line profiles in coherent forward scattering spectroscopy

Sjmtmchamica Acta, Vol. 488. No. 9. pp. 1079-1091, 1993 058‘&8547/93 s6.00 + .oLl Printed m Great Britain. 0 1993 Pergamon Preu Ltd

-Line profiles in coherent forward scattering spectroscopy*

MICHAEL Gaosst and GERD HERMANN I. Physikalisches Institut der Justus-Liebig-Universitat Giessen, Heinrich-Buff-Ring 16,

D-W-6390 Giessen, F.R.G.

(Received 4 January 1993; accepted 4 March 1993)

Abstract-Coherent forward scattering (CPS) spectroscopy is a useful tool for element determination. Owing to very different spectral profiles obtained by dichroism and birefringence in addition to the Zeeman hyperflne and isotopic structure, the line profiles of CFS appear much more complicated than those of absorption. The widths and the shapes of line protiles are important with respect to structured atomic and molecular spectral interferences as well as to saturation and roll-over effects. Furthermore, recent developments of atomic resonance monochromators focus special interest on CFS line protiles. Calculations for the CFS D, line of sodium based on the complex Voigt function in the range from the predominantly Gaussian to the Lorentzian limit are presented together with high-resolution dye laser measurements as well as integral data obtained with continuum sources.

1. INTR~~LJC~~~N

COHERENT forward scattering (CFS) spectroscopy [l] has been successfully applied to trace element determination [2-121. Using continuum sources, CFS is suitable for easy sequential or simultaneous multielement determination without the requirement of lamp exchanges. By measuring lines of very different strengths, which is possible in combination with continuum sources, CFS covers an extremely wide dynamic concentration range [13]. This results from the fact that, while continuum sources are generally poor compared to hollow cathode line sources on strong atomic lines, continuum sources are superior on weak lines that are generally weak in atomic line sources too.

The total intensity of CFS line profiles includes contributions from dichroism as well as from birefringence, both described by the complex spectral refraction index owing to the Zeeman-split line profile [1, 3, 41. In a transverse magnetic field, the effect of the birefringence function is denoted by the Voigt effect. In a longitudinal field, the Faraday function describes the circular birefringence of the resonant Faraday effect. Each of these effects appears with contributions from both dichroism and birefringence and is superimposed by hyperfine and isotopic structure, if applicable. Thus, CFS lines may appear very complex and depend on the magnetic field strength, analyte atom density, buffer gas, and pressure.

Since CFS spectra show many fewer lines than atomic emission, i.e. under conditions of common electrothermal or flame atomizer ground state resonance lines only, analytical CFS spectrometry can use monochromators of low spectral resolving power. Thus, spectrally integrated line intensities are commonly measured and the spectral CFS line profiles are of importance with respect to spectral interferences from structured background. Saturation and roll-over effects also depend on the respective profiles of the dichroic and dispersive contributions to the total transmitted line. Furthermore, recent developments of CFS resonance monochromators (CFSRM) [14-171 are focusing interest on the spectral CFS line profiles.

This paper presents theoretical results and high-resolution laser spectroscopic measurements of CFS spectral line profiles together with the related analytical curves.

* This paper is dedicated to Prof. Dr DSc. Dr h.c. mult. A. Schannann on the occasion of his 65th birthday.

t Part of thesis.

la79

1080 M. GROSS and G. HERMANN

Polarizer Polarizer Monochromstor

and detector

Fig. 1. Schematic of the experimental arrangement.

The calculations, based on the complex Voigt function for the 589.6 nm sodium II1 line (32&n-32P1j2), show significantly different behaviour for the predominantly Gaussian or Lorentzian broadening.

2. EXPERIMENTAL

2.1. Continuum source flame CFS The basic equipment employed for the experimental studies is: a common CFS spectrometer

[18], as shown in Fig. 1; a Xe high-pressure lamp (XBO-45OW/4); an air-acetylene flame between crossed polarizers; and a 0.25 m monochromator equipped with a photomultiplier tube.

The air-acetylene flame (10 cm in length) is placed between the poles of an electromagnet that produces field strengths up to 1.9 T in a gap 15 mm in width and over the full length of the flame. The measurements using the flame under atmospheric pressure have been carried out at field strengths of 1 T as typically applied in the Zeeman technique of atomic absorption spectrometry (ZAAS). As polarizers, two air-spaced calcite prisms of the Glan-Taylor type are aligned at angles of k45” with respect to the direction of the magnetic field (Voigt configuration).

