VOLUME 11, N U M B E R 5 P H Y S I C A L R E V I E W L E T T E R S 1 SEPTEMBER 1963

our range of input powers. A variety of other materials transparent at

6943 A have also been examined for nonlinear loss at P 0 « 0 . 7 x l 0 6 watts. These are listed be­low in order of decreasing fractional absorption K = {P0-Pt)/P0: 0 . 6 ^ K ^ 0 . 4 , nitrobenzene, ben­zene, carbon disulfide; 0 . 3 ^ K ^ 0 . 1 , bromoben-zene, pyridine, polymethylmethacrylate, iodoben-zene, acetone, chlorobenzene, chloroform, ac-etophenone; 0.1 ^K, trichloroethylene, cyclo-hexane, methanol, toluene, carbon tetrachloride, fused quartz, water, isopentane, 2, 2, 4-trimethyl-pentane, nitromethane. Figure 1(b) shows a typi­cal power dependence for a material in the last group.

Not all the nonlinear absorbers show the rela­tion (jozF. Benzene, for example, shows negli­gible absorption at P0 = 0. 5 xlO6 watts and has relatively little loading effect when placed in a laser resonator. However, at higher incident powers absorption rises rapidly, and is accom­panied by intense Stokes and anti-Stokes Raman emission.

The experimental results appear to rule out in-homogeneity and Raman scattering as the source of ax loss in CS2. This loss, linear in F , is con­sistent with a process in which two photons are simultaneously absorbed and a CS2 molecule is excited to the 1B2 state.8 A theoretical descrip­tion of such processes has been given^6 and we may estimate ox for two-photon absorption from KleinmanV0 formula ox = r2c2f2/n2v0

2Av, where n is the refractive index, r is the classical elec­tron radius, and &v is the width of the real, ex­cited state at 2hv0. In the derivation of this ex­pression it is assumed that the absorption occurs through a single intermediate state coupled to both the initial and final states by an oscillator strength f. Using this formula with Av = 1 x 1014

The hyperfine structures of the line B a l , 5535 A (6s2 o - 6s6/> lPl)f of the isotopes 135 and 137 of barium are of particular interest because they enable the quadrupole moment coupling factor, B, to be calculated for the level 6s6p1P1. Approxi­mate values have been found by the present au­thors1 from an earlier measurement of the struc-

sec"1, i 0 = 4. 32xlO14 sec"1, a n d / = l , we obtain ax = 1. 5xl0~4 8 cm4 sec. The observed ax corre­sponds to an effective / value of 0.1 and is fully consistent with the two-photon absorption proc­ess . In order to corroborate the two-photon mechanism, it would be of interest to extend this experiment to wavelengths greater than

o

7800 A, since there is negligible absorption in CS2 at wavelengths longer than 3900 A.

The authors are indebted to Dr. K. Dransfeld, Dr. C. G. B. Garrett, Dr. D. Kleinman, Dr. A. Koningstein, Dr. D. McCumber, Dr. P . Pershan, and Dr. P . A. Wolff for interesting discussions, and to the Bell Laboratories Analytical Chemistry Department for optical filter transmission meas­urements.

*E. J . Woodbury and W. K. Ng, P r o c . I . R . E . 50_, 2367 (1962).

2G. Eckhardt , R. W. Hellwarth, F . J . McClung, S. E. Schwarz, D. Weiner , and E. J . Woodbury, Phys . Rev. Le t t e r s 9_t 455 (1962).

3R. W. Hellwarth, in Advances in Quantum Elec t ron ics , edited by J . Singer (Columbia Univers i ty P r e s s , New York, 1961), p . 334; F . J . McClung and R. W. Hellwarth, J . Appl. Phys . 33, 828 (1962).

4 This d i ame te r is in excellent agreement with the e x ­pected diffraction width of emiss ion from a single mode of the l a s e r r e sona to r and, t he re fo re , i s a lower l imit to the sca le of angular intensity var ia t ion .

5 J . Brandmii l ler and H. Mose r , Einfiihrung in die Ramanspektroskopie (Dr. Die t r ich Steinkopff Ver lag , Darms tad t , 1962).

6Weaker sca t t e r ing corresponding to ±^vm was also observed.

7R. W. Terhune , Bull. Am. Phys . Soc. £, 359 (1963); s ee also A. L. Schawlow, Sci . Am. 209, 34 , July (1963).

8A. D. Walsh, J . Chem. Soc. 2266 (1953). 9M. Gopper t -Mayer , Ann. Physik 9, 273 (1931).

10D. A. Kleinman, Phys . Rev. 125, 87 (1962).

ture of the line given by natural barium combined with measurements of the isotope shifts and the already known ratios, for the two isotopes, of the magnetic-moment splitting factors, A, and the quadrupole-moment coupling factors, B. But the values obtained were lacking in precision on ac­count of some uncertainty in the values of the

HYPERFINE STRUCTURES OF THE RESONANCE LINE OF THE ARC SPECTRA OF THE ISOTOPES 135 AND 137 OF BARIUM

D. A. Jackson and Duong Hong Tuan Labora to i re A. Cotton, Cent re National de la Recherche Scientifique, Bellevue, Seine et Oise , F r a n c e

(Received 15 Julv 1963)

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V O L U M E 11, N U M B E R 5 P H Y S I C A L R E V I E W L E T T E R S 1 SEPTEMBER 1963

isotope shifts; Razumovski and Chaika2 found (relat ive to 138) 5.7 mK for 137 and 7 .6 mK for 135, while the p resen t au thors found, respec t ive ly , 7.7 and 8.4 mK (1 mK = 0.001 cm" 1 ) .

