Application of the atomic Faraday eftect to the trace determination of elements (Cd, Ag and Cu)—effect of the hyperfine structure on the Zeeman splitting and line-crossing

Spearochimica Acta.Vol. 34B.pp. 389to 413 Pergamon PrcgsLtd.,1979,PrintedIn GreatBritain

Application of the atomic Faraday effect to the trace determination of elements (Cd, Ag and Cu)-effect of the hyperline structure on the Zeeman splitting and line-crossing KUNIWKI KITAGAWA*

and TOSHIAKI SHIGEYASU

Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan

and TSUGIO TAKEUCHI ‘r School of Materials Science,

Toyohashi University of Technology, Toyohashi, Aichi, Japan

l-l

Hibarigaoka,

Tenpaku-cho,

(Received I August 1979)

Abstrsd-Atomic Faraday spectroscopy or atomic magneto-optical rotation spectroscopy (AMORS) combined with the electrothermal atomization was applied to the trace determination of elements (Cd, Ag and Cu). A simple tlieoretical treatment was developed for the dependence of the radiation transmitted through the Faraday configuration on the magnetic field strength. The effect of the hyperfine structure on the Zeeman splitting was related to the line-crossing between the Zeeman components and the dependence of the transmitted intensity on the magnetic field strength. The calibration graphs demonstrated a square-law dependence. The spectroscopic signal increased non-rectilinearly as the source radiance increased. Detection limits of 5 x 10-13, 2 x lo-” and 3 x 10-l’ g were obtained for Cd, Ag and Cu, respectively.

INTRODUCTION IN PREVIOUS papers

[l-3], the authors reported the application of the Faraday effect to the trace determination of cadmium by atomic spectroscopy (atomic Faraday spectroscopy or atomic magneto-optical rotation spectroscopy, AMORS) with an electrothermal atomizer. Aspects of the history and principle of the atomic Faraday effect were described and, the construction and operation of an apparatus reported. A magnetic field was applied to a graphite tube atomizer in the direction of light propagation. The atomizer was located between two plane-polarizing prisms (the polarizer and analyzer). Owing to the double refraction of circularly polarized radiation and coherency on forward resonance scattering, the plane of polarization rotated when passed through magnetized atoms. This method was found to be useful for the analysis of cadmium with the advantage that interference effect of light scattered by non-atomic species produced on atomization could be overcome. CHURCH et al. [4] STEPHENS et al. [5] applied the present method to the detection of mercury. ITO ef al. [6] applied the other magneto-optical phenomenon, i.e. the Voigt effect (double refraction of planepolarized light), to the determination of cadmium [6]. In the present study, the authors wish to report the application of the .atomic Faraday effect to the trace determination of silver and copper in addition to cadmium. * To whom all correspondence should be sent. ‘! Professor Tsugio Takeuchi died suddenly soon after the presentation of his paper on the atomic Faraday effect during the 21s~ Coil. Spectr. Int. and 8th hr. Conf, Atomic Specrr., Cambridge 1979. [l] K. KITAGAWA, T. SHIGEYASU,T. KOYAMAand T. TAKEUCHI,Abstracts 26th ZUPAC Congress, Tokyo 1977, Vol. II/III, 861. [2] K. KITAGAWA, T. SHIGEYAW and T. TAKEUCHI,Analysr 103, 1021 (1978). [3] K. KITAGAWA, T. KOYAMA and T. TAKEUCHI,Analyst 104,822 (1979). [4] D. A. CHURCH and T. HADEISHI, Appl. Phys. Lett. 24, 185 (1974). [5] R. STEPHENS, Anal. Chim. Acta 98, 291 (1978). [6] M. ITO, S. MURAYAMA, K. KAYAMA and M. YAMAMOTO, Spectrochim. Acta 32B, 347 (1977). 389

390

Kumm

KITAGAWA,TOSHIAKISHIGEYASUand TSUGIOTAKEUCHI

Principally, we shall discuss a theoretical aspect of the dependence of the intensity of radiation transmitted through the Faraday configuration on the strength of the applied magnetic field. By estimating the effect of the hyperfine structure involved on the Zeeman splitting, the line-crossings between the Zeeman components, a*-components are predicted. This will be compared with the experimental results. BASIC FORMULAS

The intensity of radiation transmitted by the following equation: l(H) =

IS

through the Faraday configuration

p(k) [sin @(k, H)12e-0(k~H’L dk.

[7] is given

(I)

here, p(k) is the spectral density of the source radiation, @(k, iYJ the rotational angle of the plane of polarization, a(k, H) the absorption coefficient, L the length of atomic vapor, k the angular frequency, s the bandpass width of the monochromator and H the magnetic field. The rotational angle @(k, H) is proportional to the difference in refractive index or dispersion function between the circularly polarized light with the anti-clockwise and clockwise motions. Detail aspects of this phenomenon have been discussed in the previous papers. This is expressed by the following equations: B(k,H)=(k=;~2)F(k,H)=$n_-n+), F(k, H) = z

k - k, - s1 + iI’/2

(2) k-ko-s2+iI’/2

(3) A A where N is the atomic density, P the matrix element for transition, c the light velocity, h = h/2?rh the Planck constant, F(k, IT) the Faraday function, k,, the angular frequency of the peak of the absorption line under zero field, 2Am the line width at half-maximum, r the reciprocal mean lifetime of the level, s1 the Zeeman shift of the a--component, s2 that of a+-component and N the atomic density. If the number of atoms NL is small enough, we can reduce equation (1) to the following equation by making the approximation sin a=@ and e-a’(k’H)L= 1, we obtain the following equations :

I p’(kF&, H)‘dk,

I(H) cc(NLP2)2&Js

(4)

where IO= j, p(k) dk the source intensity and p’(k) = p(k)/&, the profile function of the source radiation. Consequently, the transmitted intensity is expected to be proportional to the square of the number of atoms in the light beam NL and the source intensity if the magnetic field strength and source line profile are defined. In the practical experimental case, Lorentz broadening can be applied to the plasma dispersion function z. The Lorentzian form of the plasma dispersion function is given by the following expression: Z

k-ko-s,+iF/2

A

-A > =k-k,-s,+X/2’

(5)

Therefore, k-k,-sl k-k,-s, (k-k,-s2)2+~2/4-(k-ko-sl)2+r2/4

1 1 (k-k,,-s1)2+I’2/4-(k-kO-s2)2+I’2/4 [7] A. CORNEY,B. P. KIBBLEand G. W. SERIES,Pm. Roy. Sot.

A248,701 (1966).

