and Shortley, obtained the valueg ('S„"0)= -1.999(2) (Ref. 6) from the Zeemanpattern of the visible spectral lines of oxygen.

Eighteen years later Brink observed oxygen inan atomic-beam apparatus and compared the reso-nant frequencies of 'S and 'P states to obtaing~('S„"0)= -1.97(5).' In addition to using a mass-spectrometer detector, Brink observed from hissource two spectral lines 3947 and 7774 A that re-sult from transitions which terminate in the S,state.

The magnetic moment of the comparison heliumstate used in the current measurement has a longhistory of study by many techniques. When thepresent experiment was in progress the best valueof the gz('S„He)= -2.002237 35(60) was from aprevious measurement in this 13boratory. ' Re-cently, two new values have been published:g~('S„'He)=-2.00223755(20) (Ref. 9) from an op-tical pumping experiment and g~('S„'He)= —2.00223745(14) (Ref. 10) from an atomic-beam exper iment.

In the absence of nuclear spin 3nd neglectingterms quadratic in the magnetic field, the energylevels shown in Fig. 1 are given by the expression

g J /pm JB. When &m J = +1 transitions are ob-served, the g-factor ratio

g~('S„"0)/g~('S„'He)= v("0)/v('He),

where the v's are resonant frequencies in a com-mon magnetic field. Justification for neglectingpossible terms quadratic in field rests partly ontheoretical and partly on experimental evidence.The nonrelativistic interactions of an atom with theexternal magnetic field are separated into termslinear in field

W'„=(e/2m)B (L —gS)

and quadratic in field, ~

W'~ = g r', si 'n, e,sm

where y,. and 8,. are the polar coordinates of the ith

797 1978 The American Physical Society

18798

electron and 8=quadratic in th f'e ield ma

tion of B " Sh ftitsy arise from W

er perturbation th eory:

+ (2's, !w'„!~)(&!w'„!2's,„„s~ E(2 'S

has nonzero matrixt t t ofth

!

a es must have n'S, any intermedi t

n character. H , ( 'e ements for nW 2 a

„

is independentare zero

en o space cp tial portions of the w

oordinates and

tho 1 de same . ' iar ar mgu

e nonrelat

d Th odod3.f..=., W-

nonzero but indedoes not affect the

e wave functions.ec the spin portion of

Nonlinear relativis 'tic effectsspin-spin interacti

may occur throu h

c ion and rela '

to the magn ttivistic corre

ne ic-interacrec-

t' t' o t'ec ions which mar. cla-

m yre ov the expect

imes the absoluteobe

so ute shift of the levels.

using a hydrogenic ap rox'pa field of 4000G '

opoic is negl 'blg

Also since cornson

parison of hei'nances was mad ie d

V

a e experime ie din imits may be I u

and heo the frequenc .

ua

yg

formrequencies hada a functional

v=-g (p /h)B+bB'

then

v(o) g&(o), b+ [b(He) —b(0) ]

Using ratios f e)0 ojos for v(0)/v(He9270(5) at 4228 G" t ce

—b(0) ho ld be ll

sentially equale wo ratios aree, and therefore

f of th e two b coefficients.

II. EXPERIMENNT AND PROCEDURE

The atomic-beam am appartus em 1

d 'bd previously. ""M

obserys owninpi g. p

e magnet the undefygen resonances.

lected andun eflected m =Q s

re ioug the C-

nsi ion from thisg i ion

state occu

ifa stop wire. 0

si ion region the ma ransition either to md flatoms

agsi e of the sto

Th

top w ; and te ytheAu erg

(a) both the knn as the folio

c or.

ha

ges

th rajectory throu gflop-in re

- re-serv

a g ond, i.e. th eq y ppo

i ion; (c) sin le,.... .,..„ dre etected in inte r; anin egral J atoms; and

oE",„=(Zn)' (2 'S,!