2.2. Laser measurements using a sealed cell For the dye laser experiments, a similar arrangement has been used. However, instead of

the flame, a sealed evacuated cylindrical quartz cell (diameter, 15 mm; length, 40 mm) containing sodium, and argon as inert buffer gas at a low pressure (150 Pa), was placed in a heated chamber to achieve the required analyte atom density. The oven with the cell was arranged in the gap of the electromagnet described in Section 2.1. Related to the narrower line, the measurements using the cell under low pressure were carried out at field strengths of 0.5 T only. The sodium atom density is varied from 2.5 X log to 7.6 X lOi cmv3 via the cell temperature (370-540 K).

The cw dye laser (380D, Spectra Physics Lasers) was operated with rhodamine 6G and pumped by an argon ion laser (Innova 100, Coherent Inc.). With a pumping power of up to 6 W, a dye laser output up to 1 W could be obtained. However, in order to prevent saturation effects, a power below 100 mW was used for these measurements. The laser linewidth and, thus, the bandwidth of the laser spectrometer is about 1 MHz or 1 fm, which is negligible in these measurements. The spectral CFS profile for the Voigt configuration was measured by tuning the dye laser wavelength over the sodium line. The transmitted CFS intensity was recorded and plotted against the laser wavelength or frequency.

3. THEORETICAL

Coherent forward scattering is an effect of macroscopically coherent light interaction with gas atoms and is denoted by the complex index of refraction ii = rz’ + ik. The real part, it’, describes refraction and birefringence and the imaginary part, k, relates to the absorption coefficient.

In our experiments, linearly polarized light is passed through the sodium vapour in the flame or in the cell. The transverse magnetic field applied to the atoms is aligned in such a way that the transmission axes of the polarizer and analyser are oriented at angles of -~45” with respect to the field.

Line profiles in CF!S spectroscopy 1081

Owing to the Zeeman effect of the resonance line splitting into IT- and u-components, which are polarized parallel and perpendicularly with respect to the magnetic field, the atomic interaction of the incident light becomes anisotropic. Thus, light polarization is changed by birefringence and dichroism between polarizer and analyser, and light is partially transmitted through the analyser. The change of polarization and the transmitted CFS intensity depends on the density, ZVNa, of resonant atoms in the sample volume, on the interaction length, L, on the magnetic field, B, and on the oscillator strength, f, of the atomic resonance line.

The transmittance of the Voigt configuration and contributions to it from dichroism and birefringence, Id(o) + Zr,(o), can be calculated by different theoretical means [l, 3, 4, 19, 201. For the Voigt configuration (transverse magnetic field), the transmitted spectral intensity (0 = %~rc/x = angular frequency) is:

Z(w) =

=

Z(w) =

b(w) =

h(w) =

(l/8) Q(o) (exp[io&L/c] - exp[iwii,Llc])*

(l/4) Q(w) {cosh[(k,-k&L/c] - cos[(n;-nJ,)wLlc]}

exp[-(k,+k,)wLlc]

Zl(w) + Zb(w) with

(l/4) @(o) {cosh[(k,-k&L/c]-1) exp[-(k,+k,,)oL/c]

(l/4) Q(o) {l-cos[(nk-n&)oLlc]} exp[-(k,+k,)oLlc] .

(la)

(lb)

(2)

(3a)

(3b)

Q(o) is the spectral density of the incident light, which is assumed to be constant for a continuum light source. The total intensity is found by integration:

ztot = I +-{Zd(w) + Zb(w)} do . (4) -m

The complex refractive index Am = n:(w) + &(w) owing to the Zeeman component, q, which is equal to 112 - m’ (m, I?Z’ = magnetic quantum numbers of the ground and excited state, respectively), can be expressed by means of the plasma dispersion function Z(z) = Z(w, I’, 6) [l, 31, which includes Lorentzian as well as Gaussian contributions to the line shape. The imaginary part of Z(z) represents the absorption profile of the line. Both the Doppler width, 6, (aFWHM = (ln2)‘” 8/7~ = full width at half maximum in Hz) and the Lorentzian line width r(rFWHM = U21r = full width at half maximum in Hz) have to be matched to the experimental conditions for which the intensity profile is calculated:

fiq(w) - 1 = Ne*f

4E0w3me6 * z&J

exp-[(w - w’)/6]* dw’

(w’ - 00 - AwJ + ir/2 (5)

(6)

with

exp( -6) dt t _ z

4

where:

=q = (0 - wo - 60, + iU2)/6; = atomic density; r = Lorentzian radian width; = oscillator strength;

M. GROSS and G. HERMANN

radian Doppler width; electron charge; radian frequency of light; Zeeman shift;

EO = influence constant;

172, = electron mass; and

00 = atomic resonance radian frequency.