(6)

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

391

If the (T- and u+-components have the same frequency, sl= s2 and F(k, H)=O. Therefore, the transmitted intensity is reduced to zero. As stated in the previous papers, qualitatively saying, the a*-components with the contrary circular motions cancel the rotatory power. This is called ‘line-crossing’. The displacements s, and s2 can be estimated by calculation of the Zeeman pattern. We shall now consider the atomic energy levels which give rise to the Zeeman pattern. In the case of the nuclear spin I = 0, the change in the atomic energy is expressed by the following equation: AE = M,&peH(erg)

or

M,g,L=H(cm-‘)

(7)

where MJ is the magnetic quantum number (-J, -J+ 1,. . . .7- 1, J), & the Land6 factor, CL,the Bohr magneton, L, the Lorentz unit and H the magnetic field strength in Gauss. The Land6 factor is defined by the following expression [8]: &=

J(J+l)+S(S+l)-L(L+l) 25(5+ 1)

where J, S and L are the quantum numbers of total angular, spin and orbital angular momenta, respectively. The displacements s1 and s2 are given by the selection rule: fis, = (M&U&,”- MJ&.J,~),I)CLe~(~z) (AM, = M,, - MJ,, = - 1) hs, = the same term as the upper (AM, = + l),

(9) (10)

where subscripts u and 1 denote the upper and lower levels, respectively. For I# 0, there arises the hyperfine structure (hfs) with the energy change expressed by AE,,f,=~A’{F(F+l)-I(I+l)-J(J+l)}

and

F=IJ-I(,IJ-I(+l...(J+II-l,(J+I( (11)

where A’ is the coupling constant for coupling between J and I momenta and F the resultant momentum. In very weak fields, these hfs levels separately split into 2F+ 1 sublevels with the magnetic quantum number MF(MF = - F, - F+ 1, . . . , F - 1, F). The energy change in atomic level influenced by the very weak field is given by the following equation : AE’= MF&peH + AE,+

(12)

where g, is the Land6 factor for hfs, expressed by F(F+l)+J(J+ gF = &

1)

2F(F + 1)

pNF(F+ +gr--

CLe

l)+I(I+ l)-J(J+ 2J(J + 1)

1) (13)

where &+ is fhe nuclear magneton and its magnitude is ca. -c~,/1838; the second term is usually ignored. The selection rule for this case is AMF = -1, 0 and +l and gives the transition K, r and cr+. As the magnetic field strength increases, the coupling strength between .7 and 1 momenta decreases. In the extreme case where the coupling is completely broken down, each of J and I momenta is quantized separately. For this case, the change in atomic energy is expressed as follows; AE = (M,g,cc, + Mrg#N)H+

A’M,M,

(14)

where MI is the magnetic quantum number of nucleus (MI = -I, -I+ 1. . . I- 1, I). Again, the second term in the parentheses can be omitted because of its small magnitude. The selection rule for this case is given by AM,=-l(a-),

O(V)

and

This extreme case is called the Back-Goudsmit [8] H.

E. WHITE,

+l(a+)

with

M,=O.

effect.

Introduction to Atomic Spectra. McGraw-Hill New York (1934).

(15)

K~NMJKI KITAGAWA,TOSHLUI SHIGEYASUand TSUGIOTAKEUCHI

392

The present problem is an intermediate situation between the above two cases, i.e. .I and I momenta couple moderately. We treated the problem with the variation theorem which is frequently employed in the field of the magnetic resonance [9]. The required parturbation Hamiltonian is given by X=~,~L,H.J+~~CL~H.I+UI.J+B’(I.J-~~,~,)

(16)

where a is the constant of the Fermi interaction between .I and I momenta, B’ the constant of the dipole-dipole interaction between them and I, and J, are the projection of I and J momenta on the axis of the lines of the magnetic field, respectively. The constant A’ used in equation (11) includes both of the interactions. The first and second terms represent the interactions between the magnetic field and the momenta .I and I, respectively. In order to estimate the perturbation energy, the secular determinant should be defined. The diagonal elements are given by

+ (a + B’)(JM,IM,I I *J ~JM,IM,)- 3B’(JM,IM,I I& (JM,IMr). = (g+,M, + grpNMI)H + (a + B’)M,M, - 3B’M,M,

This corresponds to the atomic level energy for the Back-Goudsmit effect. The non-diagonal elements which are not zero are those adjacent to the diagonal. They are given by the following equations: (JM$&1 X /JMJ- 1iMr + 1) = grc~,tJMJIMrj H *J lJMJ- 1IMr + 1)

+g,/.&M,LM,(H.I

IJMJ-lIM,+l)+(a+B’)(JM,IM,II. -3B’(JM,IM,lI,J,

JIJM,-lIMr+l) ]JM,-liM,+l)

(18)

and (JM,IM

X lJMJ+ lIM, - 1) = ~~P~L,(JMJIMI] He J (.tA41+lIM, - 1)

+~~~(JM,IM,JH.I(JM,+lIM,-l)+(a+B’)(JM~~~II.JIJM,+lIM,-l) - ~B’(JM,IM,I I,J, [JM~- HIM, - 1).

(19)

The first and second terms in both equations are zero because (JMJ ) JMJ- 1) =O, (.TMJI JM,+ l)=O, (LM, I IM,+ 1) =0 and @MI IIM,--l)=O. The last terms are also zero for the same reason. The integral in the third term of equation (18) can be expressed as (JM,IM,I I *J] JMJ- 1IMr + 1) = (JM,IM,I I,J, + I,J, + I,Jz1JMJ- lIM,+ 1)

= (JM~[J, IJMJ- l)(IMrI I, 11Mr+ i)+(JM,I Using the following equations,

J, IJM~- lXIM,I I, IJM~- 1).

CXO

well-known in quantum mechanics [lo]:

K, IKM,)=KJ(K+M,)(K-M,+~)~KM,-~)+J(K-M,)(K+M,+~)IKM,+~)} (21)

[9] M. NERSOHNand J. C. BAIRD, Infroduction to Electron Paramagnetic Resonance. (1966). [lo] H. A. BETHE,Intermediate Quantum Mechanics. Benjamin, New York (1964).

