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Foreign gas broadening of the 51P1 level of Cd
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
FOREIGN GAS BROADENING OF THE 51P1 LEVEL of Cd ~ W. HANLE, A. SCHARMANN and P. WIRZ’ I. Physikalisches Institut der Justus-Liebig-Universität, D-6300 Giessen, W. Germany Received 12 February 1980
Level crossing in a transverse magnetic field in forward scattering is used to determine broadening cross sections by coffisions between Cd (in the 5 ‘P1 level) and rare gases. Additionally the saturation intensity of the level-crossing curve is investigated as a function of the rare gas pressures.
Recently we reported about the sensitive detection of trace elements by level crossing in forward scattering in a transverse magnetic field [1]. Thereby the sample is vapourized in a graphite furnace and the atomized particles are transported by a rare gas stream into the measuring cell. Therefore the level-crossing curve is broadened by collisions between the atoms of the trace element and the foreign rare gas. The half width of the level-crossing curve yields the cross section for the broadening. The experimental set-up is practically the same as for normal level-crossing experiments forwardinscattering [2]. A chamber with Cd atoms in is placed a transverse magnetic field. The light of an electrodeless discharge Cd lamp, polarized at an angle of 450 to the magnetic field direction, penetrates the chamber with Cd atoms and an analyzer which is crossed with respect to the polarizer. Two different effects occur in the magnetic field, One is the absorption of Zeeman components which is less important at low vapour pressures. The other is the dispersion, where at frequencies at the edges of the absorption linemagnetic the components parallel anddifferperpendicular to the field direction have ent velocities (birefringence) and therefore the outcoming light is elliptically polarized. This causes a brightening between crossed polarizers. Dedicated to Professor Dr.
f
—
with e = (~JIn2e2/mc~)NfL, Z the plasma dispersion function for magnetic field
A. Schraub on the occasion of
his 70th birthday, Part of thesis, Giessen (1979) (D 26).
240
While usually the absorption and dispersion profiles are regarded as a function of the frequency, the level-crossing presentation is the light intensity integrated over all frequencies as a function of the magnetic field. Hereby levels with m = 0 and m = ±1cross at zero field. Contrary to light emission the levels are broade,ned by the Doppler effect and in case additionally by collisions. In our arrangement the measurement chamber was connected with a pump. A valve allowed establishing different rare gas pressures in cell. The Cd-vapour 3 the corresponding to the density was 2.1 X 1010 cm temperature of the Cd reservoir (391 K). Self pressure broadening is negligible at such low densities. Fig. 1 shows three characteristic level-crossing curves in forward scattering of the 5 1P 1S 1 —5 0 transition of Cd, collisionally broadened by neon. The theory for forward scattering experiments was developed by Series et al. [3]. The observed intensity as a function of the transverse magnetic field can be written as: 2 exp [—(Z1 + D)} dw, I = p(o4( sin ~e (Z D)1 (1)
independent components Z
=
Z(~.
0,F, ~),D the plasma dispersion function for magnetic field dependent
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
lOOTorr
0.2
04 06 magnetic field strength B / T
Fig. 1. Broadening of level-crossing curves by collision with neon in forward scattering the Cdofresonance 9 cm3,oflength the cell: 4line cm).228.8 nm (Cd density: 2 X i0
components Z
=
Z(B,
w
0, F, ~),p(w) the spectral distribution of the incoming light, w0 the resonance frequency, B the magnetic field strength, F = the damping constant the 5 ‘P1 level, N the density 3), L theoflength of the measurement of atoms (cm chamber, ~ the natural linewidth, e the elementary charge, c the velocity of light, f the oscillator strength of the observed transition, ~ the Doppler width, and m the electron mass. The foreign gas collisions cause two effects, an increase of the damping constant of the resonance level which manifests itself in a broadening and a frequency shift. Taking collisions into account, the damping constant is: (A \/ A 2 ~ Ir’ _~V~+~V}~ )l~’~ h.1l-~ 15F —
—
—
g
g
— ~
g
with NFg the number of foreign gas particles per cm3, D7’
=
~fL
L IT
I (L_. + \MCd
3O4Xe
1
~11/2
)I
MFg/.j
0
200
600
400
foreign gas pressure p/Tori Fig. 2. Normalized halfwidth (HWHM) collision broadened level-crossing curves as a function of theofgas pressure of the rare gases Xe (0), Kr (i), Ar (0), He drawn lines were fitted by use of the
(s), and Ne (X). The experimental values.