In the general case, 2, and ii,, for the respective polarizations, are to be summed over all magnetic and hyperfine quantum numbers as well as isotopes. An advantage of the analytical candidate sodium is that there is one stable isotope only (23Na) and, thus, no isotopic structure. Furthermore, at magnetic field strengths I3 = 1 T, as is usually used in CFS, hyperfine structure can be regarded almost in the limit of the Back-Goudsmith effect. Thus, in a transverse magnetic field, the Dr resonance line splits into two n-components (Am = 0) and two u-transitions (Am = +l) polarized parallel and perpendicularly with respect to the magnetic field. Owing to the LandC factors for the *Sin ground (g = 2) and the *PI12 excited state (g = 2/3), the Zeeman shift as a function of the magnetic field B (T) is given by:

and the refractive given by:

A% =‘+27F* 9.33 B (GIWT)

Aw, = t21r - 18.66 B (GHz/T) (8)

indices (a,_ + q = factor depending on light polarization q) are

ii, - 1 = n; - 1 + ik, = const * f - xa,_ Zo(w, w,,,) m

fi, - 1 = n: - 1 + ik, = const . f - ~am,m~l Z*l(w, w,,,*I) . (10) m

Thus, the birefringence function [l] results in

47 - ti, = const . f. z(-Z_l + 22, - Z,) . m

(11)

The Doppler width of the Na D1 line components (temperature T in K) is:

6 FWHM = h-l * [S ln2 (kn - T/mNa)]lR

= 75.9 MHz (T/K)

(12)

and the collisional (Lorentzian) broadening owing to the buffer gas of atomic density Nb is:

rFWHM = u NJ8 kn T(llm,, + llmt,)ln3]1’2 = 2yNbco (13)

(kn = Boltzmann’s constant, u = broadening cross-section, y = broadening rate, mN, = 38.18 X 1O-27 kg, mb = mass of buffer gas atoms, c, = velocity of light).

Under given conditions, the colliding atoms are those of the buffer gas (argon or flame gas). The particle density of atoms at a given pressure, p, is Nb = plkB T. The Na D1 broadening rates for collisions with argon (T = 460 K) and with flame gas (T = 2060 K) molecules are 2yA, = 2.6 X lo-*O cm* and 2-y,, = 4 x lo-*O cm* [21], respectively.

4. RESULTS AND DISCUSSION

Calculations and measurements have been carried out with the data as given above for the cell containing argon under low pressure. This results in a predominantly

Line profiles in CFS spectroscopy 1083

x 10-5 r 0.6 r

.g 2.0 0.5 -

ld E 0.4 - z 1 .s ._ u 0.3 - .!: 1 .o

;;

3 0.5

0 -20 -10 0 10 20 -20 -10 0 10 20

x 10-s - 0.6 -

9 t t $ .=” 0.5 -

i 2.0

-

0.4 -

6 1.5- ._ 6.3 - :! ‘5 1.0

- m 0.2 -

2

\I

\I 0.5 - 0.1 -

0 I Ii I 0 I I

-20 -10 0 10 20 -20 -10 0 10 20

Frequency, v-v0 @Hz) Frequency, v-v0 @Hz)

Fig. 2. Calculated CFS spectral transmittance. Left column: NNa = 2.5 x lo9 cm-3; right column: NNa = 2.8 x lo** cmT3. Upper plots: contributions from birefringence (- - -) and dichroism (-); lower plots: total transmittance. Profiles are predominantly Gaussian

broadened. (For parameters see Section 2.2.)

Gaussian line profile. For the flame under atmospheric pressure, a predominantly Lorentzian line profile is yielded. Each set of corresponding parameters has been adapted to the respective experimental conditions (Sections 2.1 and 2.2), to allow comparison with the measurements.

