- Email: [email protected]
Oscillator strengths of Rb quadrupole lines
1. Quant. Spectrose. Radiat. Transfer, Vol. 17, pp. 747-750. Pergamon Press 1977. Printed in Great Britain
OSCILLATOR STRENGTHS OF Rb QUADRUPOLE LINES KAY NIEMAX
Institut fUr Experimentalphysik, Universitat Kiel, Germany (Received 8 November 1976)
Abstract-The oscillator strengths of the forbidden lines of Rb (5 2 S1/2 - n2D"2 and 52S1/2 - n2D"2' 4 S n S 9) have been measured in absorption, The dependence of the oscillator strength on the principal quantum number is qualitatively the same as calculated by WARNER.'I) It was found that the values for the second quadrupole doublet are extremely smalL
L INTRODUCTION
IN ARECENT paper,(2) absorption measurements are described of the oscillator strengths of the quadrupole series of Cs (62Sl/2 - n2D5/2,3/2)' Qualitatively, good agreement was found between these experimental values and theoretical oscillator strengths given by WARNER. (I) Whereas the calculations of the quadrupole oscillator strengths of Cs result in a slow decrease of f-values with increasing principal quantum number, the quadrupole oscillator strengths of Rb should show a special anomaly. According to calculations by Warner, the second forbidden doublet WS./2 - 52D s12 .3/2) has an oscillator strength which should be smaller by a factor of about 3.5 x 103 than that of the first doublet because of a minimum in the radial part of the dipole-moment matrix. On the other hand, the oscillator strength of the third doublet increases again (it is 32.5 times greater than that of the second). For higher series members than the fourth, there is again a slow decrease of oscillator strengths with increasing principal quantum number. The author is aware of only two experimental investigations on this topic [HERTEL and Ross(3) and PROKOP'EV(4)]. In both of these studies, only the first doublet (the fine structure was not resolved) was measured quantitatively. Higher lines were not detected. Hertel and Ross gave an upper limit for the second doublet. It is therefore of interest to perform new measurements to check the theoretical findings. 2, EXP ERIMENT AL DETAILS
The experimental set-up is the same as that described in previous papers.(2.S) A high-pressure Xe lamp (900 W) served as a continuous light source. The parallel light beam made by a quartz lens was sent through the Rb absorption cell. Another quartz lens focused the light onto the entrance slit of a high resolution, 10 m Ebert scanning-monochromator (with optical band pass between 12 and 6 mAl. The light at the exit slit was registered photoelectrically. The signal was amplified by a lock-in amplifier and recorded with a strip-chart recorder. The absorption cells were made of pyrex glass (lengths: 4.9 and 15.6 cm) and of stainless steel with brazed sapphire windows (length: 9.44 cm). The metal-filling procedure is described in detail in Ref. (2). The heating system of the absorption cel1 consisted of two chambers. The upper chamber, in which the observed part of the absorption cell was situated, had a somewhat higher temperature than the lower chamber with the Rb bath in order to prevent rubidium from covering the cell windows. The Rb metal was extremely pure and corresponded to the natural isotopic composition. The equilibrium vapour pressure p [torr] above the liquid metal was calculated from a formula verified by GALLAGHER and LEWIS:(6) log p = 15.8825 - 4529.6/Tb
-
2.991 log Tb + 5.9 X 10-4 Tb ,
where Tb is the absolute temperature of the Rb bath. The concentration of Rb 2 molecules can 747
748
K. NIEMAx
be neglected in the temperature interval used.(1) The rubidium atom density N can be calculated from
where Tc is the temperature in the observed part of the cell. 3. RESULTS AND DISCUSSION
If the measured absorption lines have larger half-widths than the instrumental profile, it is not necessary to make a deconvolution of the true and apparatus profile. The true absorption coefficient k(A) may be directly determined from the measured line, viz.