It should be noted that, contrary to level crossing in emission, here the linewidth of the light source is normally not large compared to the level-crossing curve. We proceeded in the following manner: The intensity was measured as a function of the magnetic field with the foreign gas pressure as a parameter (see fig. 1). The experimental result shows that the halfwidth of the level-crossing curve increases linearly with the foreign gas pressure (fig. 2). From this, a broadening factor at a fixed gas pressure was deduced. Then, at the same foreign gas pressure level-crossing curves with the still unknown cross section as a parameter were calculated using eq. (1) with eq. (2) and a light source with a gaussian profile with hnewidth deter.
Table
.
.
1
Cross sections, obtained in the present work, compared with the orientation depolarizing cross sections of Pepperl [5]. -________________________
Rare gas
the mean relative velocity of the cadmium and foreign gas atoms, g2/ir the effective cross section for broadening. Eq. (1) describes the experimentally obtained line shape without additional broadening by foreign gases [4]. For detection of the cross sections for line broadening collisions we used the same eq. (1) with the modified damping constant as shown in eq. (2).
-
Cross section for Cd5iP, (X 10—16 cm2) line broadening 31 ± 3 52 ±10 99 ±15 150 ±15
depolarizing [5]
He Ne Ar Kr Xe
212
174
±20
45
±
4
32 ± 3 89 ± 8 117 ± 11 ± 16
241
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
of the light source approximated by p (w) exp k 2] with a spectral distribution ~ X (w w 0) exp[—k(w d)2] with a shift d (k = const.). The calculated level-crossing widths differ from each other on the order of percentages only in the case of [—
—
-05
—
! :~: -2,0
~
2.5
Xe
-30 I
100
200
300
~00
500
600
700
FOREIGN GAS PRESSURE P/TORR
Fig. 3. Normalized logarithm of the saturation intensity of the level-crossing curves as a function of the pressure of the rare gases Xe (0), Kr (A), Ar (0), He (A), and Ne (X). The drawn lines were calculated using the corresponding cross sections of table 1, without taking the shift into account.
mined before. The halfwidth of the computed curves is a linear function of the cross sections. In this way, a definite cross section could be related to an experimentally measured broadening. Table 1 shows the obtained cross sections in comparison with the orientation depolarizing cross sections obtained by Pepper! [5] for the same 5 1P 1 level of Cd. Now we discuss the other collision effect, the shift. If the light source emits a continuum [p(w) = const.] the shift has no influence. But normally in our experiment a Cd lamp with a relatively small line width (0.15 cm~)was used. We calculated how strongly the pressure shift may falsify the value of the cross section for broadening. For this purpose we compared the level-crossing intensity calculated by formula (1) [supplemented by eq. (2)] for a spectral distribution
242
—
a most unfavourable ratio I : 3 of the shift and the broadening. Fig. I shows that simultaneously with the pressure
0
z
—
broadening of the level-crossing signal the intensity of the whole curve decreases. The experimental reduction of the saturation intensity in high magnetic fields is compared with the result of the theory (calculation of eqs. (1) and(2) forB = using the values of table 1 for the measured cross sections without regard00,
ing the shift) in fig. 3. The difference between theoretical and experimental values gives an idea of the order of magnitude of the shift. This is of course no method to determine shift values, but it shows that the small line width of the light source has more effect on the saturation intensity than on the halfwidth of the level-crossing signal. We are indebted to the Bundesministerium für Forschung und Technologie and the Verein Deutscher Ingenieure for helpful support. References [1] W. Hanle, A. Scharmann and P. Wirz, Phys. Lett. 69A (1978) 12. [2] W. Siegmund and A. Scharmann, Z. Phys. A276 (1976) 19.Corney, B.P. Kibble and G.W. Series, Proc. Roy. Soc. [3] A. London A293 (1966) 70. [4] A.V. Durrant and B. Landheer, J. Phys. B4 (1971) 1200. [5] R. Pepperl, Z. Naturforsch. 25a (1970) 927.