4.1. Predominantly Gaussian line profiles CFS transmittances calculated for predominantly Doppler-broadened, Gaussian line

profiles are shown in Figs 2 and 3. Nevertheless, all calculations have been carried out with the correct Voigt profile with its Gaussian and Lorenztian contributions of broadening at the respective cell temperature (370-540 K). The upper curves represent the two contributions, Id and Zb, from dichroism and birefringence, respectively; the lower curve is the sum Zt,t = Id + Zb.

At low sodium density (Fig. 2) the dichroic graph, Id, is similar to the Zeeman absorption line with the a- and u-components centred to those of absorption. The corresponding birefringent graph, I,,, contributes additional intensity on the wings of each of the absorption lines, but vanishes at their centre. On those wings that are facing towards counterpolarized Zeeman components, the two contributions of birefringence are superimposed with the same sign and yield a higher intensity than on the other side.

Thus, the total transmittance as shown by the lower plots of Fig. 2 is characterized by broader profiles with the centre of mass shifted to the space between the counterpolarized T- and u-components. At low densities, i.e. far below saturation, when the lowest order power expansion of Eqn 1 is valid, the height of the spectral profiles increases proportionally to N* and, thus, a square law is describing the analytical curve, while the spectral profiles remain similar in shape.

With increasing density of resonant atoms, first, the dichroic contribution approaches saturation (beginning in Fig. 2, right column), then, at even higher densities (Fig. 3, left column), owing to the increasing width of absorption, the CFS transmittance of


0.8 -

h .Z

0.6 -

z s .B 0.4 -

:! Z 0

ii

l r

.s 0.6

z s .s 0.4

:! Z I ‘i; 0.2 PC

0

0.8

0.6

0.2

0 -20 -10 0 10 20 -20 -10 0 10 20

Frequency, v-v0 @Hz) Frequency, v-v0 (GHz)

Fig. 3. Calculated CFS spectral transmittance. Left column: NNa = 1.3 x lOI cme3; right column: NNa = 7.6 x 1Ol3 cmm3. Upper plots: contributions from birefringence (- - -) and dichroism (-); I ower plots: total transmittance. Profiles are predominantly Gaussian


birefringent origin, which, at lower densities, is centred between the w and a- components, comes into absorption and the centre of .mass is shifted to the outer wings of the line. Atthe -highest densities of the resonant atoms (Fig. 3, right column), birefringence results in phase retardations of multiples of 21r and, thus, the birefringent contribution to the CFS line profile shows sharp spectral oscillations. Figure 4 shows high resolution laser measurements of the spectral transmission of the cell and Voigt configuration, which are in good agreement with the calculated profiles. New calculations, which consider the hyperfine structure without neglecting the residual contribution owing to the incomplete Back-Goudsmith effect, also explain the differences between the ‘it- and a-components in intensity and width.

The total intensity (Fig. 5) has been obtained by integration over the spectral line profile (Eqn 4). According to the expansion of Eqn (1) in the low-density limit, the spectral and total transmitted intensity is proportional to the square of the resonant atomic density. In this low-density range of the analytical curve, dichroism and birefringence yield equal contributions (J& do = _f&, do = (l/2)1,,) to the total intensity, Z tot 9 as can be derived in a very general form [3] for each possible line shape using the equations of Kramers and Kronig.

At higher densities of resonant atoms, the total contribution from dichroism is saturated first and, then, the total transmitted intensity caused by birefringence exceeds that by dichroism. The total intensity vs density of resonant atoms, i.e. the analytical characteristic, is still rising with the slope at a rate approximating to a square law that yields high relative sensitivity (N - AZ/Z - AN = 2). At higher densities, when spectral oscillations appear that are moving through the line profile if the density is varied, related oscillations are also found in the spectral integral and on the analytical curves, even in combination with continuum sources (Figs 5 and 6). In this range, the slope is reduced ( -Iv113). Figure 6 shows a measurement of the spectral integral of the CFS intensity obtained by using the same cell and Voigt configuration in combination with a continuum source.


I 1 I I I I I I

-15 -10 -5 0 5 10 15

Frequency, v-va (GHz)

Fig. 4. The spectral profile of the transmitted CFS intensity measured by high resolution laser spectroscopy. Upper plot: NNa = 10” crn3; lower plot: NNe = 7 x 1Or3 cmW3. Profiles are

predominantly Gaussian broadened. (For parameters see Section 2.2.)