Benjamin, New York

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and 01)

393

we obtain the following equations: J, IJM, - 1) = &d(J + MJ - l)(J-

MJ + 2) ]JMj - 2) + J(J - MI + l)(J+ MJ) IJMJ)}

(23)

I, (IM,+l)=~(J(I+M,+1)(1-M,)IIM,)+~(I-M,-1)(1+M,+2)I~M,+2)}

(24)

J, ~JM,-l)=~~(J+M,-l)(J-M,+2)~JM,-2)-~(~-M,+l)(J+M,)~JM,)}

(25)

I,, (IM,+l)=~~(I+M,+1)(1-M,)I~M~)-J(I-M,-1)(1+M,+2)IIM,+2)}

(26)

Therefore,

equation (18 and 19) are reduced to

(JM,IMrI %‘(rM,-lIMr+l)=(+%(J+M,)(J-MJ+l)(I-Mr)(r++l)

(27)

and (JMJMrI X’IJM,+lIMl-l)=@$%(J-M,)(J+M,+l)(I+Mr)(I-M,+l),

(28)

respectively. The energy values of 2F+ 1 sublevels can be estimated by subtracting AE from the diagonal elements and solving the secular equation. Table 1 shows the secular determinant. The blank elements are zero. The determinant is decomposed into subdeterminants of 1 x 1, 2 x 2, 3 x 3 . . .3 X 3, 2 X 2 and 1 X 1 rows and columns. According to the selection rule, AMF = AM, +AM, = f l(a*) and O(r) with AM, = 0, the frequency shifts of the U+ and a--components s2 and s1 are determined. If there arise multiple components, their shifts are defined to be sZ,r, s*,~, . . . sZ,” and s~,~, (6) should be replaced by the following equation: Sl,Z,* * . Sl,m Then, equation k- k,-s,,j j-1 (k-ko-S2,j)2+r2/4

-$l(k-:~~;)?r”/4J 0 , 1 -f l. k=l (k-ko-sl,k)‘+r2/4 j=1 (k-ko-S,j)2+r2/4

(29)

In this case, the transmitted intensity is expected to decrease partially in a given magnetic field while the region of magnetic field strength giving rise to a reduction in the transmitted intensity is extended. In addition, line-broadening prevents the transmitted intensity from becoming zero. This will be shown for copper.

Mp=J+I-3

MF=+J-I

M,+=2-J-I

Table 1. Secular determinant for the Zeeman splitting: (.lM,IlUr and 3MJ17Hr)are abbreviated as (M,Mr and M,M,), respectively.

394

KUNMJ~ KITAGAWA, T~~HIAK~SHIGEYAW and TSUGIO TAKELJCHI

Calculation of the coupling constants a and B’

The coupling constants related to the hyperfme structure a and B’ are estimated by a theoretical calculation with the hydrogen-like orbital and compared to values estimated by an experimental observation of the hyperfine structure by a Fabry-Perot interferometer. These values are examined also in the discussion of the line-crossing experiments.* EXPERIMENTAL The experimental arrangement is shown in Fig. 1. This is similar to that constructed for the previous study [3]. The power supply for the electrothermal atomizer was modified to give a stabilized atomization temperature by on-off control. The black-body radiation from the electrothermal atomizer was focussed on a photoconductive cell located in the lateral direction. A PbS cell was used as the photoconductive cell for controlling the temperature up to about 1100°C and a CdS cell beyond that temperature. The resulting photocurrent was converted to a voltage and the voltage was compared with a preset reference voltage. Two SCR’s turned on and off the power according to the comparator signal. The modification achieved a rapid rise in temperature of the electrothermal atomizer, by operating at a higher voltage setting of the transformer. The polarizer was rotated at 3600rev min- i by a synchronous motor. The photocurrent due to the blackbody radiation was off-set by the synchronized box-car electronic circuit [3]. In order to make sure that the electronic circuit was not saturated, the black-body radiation from the electrothermal atomizer was focussed in a ring form and removed by locating an iris diaphragm just in front of the entrance slit of the monochromator. The aperture diameter of the iris was 1.5 mm. The bandpass of the monochromator was 2.0 nm. Hollow cathode lamps of Cd(HTV), Ag(HTV) and Cu(Jarrell-Ash) and an electrodeless discharge lamp of Cd(EMI) were used as the light sources. The former were supplied with stabilized d.c. currents of 8-20 mA, and the latter with stabilized microwave powers of Xl-120 W. More stable and greater energy output was obtained from the electrodeless discharge lamp in the longitudinal direction. Although selfreversal might occur in that direction, radiation of narrow line width desirable in atomic absorption spectrometry is not required for atomic Faraday spectroscopy. The graphite tube atomizer, of the same dimensions as that used in the previous study, was located between the pole pieces of an electromagnet. All the other components, the electromagnet, the polarizing prisms, the monochromator, the photqmutiplier tube etc., are the same as those utilized in the previous experiment. The purge gas, argon was introduced into the graphite tube atomizer and the enclosing chamber at flow rates of 50 ml min-r and 1.5 1mm-i, respectively. Five r.~lof sample solution was dispensed into the graphite tube atomizer by means of a micropipette (Muromachi Kagaku), dried at 120°C for a minute and atomized at temperatures of 1400-1800 “C. The atomization temperature was measured by an optical pyrometer (Tokyo Hokushin Denki). The magnetic field strength was calibrated by a gaussmeter (Yokokawa Denki). Special grade reagents were used for preparation of standard solutions throughout this experiment. A Fhbry-Perot interferometer (Mizojiri Kogaku Co.) was used for the determination of the hfs coupling constant a. This was operated by pressure scanning and had a space of 0.3045 cm between etalon plates. The radiation from the light source was dispersed by a grating monochromator (Techtron). The monochromatic radiation emerging from the exit slit was directed into the interferometer; entrance and exit slits of 0.3 mm width were employed. A pin hole of 0.5 mm diameter was utilized for separating the resulting fringes. Behind the pin hole, a photomultiplier tube (R 106 UH HTV) was located as the detector. After amplification by a

Fig. 1. Schematic diagram of the experimental arrangement: A=light source, B =rotating polarizer, C = lens, D = electrothermal atomizer, E = electromagnet, F = photoconductive detector, G = power controller for the electrothermal atomizer, H = transformer, I = analyzer and lens, J = iris diaphragm, K = monochromator, L = photomultiplier tube, M = electronic circuit, N = strip chart recorder and 0 = insulator.

* Details of the theoretical calculation can be obtained by writing to the first author of this paper.