E —, r',.sin'8,!2 'S, )

= 2.4 x 10-'(Hz/G')B'

1=0

mF= mJ

hF =0 bm =+F

=

I=O (b) F=

ZITIJ2

TUNCAY INCESU AHSAN Ul, HU Q, AND Ho&ARD

0 is the direc '

A. SH VGA', T

thF =0 Qm =+

FIG. l. Schematic of enerl l d'd

23S stin uced transitions

ie for Zee-

state of helium and (b ~ o aF=I+J.

an (b) the ~S2 state of ao atomic oxygen.

Illl . AUGER

. DETECTOR

O -OI .STOP -WIRE

0.025 ' f

A C

Magnet ~ M

B

source

o net Mognet~RI, HalRPIM I0.011"

I~~t., t., t..t

E~H 4~H

4z 4z=0

4H 8

FIG. 2. Tr4z

rajectory geomof the atomi -bic- earn a

metry and field nfpparatus used in th

co iguratio

tectoT

tor is about 2.5 mance fromom the source to the de

J

g~ FACTOR OF METAS TABI. K ' S~ ATOMIC OXYGEN USING. . .

(d} the method is independent of the differences indeflection characteristics of the two species.

Both 'S, helium and 'S, oxygen were produced ina pulsed 50-MHz radio-frequency discharge tube.The active regian of the discharge tube, 22 cmlong and 0.8 cm in diameter, was bent into a U

shape. A slit 0.005 in. wide and 0.160 in. high inthe convex side allowed escape of the metastablebeam. The radio frequency through the tube waspulsed on for 40 p, see about 150 times per second.This procedure permitted the time of flight to thedetector to be used as a discriminator againstphotons, high-velocity atomic states, and low-velocity molecular states. The cold tungstencathode surface. of a Bendix magnetic electronmultiplier emits electrons only when struck bysufficiently excited atoms and thus further dis-criminates against ground-state atoms and mole-cules. Any charged particles in the beam are de-flected from the beam by the various apparatus'smagnetic fields.

Magnetic field stability and homogenization inthe C-magnet region were achieved by using twoKlein-Phelps-type nuclear-magnetic-resonance(NMR} systems. " One field-modulated systemlocked the C field to a particular value while asecond frequency-modulated system allowed map-ping vertically and horizontally along the beam.The first probe was fixed in position about 2 in.below the beam while the second probe was attach-ed to the movable radio-frequency hairpin struc-ture. By iterating a procedure of mapping thefield and setting correction currents in eight shimcoils," it was possible to reduce the inhomogeneityalong a 2-in. length of the beam from 60 ppm toless than 1 ppm.

Radio frequency for inducing transitions wasgenerated by an X-13 reflex klystron oscillatorwhich w'as locked to harmonics of a HP 5105A fre-quency synthesizer. The output of the oscillatorpasses through a traveling-wave tube amplifierand power leveler befor'e arriving at the 50-0terminated hairpin structure (see Ref. 16}wheretransitions in the beam are induced. Thefrequencywas generated and measured to at least 1 part in10' and was based upon the atomic time scale ofstation WWVB at 60 kHz. The two frequencies forhelium and oxygen at 3209 6 were 8990.3 and8989.6 MHz, while at 4228 G, they were about11 845.5 and 11844.7 MHz, respectively. Thesepairs of frequencies were sufficiently close to-gether so the klystron could be tuned from one tothe other by changing only the repeller voltage.