IO” 1012 1013 101’

Particle density, N (cm-))

Fig. 5. Total CFS intensity calculated by integration of spectral transmittance (Eqn 4) as a function of NNa (predominantly Gaussian broadened; for parameters see Section 2.2): (- - -),

contribution from dichroism; (-e-o-.), from birefringence; (-), total intensity.

4.2. Predominantly Lorentzian line profiles The calculations were performed with parameters according to the conditions of the

flame CFS (length, L = 10 cm; magnetic field, B = 1 T; pressure, p = 1 bar; temperature, T = 2000°C). The calculated spectral profiles are shown in Figs 7-10. They are broader and more Lorentzian-shaped. Thus, higher field strength is recommended. The arrows mark the resonance frequencies of the four Zeeman components of the line.


-_ ‘; ct

1 1012 10’3 10’4

Particle density, N (cme3)

Fig. 6. Measured total CFS intensity transmitted from a continue source vs NNa. (Profiles are predominantiy Gaussian broadened; for parameters see Section 2.2.)

I 6x10-‘,-

6 x IO-’ 5

* f 5 $ 4

a

4

.I 3 3 t ‘c (d 5 2 2

r*: I 1

0 0 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

6 x 10-7

h .r: 5

ii z

4 ._ u

.; 3

cll z

2 PC

1

0

x 10-3

5

4

3

2

I

0 1 I 20 40 60 -60 -40 -20 0 20 40 60

Frequency, v-v0 (GHz) Frequency, v-v0 (GHz)

Fig. 7. Calculated CFS spectral transmittance. Left column: NNa = 109 cm+; right column: NNe = 1Of’ cmp3. Upper plots: ~n~butions from ~~~gen~ (- - -) and dichroism (-); lower plots: total transmittance. Profiles are predominantly Lorentzian broadened. (For

parameters see Section 2.1.)

Apart from the widths of the components, the spectral profiles for low densities (iVNa) (Fig. 7) do not differ very much from those obtained for Gaussian broadening. And a variation of the atom density by a factor of 100 (Fig. 7, left and right columns) increases the transmitted intensity by a factor of 104, but has no important influence on the shape of the CFS line. Thus, the integrated total intensity (Fig. ll), for instance, as transmitted from a continuum source, obeys the square law for low atomic analyte densities and dichroism and birefringence again contribute equal fractions, as explained in Section 4.1 [3].


0.20

c 0.15 ‘Z

z

3 0.10

:! 3

s 0.05 cr:

0

0.20

.s 0.15

5 t ‘; 0.10

.s .

2 0.05

0

* . 0.15

I”, I”,

:: ::

:: I’: 0.10

:, ,u_, ,O.O;

-60 -40 -20 0 20 40 60

-60 -40 -20 0 20 40 60

Frequency, v-v0 (GHz)

0.15

0.10

0.05

0

-60 -40 -20 0 20 40 60

Fig. 8. Calculated CFS spectral transmittance. Left column: NNa = 1 X lo** cm-$ right column: NNa = 2 x lOI* cmv3. Upper plots: contributions from birefringence (- - -) and dichroism (-); lower plots: total transmittance. Profiles are predominantly Lorentzian


Similar to the description given in Section 4.1, the intensity is predominantly transmitted in the range of close-lying, perpendicularly polarized Zeeman components. The gap between the dichroic contributions from the perpendicularly polarized n- and u-components is almost filled by the contribution of birefringence. Owing to the broad linewidths, the crossed polarized total CFS u- and n-components are not resolved and the ljrofile appears with two (instead of four) spectral bands of nearly square-well formed shape. This is due to the Lorentzian pressure broadening forming line wings that extend much further than Gaussian profiles and are large compared to the Zeeman splitting at reasonable magnetic field strengths (-1 T).

With increasing atom density, the behaviour is also typical for the Lorentzian-like line profile of which the absorptive imaginary part reaches much further than the same part in the almost-Gaussian limit shown in Figs 2-6. At medium densities, saturation by absorption (right-hand sides of Eqns l-3) affects both contributions from dichroism and birefringence by roughly the same ratio (Fig. 8, left column). Thus, the slope of the logarithmic characteristic (Fig. 11) of the integrated spectral intensity (which is the relative sensitivity if a continuum source is used) is reduced to the range 0.8-2 x 101* cmP3. With further increases of Na density, the intensity, due to the birefringence between the crossed polarized Zeeman components, is completely absorbed (Fig. 8, right to Fig. 9, left columns). In the characteristics (Fig. ll), this absorption corresponds to a dip in the curve of the birefringent intensity at the density of 5 X 1013 cm-3.