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

395

d.c. amplifier (Sanei Sokki Co.), the resulting photocurrent was displayed on an x-y strip chart recorder (Watanabe Sokki Co.). The scanning pressure was converted to a voltage by a transmitter (Tokokawa Denki Co.). The voltage drove the abscissa on the x-y recorder. RESULTS

AND DISCUSSION

The hyperfine coupling constants a and B’ were calculated by a computer according to the equations described above. With these values, the Zeeman levels of atoms in the intermediate coupling state, so-called Breit-Rabbi levels were calculated and the transition allowed by the selection rule or the Zeeman splitting pattern was plotted on a typewriter connected with the computer. The theoretical pattern is compared with the experimental results of the dependence of the transmitted intensity on the magnetic field strength. The dependence of the transmitted intensity on the source radiance is also examined as well as in the previous case of cadmium. Dependence

of the transmitted intensity on the magnetic field strength

Copper. A resonance line Cu I 324.75 rmr was chosen as the analytical line. Figure 2 shows the dependence of the transmitted intensity on the magnetic field strength. In the zero field, the a*-components superimpose each other. This is so-called zero field line crossing, in which no energy can pass through the Faraday configuration. As the magnetic field becomes stronger, they are separated. This causes the increasing rotatory power, and the source radiation is allowed to pass through the optical system. However, too strong field causes such a large displacement of the a-components that the source line can not superimpose upon them. This reduces the region of frequency in which the source radiation interacts with the a-components. For this reason, the transmitted intensity decreases as the magnetic field increases beyond the strength about 8 kG. This corresponds to a decrease in the product p(k) Isin @(k, H))* in equation (1). We note that there is a sharp minimum on the curve. This is expected to be assignable to the line-crossing. The natural abundance of copper is 69.1% of 63Cu and 30.9% of 65Cu. Both isotopes have a nuclear spin momentum of I= 3/2. In the zero field, the coupling F = I + j gives rise to hfs with FII- jl . . . II+ j\. For the upper level of the analytical line *P3p, sublevels *P 3 312, $P3/2, :P3n and gP3,2 arise. In very weak fields, each of the hfs sublevels splits into 2F+ 1 magnetic sublevels with MF = -F, l-F,... , F- 1, F. For the upper level, 7 + 5 + 3 +.l magnetic sublevels are totally produced. The lower level 2S1,2 changes into &,2 and :S1,2 which give 5+ 3 = 8 magnetic sublevels. In weak fields (so-called compared with the strong field to which the Paschen-Back effect applies.), the coupling between I and j is perfectly released

CUI 324.75 nm

0

Fig. 2. Dependence

5 10 15 20 Magnetic field strength(kG)

of the transmitted

intensity on the magnetic field strength 324.75 nm.

for Cu I

396

KUHNUKI

KITAGAWA,

TOSHIAKI SHIGEYAXJ and TSUGIO TAKEUCXI

Table 2. Two extreme cases of the Zeeman splitting for Cu I 324.75 nm

No

II i_

field

Very weak field Leeman effect)

Weak field (Back-Goudsmit effect)

( hfs

TeI-lIl

L

M.

--AL3

*P 3 3/*

I

3/2

3/* l/2

1

3/2

-l/2

0

3/2

-3/2

-1

I/*

3/*

-2

l/2

I/*

-3

l/2

-l/2

l/2

-1

-1/z

-1/z

-2

-l/2

-3/Z

1

-3/2

3/2

*/3

-1

*/3

0

2

I 1

25:

l/2

0

2 l/2

-2

1

-l/2

0

-1

-312

I/*

-3/2

-l/2

-3/2

-3/2

312

l/2

3/*

-l/2

l/2

3/* -l/2

l/2 -l/2

-1

33 1 1/z

3/2

-l/2

*/3

0

2P

-3/2

l/2 -l/2

0

o 3/2

MJ

2

1

2P l 3/*

L

3/z

2 *P 2 312

Fl

-l/2

-3/2

l/2 -l/2

-3/*

i

112

-l/2

1

Table 3. Hyperfine constants a and B’ Isotope

I

Ten"

Fermi

constant

-I

(-1 ) CXlC.

obr

a

u-i> cunstjlrtt U' -1 (CI1 I

CalC.

obe.

-1.6:10 -6 (nlj="1/2) 1.6~10 -6

_

(lnj=+3/2f

107 109

*fi 4

l/2

4P 2 PI/2

0

1,925l/2

0.0713

5&'3,2

"

l/2

5s 2 51/z

lllCd

0

112

5S5PLYl

0.0068

0

-3.2x10-4

"3,d

(mr=Of 1.6~10 -4 (Inca) 5s 21 so

* Observed in this experiment.

0

0

-0.0447

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

397

.______,____________,___L--________________________

5

ii

Fig. 3. Change in energy AE for the upper level of copper 4p2Psn vs the magnetic field strength H, calculated using the calculated a- and B’-values.

(the Back-Goudsmit effect), as referred to in the preceding theory. In this case, the level energy is determined by the combination of MI and mi. However, the total number of the resulting magnetic sublevels does not alter, keeping the relation MF = MI + mj. In Table 2, they are listed for the two extreme cases. The hfs coupling constants a and B’ are listed in Table 3. Figures 3 and 4 show the theoretical Breit-Rabbi levels of the upper and lower levels. Since B’ for the upper level is very small, the pattern is almost identical to that for the case of no coupling or I = 0. Figure 5 illustrates the transition between them. This predicts that the line-crossings between the a-components occur in a region of magnetic field of 0.8-1.4 kG. On the other hand, the experimental result indicates that line-crossings arise in a region of the magnetic field of 3-4.5 kG. This discrepancy is probably either due to an erroneous value of the coupling constant a or due to an error in estimating the effective nuclear charge Z on the electron or in employing the hydrogenlike orbital. Figures 6-8 show the Zeeman patterns calculated by varying the value of the coupling constant a. Figure 9 shows the hfs obtained by the Fabry-Perot intereferometer for the analytical line Cu I 324.75 nm. The experimental value of the coupling constant Q estimated from the interferogram is listed in Table 3 together with those reported by the other investigators [ 131. Figure 9 shows the hfs obtained by the Fabry-Perot interferometer for the analytical line Cu I 324.75 nm. The experimental value of the coupling constant a estimated The transition indicates that the line-crossings occur in a region of the magnetic field of 2-4.2 kG. Thus, if an experimentally determined a-value is employed for calculations of the variation theorem, the dependence of the transmitted intensity can be predicted with a good agreement with the experimental result, even for the case in which there arise hfs and the intermediate coupling between I and I momenta. From this result, it is [ll] S. GOULSMIT,Phys. Reu. 43, 636 (1933). [12] L. C. ROES, Phys. Reu. 37, 532 (1931). [13] R. RITSCHL,Z. Physik 79, 1 (1932).

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I I I

Application of the atomic Faraday effect to the trace determination

.p

a= 0

,Ei

77ij

of elements (Cd, Ag and Cu)

*+**

ctil(*slRl

$:-l.6x10-6~2P I 3.z

*+**

.+

+*+

++++ *,*

l*+* *++*

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399

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*++**+ **+ +**+*+ ** 4 ++::+*** j*::++ O~?___________________________-_______"~_"~~~~~~~~_~

l

‘ .‘ i '::.. '.‘I'..