An on-line PDP-11 computer controlled the tim-ing, apparatus parameters, time of flight, andresonance data collect;ion for the experiment.During data taking with 40 psec/channel and a 2.5-

III. DATA ANALYSIS

In data collection and searching for systematiceffects 372 individual helium and oxygen resonan-ces were collected and fitted by least-squaresmethods to a Lorentzian line shape with a constantbackground. The resonance amplitude, peak fre-quency, and width, as well as the background, weredetermined. Figures 4 and 5 show examples offitted oxygen and helium resonances. All resonan-ces used to determine optimum rf powers werediscarded, and only five other oxygen resonances

OX 528

6000-

K'c 4000-O

I-X

2000—

00 l0 20

CHANNEL NUMBER50

FIG. 3. Time-of-flight distribution of metastable dis-sociation fragments from 02. Data-collection time was10 min. The peaks between channels 6 and 30 correspondto ~$2 atoms.

m-long apparatus, the time-of-flight spectrumcorresponding to the 'S, state of oxygen falls be-tween the 6th and 30th channels, while most of the'S, helium atoms fall between the 14th and 35thchannels. With this data-collection arrangementthe inverse relation between observed linewidthand traverse time in the radio-frequency regionwas easily demonstrated. Figure 3 shows a sample'S~ oxygen time-of-flight spectrum. For resonancedata collection we used only those atoms whicharrived at the detector between channel 10 andchannel 35, since this range included most of theslower 'S, oxygen atoms and the entire '$, heliumpeak. Alternately, the helium and oxygen resonan-ces were scanned and recorded at 20 discrete fre-quencies. Adequate data were collected in 2 or 3min on helium and in 10 to 15 min on oxygen.Usually six oxygen resonances imbedded betweenseven helium resonances were taken before alter-ing the experimental conditions.

TUN CA Y IN CESU, AHSANUUL HU Q, AND HOWARD AA. SH UGART

FINAL AVERACiE

1600 —.

I400

I58 MEA SUREMENTS

OF g ('S 0") A VERA(iES

I200—

IOOO

800—

600

400—

Resononce Frerequency II844.?I20 MHz

FRFQUENCY

E CURVEFITTED OXYGEN RESONANCE C

FIG. 4. LFIG. . Least-squares f't t.c ion time was 10 m j.n.

ORlf:NTATIONS:

2Fll'-I. D H A IR PIN

N R

ERROR I.IM ITS

HHs7o sso ss90

g =-2. Oo20. . .

Q ONE MEASUREMENT

950

;; yi'

~N /i&/ /

. ~~ //~

up

lg~7glli~ rill) tuiua9&o 940

QIJP'['El& VALUE

were eliminated for various ex eriIn an effort to d'

p rimental reasons.o discover possible s so ' systematic effects

a a were divided mto two groupsn sng to a field of 4228 C. and the other* g o pEach of these

possible orientat'r su groups accordin t'

g o the four

[each may be N (

'n a ions of the C fieield and hairpin

' e (normal) or 8 re )] y

three smallerther divided into

a. er groups each havinaving a different hair-e ratio gz('S, "p)/g~' S„'He)was

FIG. 6. Histo ramgram of all oxygen S" and "R" refer too normal and revn 2 gJ determinations

e rf hairpin.ons 0

computed for ever q yc ry oxygen resonancege o the two helium re

tak ' tb fothe

p p ov ded an nd atn subgrou s ro '

ree o systematic effects ar e Millman effect wh'

f t' f th0 e rf field direc '

16GO—

l400—

1200—

IOOO—

cn

800—COO

600

8I kHz

IV. RESULTS AND DISCUSSION

A summary of 158 measurements forin e histogram of Fi

h h' tor are ~n ications of indivif th ~ f' ldur ield and hair inp

flndi.na average. From this analysis we

(5g 16p / 3g 4& g~ S„He)=0.9999269(4).

When this result ~s combined with

oxygen isin e introduction n, the final g of 'SJ 2

400—I

200—a

Resonance Frequency ll845. 52IO MHz

FREQUENCY

RESONANCE CURVEFITTEO HELIUM

i oa S he'~. 5. Least-squares f't tsrve. Data-coll@ 't

lium resonance.c I.on time was 2 min.