At densities in the high saturation range (NNa > 2 X 1013 cme3; Fig. 10, left to right columns) the birefringent intensity on the outer wings increases more and more and at last represents the main contribution of the total intensity transmitted from a continuum source. The far-ranging absorption (according to roll-over effects in ZAAS) then eliminates the main part of the dichroic and the centre part of the birefringent


0.15 al 0.15 - .z r:

: 0.10 0.10 - ._

:! 'S 4 0.05 oz

0 -60 -40 -20 0 20 40 60 - -60 -40 -20 0 20 40 60

A 0.15 .z

z

.: 0.10

: ._ 5 2 0.05

0 -60 -40 -20 0 20 40 60 - -60 -40 -20 0 20 40 60

Frequency, V-V,, (GHz) Frequency, v-ve (GHz)

Fig. 9. Calculated CPS spectral transmittance. Left column: NNa = 5 x lOI2 cmm3; right column: NNa = 10” cme3. Upper plots: contributions from birefringence (- - -) and dichroism (-); lower plots: total transmittance. Profiles are predominantly Lorentzian broadened.

(For parameters see Section 2.1.)

0.15 A .Z ii * t 0.10 ._

f 'S 3 0.05 d

I

0.125

0.100

0.075

0.050

0.023

0 LNf 0’ ‘. p-a 0

-60 -40 -20 0 20 40 60

0 " -60 -40 -20 0 20 40 60

Frequency, v-vc (GHz)

L

-60 -40 -20 0 20 40 60

-60 -40 -20 0 20 40 60

Frequency. v-v0 (GHz)

Fig. 10. Calculated CFS spectral transmittance. Left column: NNs = 2 x 10” cme3; right column: NNn = 5 x 1Or3 cm+. Upper plots: contributions from birefringence (- - -) and dichroism (-); lower plots: total transmittance. Profiles are predominantly Lorentzian



10-l r

IO-’ - 1011 10'2 10” 10”

Particle density, N (cmm3)

Fig. 11. Total CFS intensity calculated by integrption of spectral transmittance (Eqn 4) as a function of NN. (profiles are predominantly torentzian broadened; fot parameters see Section 2.1): (- - -), contribution from dichroism; (---.), from birefringence; (-), total intensity.

intensity. Thus, no oscillations are observed because the intensity is absorbed in the range where those phase retardations of multiples of 21r occur.

Owing to this special behaviour, the calibration curve for a continuum source is very different for the ,+uentzian compared to the curve obtained in the predominantly Gaussian broadening. The calculated calibration curve has been validated by measurements with the game spectrometer using .different concentrated liquid samples. Figure 12 shows the total intensity measured with a continuum source as a function of the concentrations of liquid samples (points on the curve). The curve represents the calculated result fitted to the measurement by simple normalization. It shows good agreement between measurement and theory.

Measurements and theory for line profiles in the predominantly Lorentzian limit show a saturation plateau for the total intensity transmitted from a continuum source at high Na densities. This results from the summation of the contributions from birefringence and dichroism (Fig. 11). The contribution of birefringence has a local minimum in the medium saturation range and the sum shows a flat plateau. Using a beam of wider aperture and aperture angle results, under real analytical conditions, in an averaging, over different path lengths, of the different concentrations and, thereby, additional smoothing of the analytical characteristic. Thus, real calibration

Conceqalion @g/ml)

Fig. 12. Measured total CFS intensities transmitted from a continuum source vs NNa (profiles are predominantly Lorentzian broadened; for parameters see Section 2.1) with same curve as

in Fig. 11 fitted by choosing adequate NW. and I,.

1090 M. Gross and G. HERMANN

curves appear with their typical saturation behaviour with a slope ranging from that of a square law dependence to an almost linear behaviour in the analytically useful range.

5. CONCLUSIONS

The CFS intensity, and mainly its contributions from birefringence, appear with extremely differing spectral profiles depending on the density of resonant atoms, the pressure, the magnetic field and whether the Voigt profile is described predominantly by the Gaussian or Lorentzian line shape.

