JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Hyperfine Structure, Nuclear Moments, and Isotope Shifts of '97T1 and '98TI

SUMNER P. DAVIS, HERBERT KLEIMAN, DAVID GooRvITcH1, AND TIN AUNG*

Deparinzent of Physics, University of California, Berkeley, California 94720(Received 7 July 1966)

The hyperfine structure of 197T1 has been derived from an analysis of two lines in the optical spectrum ob-

served under high resolution. The magnetic dipole interaction constants are A (2Si) = 39443 mK and A ('Pi)=691 44 mK. The dipole moment of 157 Tl calculated from the ratio of hyperfine splittings is jup(19 7) = 1.5540.02 nm. The hyperfine structure of 198TI was not resolved. Isotope shifts measured with respect to 205T1were found to be A (197-205) = -23444 mK and A (198-205) = -229i4 mK in the 5350-A line and A (197-205) =-21044 mK and A (198-205) =-20944 mK in the 3776-A line.INDEX HEADINGS: Spectra; Thallium; Interferometer; Source.

THE hyperfine structure, nuclear moments, andTisotope shift of the thallium isotopes 199TI through201 T1 have been studied by several investigators.1 -8

The present paper reports the hyperfine structure andnuclear moment of '97T1 and the isotope shift of 1

97T1and '95TI as derived from an analysis of the 3776-A and5350-A spectral lines.

The hyperfine structure of the 2 S,, 2PI, and 2P1 levelsis determined by an analysis of the optical transitions

6S27S 2 1,> 6S

2 6p 2 P;(3776 A)and

6s 27s2 SX-4 6s26p2P 1 (5350 A).

The number of hyperfine sublevels is given by 2J+1for J<I or 2I+1 for I<J, where J is the total angularmomentum of the electrons and I is the nuclear spin.In the spectrum of 197Tl (I=- and u= 1.55 nm), eachlevel is split into two sublevels. In the spectrum of958Tl (1=2 and yu •0.002 nm),9 the hyperfine splittingis not resolved because of the small nuclear magneticmoment. Hence only a single unresolved component isexpected to appear, and only the isotope shift can bedetermined.

Since all the odd-even isotopes of thallium have thesame spin I= , and nearly the same nuclear magneticmoment, their hyperfine structure is very similar andis resolved only because of the isotope shift. The same istrue of the odd-odd isotopes of thallium, all of whichhave spin 2 and a very small value for the magneticmoment. The 3776-A line,

(6s27s 2S, -> 6s26p 2P3)

gives the hyperfine structure and isotope shift of the

* Present address: Physics Department, University of Rangoon,Rangoon, Burma.

I R. J. Hull and H. H. Stroke, J. Opt. Soc. Am. 51, 1203 (1961).2 C. J. Schuler, M. Qif tan, L. C. Bradley III, and H. H. Stroke,

J. Opt. Soc. Am. 52, 501 (1962).'M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310

(1949).4 H. Kopfermann and W. Walcher, Physik Z. 127, 465 (1944).5 H. Schiuler and H. Bruck, Physik Z. 55, 578 (1929).G J. Wulf, Physik Z. 69, 70 (1931).7 H. Schiler and I. E. Keyston, Physik Z. 70, 1 (1931).8 D. A. Jackson, Physik Z. 75, 233 (1932).Nuclear Data Sheets (Academic Press, New York, 1965).

2Si and 2P. levels. The 5350-A line,

(6s27s

2S. -> 6S

26p 2

pg),

gives the hyperfine structure and isotope shift of the2Sj level as perturbed by the unresolved 2

P3 splitting.Using the value of A (2 S.) from the 3776-A line, we canestimate the value of A (2PI).

I. EXPERIMENTAL

A. Sample Preparation

The radioisotopes 197T1 and '98TI were made at theBerkeley 88-in. cyclotron. The reactions used were'97Au (a,xn) reactions employing alpha energies ofbetween 50 and 75 MeV to produce the thalliumisotopes. The targets for the runs consisted of stackedgold foils. The gold was vacuum distilled, after whichthe gold was rolled into a foil of the appropriate thick-ness. During the rolling of the foil, it was annealed soas to prevent cracking resulting from brittleness. Thegold foil was then washed in boiling nitric acid for aboutten minutes to eliminate surface contaminants. Afterrinsing with distilled water, the foil was placed in thetarget holder and bombarded.

Altogether five cyclotron runs were made. The radio-isotopes produced and their relative abundances aswell as other pertinent information concerning each

TABLE I. Summary of cyclotron bombardmentsand spectrograms measured.

Total Numberirradi- Thallium interfero-ated isotopes produced grams

Target Energy current and relative measuredRun (Au foils) (MeV) psA .h abundances 53,50 37,76

A A

1 three 65 20 Top foil: 196,197,19aT1 5 53 mil Middle foil: 197196;

1198`Tl

Bottom foil: 198,15.1999TT

2 two 65 30 Top foil: '97,196TI5 mil Bottom foil:

197-.