. . . '.... . .*.. .... .. .* . .*. '. *.. '.. .... .... . . .. . . ".. +. .. .. .. .. ... .. I.

. ..

..

..

-li_______________--_______L-1111_____~~~~~~”~~~~~~~~__ 0

5

H(kGI

i

d

1

Figs. 6-8. Variation in the Zeeman splitting pattern with the a-value for the lower level.

marked that the effective nuclear charge for the s-electron of copper might be larger (2 = 4.2) than that expected (Z = 3.1) owing to its penetrating character. The B’constant cannot be experimentally obtained because of its small value and the broadening of the absorption lines. However, if the experiment of the atomic Faraday spectroscopy be carried out with an atomizer evacuated, the constant may be determined. It is likely that the effective nuclear charge for the non-penetrating p-electron is

______~_____~~~~_______~“~~________~~___~__~__~_

HotG)

Fig. 7.

1

400

KUNIYUKI KITAGAWA, TOWIAKI SHIGEYASUand TSUGIO TAKEUCHI ____________________“~~~~~~~~~~~~~~~_~~____”_~+“” ****

l +/++*+*+ ++ *+f ++.** +ff

cm4(*%p)

a=03

*f

+

+*

~=-l.6x166 ( *P3E)

f +*+* *.+ +*f +*+l++ l*+** *** + l ++ **+* +*+* +*ff +*++ *++++**I** l+++ff l

l

..+*

++::+*++* ++~~:~~~,,+++*“’ *t*++** : :

*+**+++

++*

+*f

++

l+** *++ +*** t. l*+*+ l++ +*I++* .:.. *+ ++::++ *+++* .:.:.. +++* ++:+* .::.. l++** +*+* ..*:.. *.*. *+ +:+ +*ff ++*+ . . .‘;*. ;t? .*+ +++ l*+*++ *+*+* +**

l

.+:*--.*:+ l:+..*+++

+t*.

+*++++

“__________~__+~~-~~~~~~~+.~~~~~.~________________ ++++t::,** . ..*. . . . . . . . . +::i::+* l++* ***. *. ... .... .++t ++ff +* *. +*+* .. .... .... +t+++* ‘. . . . . .::+*

‘1.

* . . . . *

‘..

.a...

.

.

.

‘:“”

.

.

.

.::::i..

.

.

.

.

.

.

. . . .

.

. . .

. . . ‘..‘..“:.:** .:.. . . .

.

*..

. .

* ’ . . .

*.. .*..

. .

*.

......

..* . . . .:.:.. . . . . ..* ..* *.

. . .

. .

. . . *...

“::.. *..

*.*.

. . .. . . . .

‘..

**. “..J:. *. ... *. *.. . . . . . . *. . *.. *.. ”

. .

. .

.*

-..* -. ‘..

. .

________________________j____________________”~~~ H(kO

Fig. 8.

di@erent from that for the penetrating s-electron. The behaviour of the sublevel for the lower state is very interesting in that the region in which deep coupling between I and j occurs is only up to a field of about 0.8 kG and that the almost extreme situation of the Back-Goudsmit effect arises near a field of 10 kG. The results of other studies of the line-crossing [14], in which the ratio of the atomic absorption of u* to n-components was measured, agree with our prediction and experimental results. Figure 13 shows the dependence of the transmitted intensity on the magnetic field strength for the other resonance line 327.40 nm which arises from the same electron

S420n

-1

1

i

Fig. 9. Trace of scanned interferogram for Cu I 324.75 nm.

[14] H. KOIZUMIand M. KATAYAMA, Phys. L&r. 64A, 285 (1977).

Application of the atomic Faraday effect to the trace determination of elements (Cd, Ag and Cu)

401

cu ~2p3~ ~i

a=o c~

~~t ~

~=4.6 xlff ~

..

**

0~*: . . . . .

% . . . . . . . . . . . . . . . . . . . . . . . .

........................

,

Fig. 10, A E vs H for the upper level of copper ~P~/2, calculated with the calculated a- and B'-values,

configuration of the upper state but a different term (4s2S1/2-4p~Pl/2). It is obvious that no line-crossings take place. Figures 14 and 15 demonstrate the calculated Breit-Rabbi levels and transition. It is theoretically predicted that no line-crossing occurs for this line regardless of the magnitude of the a-constant. From an analytical point of view, this line may be preferable to the line 324.7 nm for the sharp dip due to

2~p

Cu 4s

B':o

oi

.

.

.

.

.

.

.

.

.

i

.

.

.

.

"-"--~;;

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

H(kG)

Fig. 11. A E vs H for the lower level of copper

.

.

i

10

zSln, calculated with the experimental

a-value.

402

KUHMJKI KITAGAWA, ,

TCXHIAKI SHIGEYASU and TSUGXO TAKEUCHI

j”_l_““““““l”““““__~1-____-1---_---1__-_~~~””____.

flf +

-1

I++

t.

**

+*+* ff *f 1 *+* +** ++f **+

Cu I 321.75nm a,=O.l95cf$( %,/L) B=-1.6x10- ( 2Pj~,

++++++:::*$-*+ ++::: +*** *++* *::** ++***’ *++** +f* ++‘f *++ *++ *+** +*+ +++++* +*+ **+ +++.+* ..::* i* +*.::++*+ **++:.* *+*+** +*:t.:j.*’ +++*+** / +*$$i:::+*+ ::,*,:,,::::+“:*.* l +* l *‘*‘:$+.‘:+~,*+ i**.:~;:~;“‘““’ +:...,*::.““’ . ..,“,‘.“““‘~‘:,:~~:?:‘~~+*:t~*... .a : ‘::‘:‘**,,,*+ *f” +**+ +.*+ I...,, .:.:.,*+ ~~+“~~“,‘~+‘~“.“““““’ . .I;$*:*++;,?’ ;? ;*t.,++ .+*a* ()/_______+’ _:..;**;_;t_-_.: ____-____________ ____;;;;*, *+*+ ‘..*‘.‘~~,,“.**.“~.,,,,’ .*.I** +:::‘+*:“‘:~~‘;;;~~,‘*.~~“““’ II +**” *++*.+ **++* ,,,* ;;;“““‘~“‘..~.!‘.‘.’ ..‘“,~““‘“” pl:.,:I:~:.““” I , *I I I I I I : i . .. I I I ; . . I . .. .. ... .. .. “‘!:!! ,,,I ., ‘..*:r:!;:;;.., .. .. .. . ..*. II. . 101.1.. . ..** ‘:*m.‘. ..;a-... ‘.:$‘s* .* ..:...;;. .*‘..“.. -.. -*.. ... ’ *.:.. .:.. -.. ... *** *. *, ‘::,..“.. ..a. ..:.. .* ..,:*::::. *’ **.* . . * .., .I. . *,*..* . . . “:.. . . .*-..* *. .‘. “:.. ..:... . . . ‘.. ‘., ..: aI . . *. . . *.. ’ ‘. . . .*:y.*._ . *. *.:**. *. ..