(Bg 16p~ = p~/J = -2.0020910(10).This value and the 0.5 m

about 82/ of tho o e measurementsgram in Fig. 6.

ts shown in the histo-

The m ic as beenmeasurement wh' h h described hereeczsion determination

of the S metastable state ofa e state of atomic oxygen. No

g J FACTOR OF METASTABI, E ' S2 AT() MIC OXYGEN USING. . .

accurate theoretical computations have been pub-lished with which the measurement may be com-pared. However, after preliminary results wereobtained, " Hegstrom, using an approximate butsimple computation which works well for '8, He,found that the same procedure predicts the '8,oxygen g» to within 10 ppm. "

The combination of time-of-flight detection withan atomic-beam magnetic-resonance apparatusproved to be a sensitive technique for separatinga particular discharge fragment from photons orother species affecting the beam detector. Addi-tionally, the method allows limited control of themagnetic-resonance linewidth by selecting the vel-ocity interval detected.

ACKNOWLEDGMENTS

%e thank Peter J. Mohr, Michael H. Prior, andCharles Schwartz for their helpful counsel on thepossible contributions of quadr atlc ZeeIQan shjLfts

in helium and oxygen. One of the authors (T.I.)appreciates the hospitality of the Atomic BeamGroup, Department of Physics and LawrenceBerkeley Laboratory of the University of Californ-ia. He acknowledges the assistance of a grantfromUNESCO. This research was supported in j.974by the U. S. Atomic Energy Commission. Theresearch group is now part of the Division ofChemical Science, Office of Basic Energy Sciencesof the U. S. Department of Energy.

. *Present address: Physics Dept. , Middle East Techni-cal University, Ankara, Turkey.

)Present address: Physics Dept. , University of Mis-souri, Rolla, Missouri 65401.

~B. S. Freund, J. Chem. Phys. 54, 3125 (1971); C. E.Moore, Atomic Energy Levels, U.S. Natl. Bur. Stand.Circ. No. 467 (U.S. GPO, Washington, D.C., 1949),Vol. 1.

C. E. Johnson, Phys. Bev. A 5, 2688 (1972).SW. C. Wells and E. C. Zipf, Phys. Bev. A 9, 568 (1974}.46. Novak, W. L. Horst, and J. Fricke, Phys. Rev. A

17, 1921 (1978).'C. A. Nicolaides, Chem. Phys. Lett. 17, 436 (1972).6C. C. Kiess and G. E. Shortley, J. Res. Natl. Bur.

Stand. 42, 183 (1949).G. O. Brink, J. Chem. Phys. . 46, 4531 (1967).E. Aygun, B. D, Zak, and H. A. Shugart, Phys. Bev.Lett. 31, 803 (1973).

G. M. Keiser, H. G. Robinson, and C. E. Johnson, Phys.Bev. Lett. 35, 1223 (1975).B. E. Zundell and V. W. Hughes, Phys. Lett. 59A, 381

(1976).B. H. Garstang, Rep. Prog. Phys. 40, 105 (1977).Tuncay Incesu, Ph. D. thesis (Middle East TechnicalUniversity, Ankara, Turkey) (unpublished) „alsoLaw-rence Berkeley Laboratory Report No. 3351, 1974 (un-published).

'3P. A. Vanden Bout, V. J. Ehlers, W. A. Nierenberg,and H. A. Shugart, '

Phys. Rev. 158, 1078 (1967).M. P. Klein and D. E. Phelps, Bev. Sci. Instrum. 38,1545 (1967).

~W. A. Anderson, Rev. Sci. Instrum. 32„241(1961).P. A. Vanden Bout, E. Aygun, V. J. Ehlers, T. Incesu,A. Saplakoglu, and H. A. Shugart, Phys. Bev. 165, 88(1968).

VK. D. Boklen, Z. Phys. 270, 187 (1974).8T. Incesu, A. Huq, and H. A. Shugart„ in Fourth Inter-national Conference on Atomic Physics, Heidelberg,

- Abstracts, 1974 (unpublished), p. 231; also Bull. Am.Phys. Soc. 19, 1177 (1974).

19B. A. Hegstrom (private communication).