It was therefore decided to m e a s u r e d i rec t ly the hyperfine s t r u c t u r e s of the l ines of these i s o ­topes , using enr iched i so topes ; this would give ent i re ly independent de terminat ions of the fac tors A and B, and would a l so give more accu ra t e va l ­ues of the isotope shif ts . On account of the very smal l separa t ions of the hyperf ine-s t ructure com­ponents, the i r resolut ion r e q u i r e s the use of an a tomic beam of the Jackson-Kuhn type with high coll imation. This would sca rce ly be possible with the conventional a tomic beam, ex te rna l to the in t e r f e romete r , on account of the re la t ively la rge amount of ba r ium which would be requ i red ; but the recent ly developed technique3 of operat ing the a tomic beam within a spher ica l F a b r y - P e r o t in t e r fe romete r reduces the amount of meta l r e ­quired to such an extent that sa t i s fac tory r e s u l t s can be obtained with the l imited amounts of en­r iched isotopes avai lable . The enriched isotopes (in the form of carbonates) were obtained from Oak Ridge National Labora tory ; they w e r e con­ver ted to the meta l l ic s ta te by an e lec t ro ly t ic p r o c e s s . Both the sample enr iched in 137 and that enr iched in 135 contained the isotope 138. Consequently, the s t r u c t u r e revealed by the a tom­ic beam a lso showed, in addition to the th ree components of the odd isotope concerned, the single line of the isotope 138; this made it pos s i ­ble to m e a s u r e the isotope shifts (assuming the normal intensity r a t ios of the hyperfine compo­nents) . The s t r u c t u r e s were observed with i n t e r ­f e r o m e t e r s of 6-cm and 10~cm rad ius of curva­tu r e , with a tomic beams of coll imation 24:1 and 35:1 . The ave rages of m o r e than 50 m e a s u r e ­ments for each in t e r f e romete r a r e

Ba137: 0(138); 2 . 1 , 8 .7 , 18.5 mK;

Ba135: 0(138); 3 . 5 , 10 .2 , 17.8 mK.

The probable e r r o r is ±0. 2 mK. Figure 1 is a reproduct ion of a sma l l pa r t of a

record ing of the absorpt ion produced by an a tom­ic beam of coll imation 35:1, of ba r ium enr iched in the isotope 135 (containing 67% of 135 and 13% of 138), within a spher ica l F a b r y - P e r o t i n t e r ­fe romete r of 10-cm rad ius of cu rva tu re . The s t r u c t u r e is repea ted in five o r d e r s .

F r o m the above m e a s u r e m e n t s it follows, a s ­suming the no rma l (inverted) intensity r a t i o s 3:2:1 (in o rde r of increas ing wave numbers ) , that

1 I 1 I I I y o 25 mK

FIG. 1. S t ruc ture of the line 5535 of Ba I, produced by an a tomic beam of ba r ium enriched in Ba135, showing a, the component due to Ba138, and A, B, and C the component due to Ba135 at 3 . 5 , 10, and 18 mK.

the isotope shifts for 137 and 135 a r e , r e s p e c ­tively, 7. 0 and 8 .1 mK; the e r r o r i s unlikely to exceed 0. 3 mK.

The values of the magne t ic -moment spli t t ing fac tors , A , and of the quadrupole-moment coupling fac to rs , By in the level 6s6p1P1, found from the above m e a s u r e m e n t s , and thei r r a t io s for the two iso topes , a r e

A ( 1 3 7 ) _ - 3 . 6 ^ 0 . 1 A(135) - 3 . 2 8 ± 0 . 1

B(137) = 1 . 9 4 ± 0 . 1 5(135) 1 . 1 9 ± 0 . 1

= 1 . 1 0 ± 0 . 0 3 ,

= 1 . 6 , ± 0 . 1 .

The r a t io s of these fac tors , der ived from nuclear resonance m e a s u r e m e n t s , a r e A(137)/A(135) = 1.118 (Hay4 and Walchli and Rowland5) and £(137)/£(135) = 1. 54 (Williams and McGrath 6) . The good ag reemen t between these values of the ra t ios and the p resen t a u t h o r s ' spec t roscopic values is of pa r t i cu la r in te res t in the case of the quadrupole momen t s , s ince Kali teevski , Fradkin, and Chaika,7 from the in te rva l s of th ree compo­nents of the l ines 4599.7 and 4573.9 A found £(137) /£(135) = 0 .7 , with a probable e r r o r of ± 0 . 5 .

*D. A. Jackson and Duong Hong Tuan, P r o c . Roy. Soc. (London) A274, 145 (1963).

2A. N. Razumovski and M. P . Chaika, Opt. Spectry. (USSR) 12(3), 188 (1962).

3D. A. Jackson, P r o c . Roy. Soc. (London) A263, 289 (1961).

4R. H. Hay, Phys . Rev. 6£, 75 (1941). 5H. E. Walchli and T . J . Rowland, Phys Rev. 102,

1334 (1956). 6R. M. Wil l iams and J . W. McGrath, Phys Rev. 127,

184 (1962). TN. I. Kal i teevski , E. E . Fradkin , and M. P . Chaika,

Zh. E k s p e r i m . i T e o r . F i z . 3!9, 954(1960) [ t rans la t ion: Soviet P h y s . - J E T P 12, 661 (I960)] .

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