7’ ; zj

l

-lI”___,“““_““__““““_^-_-__

0

i__________“_“““,___“____

5

H (kG)

16

Fig. 12. Zeeman splitting pattern for Cu I 324.75 nm, calculated with the experimental u-value for the lower level: (II)?r-component.

the line-crossings

interferes with the stability of the transmitted intensity if any variation in magnetic flux exists. Sifuer. Figure 16 shows the dependence of the transmitted intensity on the magnetic

field strength, for the analytical line of Ag I 328.07 nm (5s2S1,,-55p2P3,J. It is apparent from Fig. 16 that no significant, line-crossing takes place. The natural abundance of silver is 51.85% of lo7Ag and lo9Ag. Both isotopes have a nuclear spin momentum of I= l/2. The calculated a and H-constants are listed in Table 3. The examination by the Fabry-Perot interferometer indicated that the line was single. This was also found in an other experiment [15]. As expected from the calculated coupling

Fig.

13.

Dependence of the transmitted intensity on the magnetic field strength for Cu I 327.40 nm.

[15] S. FRISCH, 2. Physik 71, 89 (1931).

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

403

lj -j

li

__“-_“__--“____“-““_-1-11-___________”~”_””~~~~~~ 5

KG)

i6

Fig. 14. AE vs. H for the upper level of copper 4p2P,,,, calculated with the calculated a- and H-values.

constant, the Fermi-contact effect is in practice small for the %-electron. Figures 17-19 show the calculated levels for the upper and lower levels, and the transition, respectively. Here, the upper level changes into hfs $P,,, and fPsn while the lower level changes into f& and $S1,,. The former splits into 5 + 3 = 8 magnetic sublevels and the latter into 3 + 1 = 4 magnetic sublevels. The calculated transition pattern predicts that

.--__ +::I :iii: .:

.----~~--“~~~~~~“___~~,-L-__-_

5

___“.._____““__..““__j H&G)

10

Fig. 15. Zeeman splitting pattern for Cu I 327.40 nm, calculated with the experimental a-value for the lower level.

404

KWMW

~AGAWA,T~~

SHIGFZYASU and TSUGIOTAIWUCHI

I &J I 328.07 nm ? J

0

Fig.

16. Dependence

15 20 5 10 Magnetic field strerx$h(kG)

of the transmitted

intensity on the magnetic 328.07 nm.

field strength

for AgI

no line-crossings take place for this line irrespective of the magnitude of the aconstant. The reduction in the transmitted intensity with an increase in magnetic field beyond about 7 kG is interpreted in the same manner as for the copper line. Because of the different nuclear spin moment, there arises no line-crossing for the line of silver resulting from the transition between the same terms as those of copper. Of the same group of elements, gold isotope ‘“‘Au(lOO% natural abundance) has a nuclear spin momentum of I = 3/2, and the calculated u-value for the bs-electron has a magnitude comparable to that for the 4s-electron of copper. Therefore, some line-crossings are expected for the analytical line Au I 242.80 nm (2S1,2- 2P3,2). The results for gold will be described elsewhere.

-*

*x.

l*

l*

**

l*

l*

**

l **

-,! **

l* **

,li’_______________________

L_________________-_____

5

Fig. 17. AE vs. H for the upper level of silver 5p2Psn, B’-values.

H(kG)

calculated

* *I

Y

ii,

with the calculated

a- and

Application of the atomic Faraday effect to the trace determination

4 5s2q2

.$

a=-O.om g=o

4

of elements (Cd, Ag and Cu)

a-r+*

:i

_,,____________________,__,L-_--’____”___~~~_~~~~__~~___

0

5

-1;

H&G)

Fig. 18. AE vs. H for the lower level of silver Ss*S,,,, calculated with the calculated a- and B’-values: the a-value has been corrected by multiplying with the ratio of the experimental to calculated values for copper.

*::*

+:*

l:*

l::+

+:* _++

,I___________________-_---

0

Fig. 19. Zeeman

splitting pattern for AgI

L,___________________--__I

5

328.07 nm, calculated B’-values.

ii

10

with the calculated

a- and

405

406

KUNMJKI

KTTAGAWA,

TOSH~AKI SHIGEYASU and TSUGIO TAKEUCHI

Cadmium. The analytical line of cadmium Cd 228.8 nm is the result of the transition 5s’ ‘S,-5s5p IPI. The natural abundance of cadmium is 0.857% of “*Cd, 12.39% of ‘l°Cd, 12.75% of ‘llCd, 24.07% of ‘l*Cd, 12.26% of l13Cd, 28.86% of ‘14Cd and 9.58% of ‘16Cd. The isotopes with even atomic mass have a nuclear spin momentum I = 0 while those with odd mass a momentum I = l/2. For the former case, there arises no hfs. Under a magnetic field, the upper level splits into magnetic sublevels with A4, = -1, 0 and 1, and the lower levels are unchanged. For the latter isotopes, hfs 3,iP1 and l,:P1 arise from the upper level and ,,$, from the lower. The former hfs split into 4 + 2 = 6 magnetic sublevels and the latter into two magnetic sublevels. For the isotopes with I = 0, the Zeeman splitting pattern can be readily caculated by equation (7), while to those with I= l/2 the variation theorem should be applied. The function of Dirac electron for two valence electrons has not been given. However, in the lower state, the relative anti-parallel spins produce no apparent Fermi interaction, i.e. a = 0. For the upper state, the Fermi interaction by Ss-electron should be corrected by the following expression [B]: a’ = a(gi - 1)/2. As & = 1 for ‘P, term, a’ = 0. Since the resultant spin momentum S = 0, the remaining momentum is the angular momentum =l. Because no L-S coupling is formed in this case, the dipole-dipole coupling constant B’ is calculated by substituting the Schrijdinger wave function of the Sp-electron for the Dirac electron. An experimental value of B’ for ‘P, has been estimated by the other investigators [16]. We also attemped to determine the value by the scanning of the Fabry-Perot interferometer. Although self-reversal was revealed, no pronounced result informing us of the interaction was manifested. The calculated and earlier reported values are listed in Table 3. Figures 20-22 demonstrate the Breit-Rabbi levels for the upper and lower states, and the transition calculated with the experimental value of B’, respectively. Although the calculated pattern predicts a line-crossing at a field strength of about 0.2 kG, between a

Cddp,

$

a=0

z!

cm-’

B’=-0.0447

.*: **** .: *****::******j * l****:***::***** I ************* *****::**::,**** l*** ******** l*** ***2**** *********:*** :I”1 II*** l *“P**“” **g$*** 1:.sijc l********: Otl” :OtPftXr::DtPt::Dt:tPEPO *********: $::::::::S:t j”:“********* I ***** **** l*** ***I( *****I*** ***** ********* l*** **** l*** **** **** l*** ************** ‘“***~“**~~“**** *****::** l*** I **::***:i “**I 7

%i

l

_‘d___________________‘-____

l______,_I_______________~ 5

H(kG)

10

Fig. 20. AE vs H for the upper level of cadmium 5sW’P,, calculated with the experimental B’-value: curves are plotted for both isotopes (I= 0 and l/2).