19TI 3

3 one 75 30 196,197TI 11 mil

4 one 70 33 196 197TI 52.5 mil

5 one 50 40 197 19S8Tl 4 73 mil

1604

VOLUME 56, NUMBER 11 NOVEMBER 1966

HYPERFINE STRUCTURE OF 1"7TI AND 198Ti

cyclotron bombardment are presented in Table I.The isotopes produced and their relative abundanceswere obtained by observing the 2537-A ('P, ->'So)

line of the mercury spectrum, since the thallium isotopesdecay into mercury isotopes.

The light sources used in this investigation wereelectrodeless discharge tubes. The construction of suchsources has been throughly described in a previouspaper.1 The only difference in the preparation of thepresent light source was that tubes containing themultiple stacked gold foils were made simultaneouslyin a multiple quartz-tube manifold.

The finished discharge tubes were excited by using aRaytheon microwave generator at 95% power. It wasnecessary to heat the tubes with an oxygen-gas flamein order to keep the thallium in the discharge. As themercury in the discharge built up, owing to the decayof the thallium isotopes, the thallium discharge wasquenched. The molecular impurities did not overlapthe thallium lines at 5350 and 3776 A. The heatingrequired to keep the thallium in the discharge renderedthe tube useless after about four or five hours, by thebuildup of pressure due to molecular impurities.

B. Spectroscopic Instruments and Measurements

The two thallium lines were observed with a Fabry-Perot interferometer used in conjunction with a mirrormonochromator and variable bandpass filter.

The mirror monochromator consists of two 3-mfocal-length mirrors and a 13-cm Harrison plane grating.The grating has 300 grooves/mm, is blazed at 63°, andis used in a Czerny-Turner mounting. In conjunctionwith the mirror monochromator, a quartz-prism pre-disperser was used as a variable bandpass filter.11 Theband width of the filter is approximately 100 A.

Two sets of dielectric-coated Fabry-Perot plateswere used for the investigation of the thallium lines.'2

For the 3776-A line, a 7-layer Sb2,3 and cryolite(T= 10%) dielectric coating was used on the Fabry-Perot plates in conjunction with a 20-mm 6talon givinga free spectral range of 0.250 cm-l, a resolving limit of0.028 cmul, and a resolving power of 1.OX 106. The5350-A line was investigated with a 15-layer ZnS andcryolite (T= 3%) dielectric coating on the Fabry-Perot plates, in conjunction with a 15-mm 6talon,giving a free spectral range of 0.333 cm-', a resolvinglimit of 0.025 cm-', and a resolving power of 0.8X 106.

To identify the thallium decay products, the mercuryline at 2537 A was examined with the grating alone.The plates were measured on a semiautomatic com-parator, and the interferograms were reduced on anIBM 7094 computer, using a least squares procedure.

'0 H. Kicleiman and S. P. Davis, J. Opt. Soc. Am. 53, 822 (1963).1"J. Reader, L. C. Marquet, and S. P. Davis, Appl. Opt. 2,

963 (1963).12 S. P. Davis, Appl, Opt. 2, 727 (1963).

197A 1973

198 197C

FPG. 1. Interferogram of 3776 A.

Before and after each exposure of the radiothallium,an exposure was made to a natural thallium lamp. Thislamp, which was an air-cooled Osram Lamp run at 9.6A to avoid self-reversal, was used as a standard.

RESULTS

The magnetic-dipole interaction constants, the nuclearmoments, and the isotope shift can be deduced from astudy of the hyperfine structure. Since AW= AF, whereAW is the energy difference between the hyperfinestructure levels of total angular momentum F and F-1,and A is the magnetic-dipole interaction constant, thevalues of A can be found from the measurement of thesplittings of the hyperfine components. The nuclearmoments are found from the relationship

A =guIH(0)/IJ,

where gq is the magnetic-dipole moment of the nucleusof spin I and H (0) is the average magnetic field atthe nucleus due to the orbital electronic motion of thetotal electronic angular momentum J. Since

IA/I= H (O)/J

depends only upon the electronic structure of theelement, it is a constant within an isotopic sequence,to within the accuracy of optical spectroscopicmeasurements.

The magnetic moment gx and the A factors of 205T1have been measured using an atomic-beam light source.2

The magnetic moment of '97TI was obtained from therelationship

.I (197 ) = EA (197)/A (205]yJ I(205)

since 1= 2 for both isotopes.The isotope shift between different isotopes is found

from the measurement of the displacements between thecenters of gravity of the hyperfine structure of thedifferent isotopes.