In the limit of low analyte density, the CFS transmittance rises proportionally to the square of the density of the resonant atoms. At these concentrations, dichroism and birefringence cause equal contributions to the total intensity transmitted from a continuum source insofar as there is no difference whether the line profile is more Lorentzian- or more Gaussian-like. The spectral line profile is very roughly that of the Zeeman split absorption line with the line centres of mass of the Zeeman components slightly shifted towards the spaces between crossed polarized components. Thus, at concentrations typical for analytical applications, the spectral bandwidth of CFS is roughly the same as that of absorption lines.

In the saturation range of higher density, NNa, the lines show a very different behaviour, depending on whether line broadening is predominantly Lorentzian or Gaussian. While saturation first affects the dichroic part, the birefringent and total CFS transmission is further rising in the predominantly Gaussian situation. In the mainly Lorentzian case, the medium saturation range is characterized by a relative minimum in the birefringent contribution and higher dichroic transmission. At very high densities; the highest transmittance occurs on the wings far outside the absorption line. This far-wing transmittance is due mainly to, the birefringence. The total linewidth is then much broader than that of the absorption line. In the Gaussian situation, oscillations occur that can also be found in the calibration characteristics, even in combination &fh a continuum source.

The analysis of the spectral CFS line profile, and its contributions from dichroism and birefringence, is suitable in explaining the saturation properties of the CFS calibration characteristics. The exact spectral distribution, which can be relevant for spectral interferences of structured background in CFS and in combination with an atomic resonance monochromator CFSRM [14-171, depends not only on the density of the resonant atoms, species and pressure of buffer gas, but also on the magnetic field.

Acknowledgements-The authors are indebted to the Bundesminister fur Forschung und Technologie and to the Projekttragherschaft Wassertechnologie, Kemforschungszentrum Karlsruhe, for support.

REFERENCES

[l] A. Comey, B. P. Kibble and G. W. Series, Proc. R. Sot. 293A, 70 (1966). [2] D. A. Church and T. Hadeishi, Appl. Phys. Left. 24, 185 (1974). [3] G. Hermann, CRC Crit. Rev. Anal. Chem. 19, 323 (1988). [4] G. Hermann, Anal. Chem. 64, 579A (1992). [S] K. Kitagawa, T. Nanya and S. Tsuge, Spectrochim. Acta 368, 9 (1981). [6] A. D. Kersey and J. B. Dawson, Anal. Proc. R. Sot. Chem. 18, 187 (1981). [7] P. Win, H. Debus, W. Hanle and A. Scharmann, Specfrochim. Acfa 378, 1013 (1982). [8] G. S. Jolly and R. Stephens, Anal. Chim. Acta 139, 323 (1982). (91 M. Yamamoto, S. Murayama, M. Ito and M. Yasuda, Spectrochim. Acta 35B, 43 (1980).

[lo] M. Namiki and K. Hirokawa, Fresenius’ Z. Anul. Chem. 316, 795 (1983). [ll] L. A. Davis and J. D. Winefordner, Anal. Chem. 59, 309 (1987). [12] G. T. Valente and R. Stephens, Specfrochim. Acto 428, 973 (1987). [13] G. Hermamt, M. Jung, G. Lasnitschka, R. Moder, A. Scharmann and X. Zhou, Spectrochim. Acta

45B, 763 (1990). [14] G. Jolly and,R. Stephens, Anal. Chim. Acta 116, 365 (1980). [15] K. Hirokawa and H. Matsuta, Anal. Chem. 63, 1747 (1991).


[16] H. Matsuta, K. Hirokawa, G. Hermann and C. Schwabe, 53rd Forum of Analytical Chemistry of the Japan Society of Analytical Chemistry, Akita, Japan (1992).

[17] H. Matsuta, K. Hirokawa, G. Hermann and C. Schwabe, Spectrochim. Acta 48B, 1093 (1993). [18] M. Gross, G. Hermann and A. Scharmarm, Spectrochim. Acta 44B, 597 (1989). [19] J. J. Kankare and R. Stephens, Spectrochim. Acta XXI, 849 (1980). [20] M. Yamamoto and S. Murayama, J. Opt. Sot. Am. 69, 781 (1979). [21] M. J. Jongerius, A. R. D. van Bergen, Tj. Hollander and C.Th.J. Alkemande, J. Quant. Spectrosc.

Radiat. Transfer 25, 1 (1981).

line profiles in coherent forward scattering spectroscopy

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