[16]

S. S-N,

Ann.

Physik

84, 638 (1928).

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

407

_li”““___““““_“““_“_------_i__“____”_”””___________. 0

5

H(kG)

Fig. 21. .AE vs. H for the lower level of cadmium Ss2’S,,.

t+--component for I= 0 and a ~+-component for I = l/2, the experimental result, shown in Fig. 23, does not distinctly indicate it. Probably, the effect is concealed by the Lorentz broadening of the com~nents. In addition, because of the natural abundance of the isotopes with odd atomic ‘mass is only a quarter of the total, they have no significant effect on the shape of the curve.

“~I”“__“““““““““““~“““““~““1”“~“”””””””””””””””“~““”

0

5

Ii

10

Fig. 22. Zeeman splitting for Cd I 228.80 nm, calculated with the experimental P-value upper level.

for the

408

Km

IGTAGAWA,

0

TOSHL~KI !WIGEYASJ and TSUGIO TAKEU~

2

4

6

8

10

Magnetic field strength(kG)

Fig. 23. Dependence

of the transmitted

intensity on the magnetic field strength for Cd1 228.80 nm.

Dependence of the transmitted intensity on source radiance. Figures 24 and 25 show the dependence of the transmitted intensity on the source radiance. Contrarily to expectation by equation (4), the experimental graphs are not rectilinear but somewhat concave at high source radiance. Presumably, the increase in lamp current causes an increase in line width of the source radiation. As the line width increases, the convolution term p’(k) /sin Q(k, H)I’ m * equation (6) becomes larger, leading to an increase in the transmitted intensity. The dependence of the transmitted intensity on the line width of the source radiation was calculated by numerical integration. Since the pressure in the light source is low, the Gaussian form is applied to the source profile function p’(k). Figure 26 shows the result of the calculation. The calculation coincides with the experimental results. For practical purposes, it is pointed out that a radiation source with a greater line width is preferable for the present technique than that with a narrow one. This originates from the displacement of the a-components from the original frequency. In atomic absorption spectrometry, the line-broadening of source radiation is a disadvantage as the sensitivity in absorption is reduced, while in the present technique it is an advantage. Alternatively, a tunable light source could be used preferably. A magnetized electrodeless discharge lamp or a tunable laser could be utilized as such light source.

Source intensity(a.4

Fig. 24. Dependence of the transmitted intensity on the source radiance for Cu I 324.75 nm.

Application

of the atomic Faraday effect to the trace determination

Cd

of elements

(Cd, Ag and Cu)

409

I 228.80 nm

Source intensity(a.4 Fig. 25. Dependence

of the transmitted

Efect of rapid rise in atomization

intensity on the source radiance for Cd I 228.80 nm.

temperature

Figure 27 demonstrates the curve of the square root of the transmitted intensity vs the time required to attain the final atomization temperature. As the time decreases, the transmitted intensity increases. The sample may be atomized before the final or equilibrium temperature is established. For this reason, rapid heating favours the production of a condensed cloud of atoms and prevents the vaporization of the sample as non-atomic species. As the atomization takes place while the temperature of atomizer is rising [17], the rate of heatmg is critical and therefore, should be carefully controlled. Calibration graphs and detection limits As discussed above [equation (4)], the transmitted intensity is expected to be proportional to the square of the number of atoms in the light beam or mass of element introduced. Calibration graphs were plotted using magnetic field strengths of 4, 5 and 6 kG for Cd, Ag and Cu. The responses showed a square-law dependence on the amount of analyte up to amounts of about three orders of magnitude above the detection limit. However, they were curved for larger amounts where the absorption term played an important role or the transmitted intensity was reduced by atomic

lo-

H=4 kG NL=lO’ Cd I 228.80 nm

5-

O25

30

35

40

45

!.BM

l-f?)

Dopplerwidthof scurce line Fig. 26. Theoretical

curve of the dependence of the transmitted source radiation.

[17] M. YANAGISAWA,H. KAWACWCHIand B. L. VALLEE, Anal.

intensity

Biochem.

on the line-width

95, 8 (1979).

of

410

KUNMJKI

KITAGAWA,

2

0

TOSHIAK~SHIGEYAW and TSUGIO TAKEUCHI

1 Rising timecsec)

Fig. 27. Dependence

of the transmitted intensity on the time required for establishing the equillibrium temperature in the atomization of copper.

absorption. As reported previously, this was corrected by taking a ratio between the intensities transmitted through the crossed and parallel configuration. This cancels the absorption effect and the variation in the source radiance. Even if the correction was applied, the calibration graphs bent for higher amounts of analyte. This is probably due to the Lorentz distortion of the absorption lines of the cT-components. This will be investigated by employing the frequency-tunable light source stated above. On the basis of a signal to noise ratio of two, the present technique gave a detection limit for cadmium of 5 x lo-l2 g with the hollow-cathode lamp with a discharge current of 15 mA and 5 x 10-13g with the electrodeless discharge lamp supplied with a microwave power of 120 W; for silver the limit was 2 x lo-“g with the hollow-cathode lamp with a current of 15 mA, and for copper it was 3 x lo-“g with the hollow-cathode lamp with a current of 15 mA. These are comparable to those obtainable by atomic absorption spectrometry. We have not discussed an other aspect important in the practical analysis, that is the freedom of atomic Faraday spectroscopy from the background scattering by non-atomic species. This advantage was found to be valid for the elements silver and copper as well as cadmium referred to previously [3]. CONCLUSION

The atomic Faraday spectroscopy has been applied to the trace determination of cadimum, silver and copper. Using the variation theorem, we developed a theoretical approach that agreed closely with the experimental observation of the dependence of the transmitted intensity on the magnetic field strength and for the line-crossings between m+ and cr--components. Under optimum conditions of magnetic field, some aspects of practical analysis were examined. It was found that the atomic Faraday spectroscopy combined with an electrothermal atomizer presented detection limits for these elements comparable to those obtained by conventional atomic absorption spectrometry. Acknowledgements-This research was supported partly by the Grant-in-Aid from the Ministry of Education of Japan. We thank Dr. J. B. DAWSON and Professor T. S. WEST for helpful discussions and advice.