k(A) = (IlL) In [1o(A)II(A)],
(I)
where Io(A) and I(A) are the wavelength-dependent intensities of the incident and the transmitted light and L is the absorption length. Using the Ladenburg relation (2)
the oscillator strength I can be determined if the particle density N is known. In general, the absorption of the lines was kept very weak (kL ~ 1), so that formula (2) becomes
(3) The absorption profiles for the transitions 52S 1/2 - n 2D 512 and 52S 112 - n 2D3/2 (4:5 n :5 9) have been measured by increasing the particle density up to about 3 x 10 17 cm- 3, which corresponds to a Rb-bath temperature of about 430°C. At each particle density, several scans were made and 2 averaged. Except for the oscillator strengths of the first forbidden doublet WSII2 - 4 D 5I2.3/2), all I-values were determined using only the metal-absorption tube with 9.44 cm absorption length. We used the pyrex absorption cells also for the first doublet. As for the quadrupole lines of CS,(2) no effect of the windows on the absorption data was found. All integrals of the absorption profiles were obtained by planimetry. Table I presents the measured oscillator strengths. Unfortunately, it was not possible to determine the values of the 52 SI/2 - 52D 512 and 52 S1/2 - 52D3/2 lines. Both values are extremely small. Molecular bands, whose absorptions grow with the square of the particle density, appear at the place where the lines should be situated. They did not allow us to observe these lines. The value given in Table 1 should be an upper limit for the oscillator strengths. This was estimated by measuring the absorption under the molecular band structure. The line profiles of the 52 SII2 - 92D512.3/2 lines (fine structure separation about 69 mA) are strongly blended at particle densities where they can be observed (pressure broadening). Therefore the individual data for these lines have higher uncertainty than for the other lines. But the sums of both oscillator strengths are within the normal limits of error. The errors cited in Table 1 are given by the experimental accuracy. The total estimated error should not greatly exceed 20%. Here the error in the vapour-pressure data(6) is included. In addition to the present data, the theoretical oscillator strengths of WARNER(I) and the experimental values of HERTEL and Ross(3) and of PROKOF'Ey(4) are presented in the table. A comparison with the I-values of Warner, which is also given graphically (see Fig. 1), shows good quantitative agreement for the first quadrupole doublet. For higher members of the forbidden series, the course of the series is qualitatively the same. Especially the minimum in the radial part of the dipole-moment matrix for the second quadrupole doublet is verified. Furthermore, the measured ratios of the oscillator strengths 1(5' SII2 - n2 D 512 )11(5 2S 112 - n2 D 3/2 ) are, except for the third doublet, in agreement with the Burger-Dorgelo rule which demands a ratio of 1.5. The reason for the discrepancy in the case of the third doublet is not known. A comparison with the experimental values of HERTEL and Ross(3) (electron impact technique) and PROKOF'EV(4) (hook method) shows that the values for the first doublet given in the present work are smaller by a factor
749
Oscillator strengths of Rb quadrupole lines 10- 5
f
~
Rb: 5 251/2 - n 2D5/2.3/2
10- 6
•
\
WORK
3
0
II II II II
10- 7
-n 2Ds/ 2} ___ THIS - n 2° /2
\ \
-
"
n 20
-n
} 2 5/2 -WARNER 03/2
II
/ ___ -
,'i
1\( II
II
10- 8
//
A_
-e-
-
-A_ _
...
/I~
<.
\, \ II
~U ~
10- 9
"
~I
1O-10'--L--+--t-----t---+---t----j--' 6 8 9
n -----£=0 Fig. I. Plots of the quadrupole oscillator strengths against the principal quantum number.
Table I. Comparison of experimental and theoretical oscillator strengths
()I)
5 2 51 /2-
LINE
4 2°5/2
5165.2
4 2°3/2
5165.1
5 2°5/2
3889.4
?
WARNER (1)
THIS WORK
( 1 . 35
:.1 )-6
(8.98 :.81-
~2
.0
7
1.94- 10
6 2"5/2
3484.6
6 2°3/2
3484.9
(1. 64 ::.2)
7 2°5/2
3301.4
(2.11 :.2) -8
-8
-8
3301.5
(1. 4
:.2)
8 2°5/2
3201.9
(1. 6
::.2)-8
'3202.0
(1. 05 ::.21- 8
3141.5
(7.96 :1.5)-9
3141.6
(5.2
::
1.5
4.08- 6
1.5
<2.72- 7
.0)-9
PROKOF' EV (4)
7.87- 6
9.45- 9
(2.11 ::.2)-8
7 2°3/2
?
6.85- 7
2.91- 10
3889.9
9 -°5/2 2 9 °3/2
1.03- 6 1.5
-9
5 -°3/2
8 2°3/2
HERTEL (3)
1. 29 6.3
1.1 1. 51 7.3
9.0 1. 52 6.0
6.9 1. 53
-9
1.5
-8 -9
1.5
-9 -9
1.5
-9
3.65- 9
1. 89
of about 1.8 and 3.5, respectively. Here the relative transition probability given by Prokof'ev is calibrated with the absolute oscillator strengths for the resonance lines obtained by GALLAGHER and LEWIS(8) from Hanle-effect measurements. The estimate for the oscillator strength of the second doublet given by Hertel and Ross can be reduced by at least two orders of magnitude. In conclusion, it should be noted that the Coulomb approximation including spin-orbit interaction(l) is a useful tool for calculating oscillator strengths of S-D transitions. This conclusion follows also from the recent work on the S-D series of Cs.(2) Acknowledgement-I would like to thank Prof. Dr. J. lJSRT Vol. 17. No. 6-E
RICHTER
for helpful discussions of this work.