PHYSICS LETTERS
26 May 1980
FOREIGN GAS BROADENING OF THE 51P1 LEVEL of Cd ~ W. HANLE, A. SCHARMANN and P. WIRZ’ I. Physikalisches Institut der Justus-Liebig-Universität, D-6300 Giessen, W. Germany Received 12 February 1980
Level crossing in a transverse magnetic field in forward scattering is used to determine broadening cross sections by coffisions between Cd (in the 5 ‘P1 level) and rare gases. Additionally the saturation intensity of the level-crossing curve is investigated as a function of the rare gas pressures.
Recently we reported about the sensitive detection of trace elements by level crossing in forward scattering in a transverse magnetic field [1]. Thereby the sample is vapourized in a graphite furnace and the atomized particles are transported by a rare gas stream into the measuring cell. Therefore the level-crossing curve is broadened by collisions between the atoms of the trace element and the foreign rare gas. The half width of the level-crossing curve yields the cross section for the broadening. The experimental set-up is practically the same as for normal level-crossing experiments forwardinscattering [2]. A chamber with Cd atoms in is placed a transverse magnetic field. The light of an electrodeless discharge Cd lamp, polarized at an angle of 450 to the magnetic field direction, penetrates the chamber with Cd atoms and an analyzer which is crossed with respect to the polarizer. Two different effects occur in the magnetic field, One is the absorption of Zeeman components which is less important at low vapour pressures. The other is the dispersion, where at frequencies at the edges of the absorption linemagnetic the components parallel anddifferperpendicular to the field direction have ent velocities (birefringence) and therefore the outcoming light is elliptically polarized. This causes a brightening between crossed polarizers. Dedicated to Professor Dr.
f
—
with e = (~JIn2e2/mc~)NfL, Z the plasma dispersion function for magnetic field
A. Schraub on the occasion of
his 70th birthday, Part of thesis, Giessen (1979) (D 26).
240
While usually the absorption and dispersion profiles are regarded as a function of the frequency, the level-crossing presentation is the light intensity integrated over all frequencies as a function of the magnetic field. Hereby levels with m = 0 and m = ±1cross at zero field. Contrary to light emission the levels are broade,ned by the Doppler effect and in case additionally by collisions. In our arrangement the measurement chamber was connected with a pump. A valve allowed establishing different rare gas pressures in cell. The Cd-vapour 3 the corresponding to the density was 2.1 X 1010 cm temperature of the Cd reservoir (391 K). Self pressure broadening is negligible at such low densities. Fig. 1 shows three characteristic level-crossing curves in forward scattering of the 5 1P 1S 1 —5 0 transition of Cd, collisionally broadened by neon. The theory for forward scattering experiments was developed by Series et al. [3]. The observed intensity as a function of the transverse magnetic field can be written as: 2 exp [—(Z1 + D)} dw, I = p(o4( sin ~e (Z D)1 (1)
independent components Z
=
Z(~.
0,F, ~),D the plasma dispersion function for magnetic field dependent
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
lOOTorr
0.2
04 06 magnetic field strength B / T
Fig. 1. Broadening of level-crossing curves by collision with neon in forward scattering the Cdofresonance 9 cm3,oflength the cell: 4line cm).228.8 nm (Cd density: 2 X i0
components Z
=
Z(B,
w
0, F, ~),p(w) the spectral distribution of the incoming light, w0 the resonance frequency, B the magnetic field strength, F = the damping constant the 5 ‘P1 level, N the density 3), L theoflength of the measurement of atoms (cm chamber, ~ the natural linewidth, e the elementary charge, c the velocity of light, f the oscillator strength of the observed transition, ~ the Doppler width, and m the electron mass. The foreign gas collisions cause two effects, an increase of the damping constant of the resonance level which manifests itself in a broadening and a frequency shift. Taking collisions into account, the damping constant is: (A \/ A 2 ~ Ir’ _~V~+~V}~ )l~’~ h.1l-~ 15F —
—
—
g
g
— ~
g
with NFg the number of foreign gas particles per cm3, D7’
=
~fL
L IT
I (L_. + \MCd
3O4Xe
1
~11/2
)I
MFg/.j
0
200
600
400
foreign gas pressure p/Tori Fig. 2. Normalized halfwidth (HWHM) collision broadened level-crossing curves as a function of theofgas pressure of the rare gases Xe (0), Kr (i), Ar (0), He drawn lines were fitted by use of the
(s), and Ne (X). The experimental values.