APPENDIX Assignments

of the lines of the Zeeman

patterns shown in ihe oarious figures

The assignment of each line is given in terms of M, and Mr for the lower and upper level respectively. The

‘column number’ designating the line is counted in each figure from bottom to top at 10 kG.

5

6

71

0.5

1.5

1.5

1.5

9

0.5

1.5

-0.5

1.5

92

-0.5

1.5

0.5

1.5

30

-0.5

1.5

-1.5

1.5

73

0.5

0.5

1.5

0.5

11

0.5

0.5

-0.5

0.5

90

-0.5

0.5

0.5

0.5

-1.5

0.5

28

-0.5

0.5

75

0.5

-0.5

1.5

-0.5

12

0.5

-0.5

-0.5

-0.5

89

-0.5

-0.5

0.5

-0.5

26

-0.5

-0.5

-1.5

-0.5

76

0.5

-1.5

1.5

-1.5

14

0.5

-1.5

-0.5.

-1.5

87

-0.5

-1..5

0.5

-1.5

24

-0.5

-1.5

-1.5

-1.5

74

0.5

0.0

1.5

0.0

11

0.5

0.0

-C.S

0.0

90

-0.5

0.0

0.5

0.0

27

-0.5

0.0

-1.5

0.0

70

0.5

1.5

1.5

1.5

8

0.5

1.5

-0.5

1.5

93

-0.5

1.5

0.5

1.5

31

-0.5

1.5

-1.5

1.5

72

0.5

0.5

1.5

0.5

10

0.5

0.5

-0.5

0.5

91

-0.5

0.5

0.5

0.5

29

-0.5

0.5

-1.5

0.5

75

0.5

-0.5

1.5

-0.5

12

0.5

-0.5

-0.5

-0.5

88

-0.5

-0.5

0.5

-0.5

26

-0.5

-0.5

-1.5

-0.5

77

0.5

-1.5

1.5

-1.5

15

0.5

-1.5

-0.5

-1.5

86

-0.5

-1.5

0.5

-1.5

23

-0.5

-1.5

-1.5

-1.5

63

0.5

1.5

1.5

1.5

1

0.5

1.5

-0.5

1.5

41

-0.5

1.5

-1.5

1.5

68

0.5

0.5

1.5

0.5

KUNMJKI K~TAGAWA,T~~HIAICISHIGEYAW and TSUGIO TAKEUCHI

412

Table Al. (Cmtd) Figure

COlUrm

Loner

level

:.pper

::J

5

-0.5

0.5

35

-0.5

0.5

73

0.5

-0.s

11

0.5

-0.5

90

-0.5

-0.5

26

-0.5

-0.5

18 78 16

0.5

-1.5

0.5

-1.5

-0.5 -0.5

-1.5 -1.5

level ::

yJ -0.5 0.5 -1.5 1.5 -0.5 0.5 -1.5 1.5 -0.5 0.5 -1.5

0.5 0.5 0.5 -0.5 -0.5 -0.5 -0.5 -1.5 -1.5 -1.5 -1.5

67

0.5

1.5

1.5

1.5

35

0.5

1.5

0.5

1.5

0.5

1.5

5

-0.5

98

-0.5

1.5

67

-0.5

1.5

-0.5

36

-0.5

1.5

-1.5

70

0.5

0.5

39

0.5

0.5

8

0.5

0.5

0.5

1.5 1.5 1.5 1.5

1.5

0.5

0.5

0.5

-0.5 0.5

0.5

94

-0.5

0.5

63

-0.5

0.5

-0.5

0.5

31

-0.5

0.5

-1.5

0.5

0.5

74

0.5

-0.5

1.5

-0.5

43

0.5

-0.5

0.5

-0.5

0.5

-0.5

12

-0.5 0.5

-0.5 -0.5

69

-0.5

-0.5

58

-0.5

-0.5

-0.5

-0.5

26

-0.5

-0.5

-1.5

-0.5

79

;,

0.5

97

80

12

c.5

XI

0.5

-1.5

48

0.5

-1.5

17

0.5

-1.5

1.5

-1.5

0.5

-1.5

-0.5 0.5

il.5 -1.5

82

-0.5

-1.5

51

-0.5

-1.5

-0.5

-1.5

20

-0.5

-1.5

-1.5

-1.5

U.3

I.:,

27

O.!J

I..l

12

0.5

1.5

91

-0.5

1.5

72

-U-J

i.5

31

0.5

0.5

15

0.5

0.5

-O.> 0.5 -0.2 0.5 -0.5

1.5 1.5 1.5 0.5 0.5

I

Application of the atomic Faraday effect to the trace determination

of elements (Cd, Ag and Cu)

Table Al. (Coned)

87

-0.5

0.5

71

-0.5

U.5

35 19

19

22

0 . L.

-0.3

OVS

-0.5

a2

-0.5

-0.5

66

-0.5

-0.5

40

0.5

-l.S

24

0.5

-1.5

0.5 -0.5 0.5 -0.5 0.5 -0.5

O.!, 0.5 -0.5 -0.5 -0.5 -0.5

0.5

-1.5

-0.5

-1.5

75

-0.5

-1.5

5Y

-0.5

-1.5

-0.5

O.!J

-1.S -1.5

75

0.5

0.5

1.5

0.5

42

0.5

0.5

0.5

0.5

11

0.5

0.5

-0.5

0.5

90

-0.5

0.5

0.5

0.5

59

-0.5

0.5

-0.5

0.5

26

-0.5

0.5

-1.5

0.5

74

0.5

-0.5

1.5

-0.5

42

0.5

-0.5

0.5

-0.5

11

0.5

-0.5

-0.5

-0.5

90

-0.5

-0.5

0.5

-0.5

59

-0.5

-0.5

-0.5

-0.5

27

-0.5

-0.5

-1.5

-0.5

77

0.0

0.5

1.0

0.S

50

0.0

0.5

0.0

0.5

24

0.0

0.5

-1.0

0.5

72

0.0

-0.5

1.0

-0.5

51

0.0

-0.5

0.0

-0.5

29

0.0

-0.5

-1.0

-0.5 0.0

74

0.0

0.0

1.0

irl

0.0

0.0

0.0

0.0

27

0.0

0.0

-1.0

0.0

413