The measured hyperfine structures and isotope shiftsof '97T1 and "51TI were derived from 21 interferograms of3776 A and 9 interferograms of 5350 A. Typical inter-ferograms are shown in Figs. 1 and 2. In Table II thehyperfine-structure splittings and nuclear moment of197T1 are given. In Table III the isotope shifts for '97TI

U S Z-

197A

198 \1978

FIG. 2. Intedrfrogram i 15350 A.

1605November 1966

DAVIS, KLEIMAN, GOORVITCH, AND AUNG

TABLE II. Hyperfine-structure splittings andnuclear moment of "2 T1.

A (2S,2) A ('PI2) A (-P32 2) pr (nm)Line (mK) (mK) (MK) From From

1 (2S1,2) A ('Pte2)

3776 A 39443 691±4 ... 1.544±0.02 1.56±40.025350 A ... ... 9.6±4 *-4Summary 394±43 691±4 9.6±t4 1.55±0.02

and 198TI are given relative to 2051T1. The measuredhyperfine structures of the 3776-A line and the 5350-Aline are shown in Figs. 3 and 4.

The typical exposure time of the radioactive thalliumlamp in runs one through four was ten minutes. Beforeand after each exposure of the lamp, an exposure of thestandard was taken. Although the fractional-ordernumber of the standard sometimes changed during theexposure, a linear approximation was used to get thefractional-order number used in placing the isotopeshifts of '97T1 and 198T1 relative to 205T1. This proceduregave an average error of ±4i mK. In run five, the ex-posure time of the radiothallium was only one minute.Hence only one exposure was made of the standardand the results derived from run five were given twicethe weight as the results from runs one through four.The error in placing the centers of gravity of 17121 and'TM relative to 205I1 is ±4 mnK.

The error given for the A factors and magneticmoment of 197T1 are root mean square errors. The rmserrors are based upon an analysis of nine interferograms

TABLE III. Isotope-shift data for 197Tl and ';TI.

Line A(197-205) A(198-205)

3776 A -2104±4 mK -209±4 mK5350 A -234±4 mK -22944 mK

in 5350 A and sixteen interferograms in 3776 A. Eachinterferogram was measured three times, giving 27measurements of the 5350-A and 48 measurements ofthe 3776-A line.

In addition, one component of I991M was measured inthe green line 5350 A. The value of the 199T1 relative tothe center of gravity of 201 T1 was measured to be 85+4mK (see Fig. 4). Hull and Stroke measured this '91Tlcomponent to be 8344 mIl relative to the center ofgravity of I5Tt.1 The agreement is well within experi-mental error.

From the measured values of the hyperfine-structuresplitting of the 3776 A of 197T1,

A QSj) = 394±43 mnKand

The ratioA (2 P>)=691±t4 mK.

A QSO)/A QPT) = 0.570±t0.006

is found to agree with the value

A (28)/A PC) = 0.577

found in natural thallium by other investigators usingatomic beam techniques.13-'5

T1197

6s2

6s 6 p

198197B

- 284- 209

T1190F

0

TI 19 7

F

0

6s

6s 6p P

TI 19 8 TI 199

t398l mK

F

-oI

A B

0

197A

I- 519

C. g.

205

W0

1 97C

407

v (m K)FIG. 3. Measured hyperfine structure of 3776 A.

198 197B 199B

-229 - 137 - 85

C.g.205

0

v (miK)

FIG. 4. Measured hyperfine structure of 5350 A.

13 A. Lurio and A. G. Prodell, Phys. Rev. 101, 79 (1956).14 A. Berman, Phys. Rev. 86, 1005 (1952).15 A. Odintsov, Opt. Spectry 9, 75 (1960).

197A

- 678

1606 Vol. 56

1

Fl

HYPERFINE STRUCTURE OF 197 TI AND 198TI

From the measured values of the hyperfine splittingof the 5350-A line of '97T1,

A (2S-)-WA (2P@) = 3781:3 mK.Since

A (2SI) = 3944:3 mK

as derived from the 3776-A line,

A (2P2) = 9.61:4 mK.The ratio

A (2S-)/A (2 P3)=41:417

was found to agree with the value"

A (2S,)/A (2PA) = 46.4

Here we have used the theoretical intensity pattern ofelectric-dipole radiation to deduce the splitting factorof the 2P3 term.

1607

The measured values of the magnetic moment are tobe compared with the Schmidt limit value of 2.79 nm.As Hull and Strokel pointed out, configuration inter-actions can improve the agreement between theory andexperiment. They considered admixtures of the protonconfigurations

(lh11/2 )12 si

and the neutron configuration

(3py) (1i13/2)'1

(N is the number of neutrons for the isotope under con-sideration), and found magnetic moments of approxi-mately 1.34 and 1.60 nm, respectively, for the otherodd-mass thallium isotopes.

The isotope shifts of '97T1 and 198T1 relative to 205T1are given in Table III. It should be noted that thetrend towards increased staggering with lower neutronnumber is continued.

November 1966