It should be noted that, contrary to level crossing in emission, here the linewidth of the light source is normally not large compared to the level-crossing curve. We proceeded in the following manner: The intensity was measured as a function of the magnetic field with the foreign gas pressure as a parameter (see fig. 1). The experimental result shows that the halfwidth of the level-crossing curve increases linearly with the foreign gas pressure (fig. 2). From this, a broadening factor at a fixed gas pressure was deduced. Then, at the same foreign gas pressure level-crossing curves with the still unknown cross section as a parameter were calculated using eq. (1) with eq. (2) and a light source with a gaussian profile with hnewidth deter.
Table
.
.
1
Cross sections, obtained in the present work, compared with the orientation depolarizing cross sections of Pepperl [5]. -________________________
Rare gas
the mean relative velocity of the cadmium and foreign gas atoms, g2/ir the effective cross section for broadening. Eq. (1) describes the experimentally obtained line shape without additional broadening by foreign gases [4]. For detection of the cross sections for line broadening collisions we used the same eq. (1) with the modified damping constant as shown in eq. (2).
-
Cross section for Cd5iP, (X 10—16 cm2) line broadening 31 ± 3 52 ±10 99 ±15 150 ±15
depolarizing [5]
He Ne Ar Kr Xe
212
174
±20
45
±
4
32 ± 3 89 ± 8 117 ± 11 ± 16
241
Volume 77A, number 4
PHYSICS LETTERS
26 May 1980
of the light source approximated by p (w) exp k 2] with a spectral distribution ~ X (w w 0) exp[—k(w d)2] with a shift d (k = const.). The calculated level-crossing widths differ from each other on the order of percentages only in the case of [—
—
-05
—
! :~: -2,0
~
2.5
Xe
-30 I
100
200
300
~00
500
600
700
FOREIGN GAS PRESSURE P/TORR
Fig. 3. Normalized logarithm of the saturation intensity of the level-crossing curves as a function of the pressure of the rare gases Xe (0), Kr (A), Ar (0), He (A), and Ne (X). The drawn lines were calculated using the corresponding cross sections of table 1, without taking the shift into account.
mined before. The halfwidth of the computed curves is a linear function of the cross sections. In this way, a definite cross section could be related to an experimentally measured broadening. Table 1 shows the obtained cross sections in comparison with the orientation depolarizing cross sections obtained by Pepper! [5] for the same 5 1P 1 level of Cd. Now we discuss the other collision effect, the shift. If the light source emits a continuum [p(w) = const.] the shift has no influence. But normally in our experiment a Cd lamp with a relatively small line width (0.15 cm~)was used. We calculated how strongly the pressure shift may falsify the value of the cross section for broadening. For this purpose we compared the level-crossing intensity calculated by formula (1) [supplemented by eq. (2)] for a spectral distribution
242
—
a most unfavourable ratio I : 3 of the shift and the broadening. Fig. I shows that simultaneously with the pressure
0
z
—
broadening of the level-crossing signal the intensity of the whole curve decreases. The experimental reduction of the saturation intensity in high magnetic fields is compared with the result of the theory (calculation of eqs. (1) and(2) forB = using the values of table 1 for the measured cross sections without regard00,
ing the shift) in fig. 3. The difference between theoretical and experimental values gives an idea of the order of magnitude of the shift. This is of course no method to determine shift values, but it shows that the small line width of the light source has more effect on the saturation intensity than on the halfwidth of the level-crossing signal. We are indebted to the Bundesministerium für Forschung und Technologie and the Verein Deutscher Ingenieure for helpful support. References [1] W. Hanle, A. Scharmann and P. Wirz, Phys. Lett. 69A (1978) 12. [2] W. Siegmund and A. Scharmann, Z. Phys. A276 (1976) 19.Corney, B.P. Kibble and G.W. Series, Proc. Roy. Soc. [3] A. London A293 (1966) 70. [4] A.V. Durrant and B. Landheer, J. Phys. B4 (1971) 1200. [5] R. Pepperl, Z. Naturforsch. 25a (1970) 927.