750
I. 2. 3. 4. 5. 6. 7. 8.
K. NIEMAX
REFERENCES B. WARNER, Mon. Not. R. Astr. Soc. 139, 115 (1968). K. NIEMAX, JQSRT in press. 1. V. HERTEL and K. J. Ross, 1. Phys. B: Atom. Molec. Phys. 2, 484 (1969). V. K. PROKOP'EV, Z. Phys. 57, 387 (1929); Zhur. eksptl. teoret. Fiz. I, 123 (1931). G. PICHLER, JQSRT 16, 147 (1976). A. GALLAGHER and E. L. LEWIS, J. Opt. Soc. Am. 63, 864 (1973). A. N. NESMEYANOV, Vapour Pressure of the Chemical Elements, p. 445. Elsevier, Amsterdam (1963). A. GALLAGHER and E. L. LEWIS, Phys. Rev. AIO, 231 (1974).
OSCILLATOR STRENGTHS OF Rb QUADRUPOLE LINES KAY NIEMAX
Institut fUr Experimentalphysik, Universitat Kiel, Germany (Received 8 November 1976)
Abstract-The oscillator strengths of the forbidden lines of Rb (5 2 S1/2 - n2D"2 and 52S1/2 - n2D"2' 4 S n S 9) have been measured in absorption, The dependence of the oscillator strength on the principal quantum number is qualitatively the same as calculated by WARNER.'I) It was found that the values for the second quadrupole doublet are extremely smalL
L INTRODUCTION
IN ARECENT paper,(2) absorption measurements are described of the oscillator strengths of the quadrupole series of Cs (62Sl/2 - n2D5/2,3/2)' Qualitatively, good agreement was found between these experimental values and theoretical oscillator strengths given by WARNER. (I) Whereas the calculations of the quadrupole oscillator strengths of Cs result in a slow decrease of f-values with increasing principal quantum number, the quadrupole oscillator strengths of Rb should show a special anomaly. According to calculations by Warner, the second forbidden doublet WS./2 - 52D s12 .3/2) has an oscillator strength which should be smaller by a factor of about 3.5 x 103 than that of the first doublet because of a minimum in the radial part of the dipole-moment matrix. On the other hand, the oscillator strength of the third doublet increases again (it is 32.5 times greater than that of the second). For higher series members than the fourth, there is again a slow decrease of oscillator strengths with increasing principal quantum number. The author is aware of only two experimental investigations on this topic [HERTEL and Ross(3) and PROKOP'EV(4)]. In both of these studies, only the first doublet (the fine structure was not resolved) was measured quantitatively. Higher lines were not detected. Hertel and Ross gave an upper limit for the second doublet. It is therefore of interest to perform new measurements to check the theoretical findings. 2, EXP ERIMENT AL DETAILS
The experimental set-up is the same as that described in previous papers.(2.S) A high-pressure Xe lamp (900 W) served as a continuous light source. The parallel light beam made by a quartz lens was sent through the Rb absorption cell. Another quartz lens focused the light onto the entrance slit of a high resolution, 10 m Ebert scanning-monochromator (with optical band pass between 12 and 6 mAl. The light at the exit slit was registered photoelectrically. The signal was amplified by a lock-in amplifier and recorded with a strip-chart recorder. The absorption cells were made of pyrex glass (lengths: 4.9 and 15.6 cm) and of stainless steel with brazed sapphire windows (length: 9.44 cm). The metal-filling procedure is described in detail in Ref. (2). The heating system of the absorption cel1 consisted of two chambers. The upper chamber, in which the observed part of the absorption cell was situated, had a somewhat higher temperature than the lower chamber with the Rb bath in order to prevent rubidium from covering the cell windows. The Rb metal was extremely pure and corresponded to the natural isotopic composition. The equilibrium vapour pressure p [torr] above the liquid metal was calculated from a formula verified by GALLAGHER and LEWIS:(6) log p = 15.8825 - 4529.6/Tb
-
2.991 log Tb + 5.9 X 10-4 Tb ,
where Tb is the absolute temperature of the Rb bath. The concentration of Rb 2 molecules can 747
748
K. NIEMAx
be neglected in the temperature interval used.(1) The rubidium atom density N can be calculated from
where Tc is the temperature in the observed part of the cell. 3. RESULTS AND DISCUSSION
If the measured absorption lines have larger half-widths than the instrumental profile, it is not necessary to make a deconvolution of the true and apparatus profile. The true absorption coefficient k(A) may be directly determined from the measured line, viz.
k(A) = (IlL) In [1o(A)II(A)],
(I)
where Io(A) and I(A) are the wavelength-dependent intensities of the incident and the transmitted light and L is the absorption length. Using the Ladenburg relation (2)
the oscillator strength I can be determined if the particle density N is known. In general, the absorption of the lines was kept very weak (kL ~ 1), so that formula (2) becomes
(3) The absorption profiles for the transitions 52S 1/2 - n 2D 512 and 52S 112 - n 2D3/2 (4:5 n :5 9) have been measured by increasing the particle density up to about 3 x 10 17 cm- 3, which corresponds to a Rb-bath temperature of about 430°C. At each particle density, several scans were made and 2 averaged. Except for the oscillator strengths of the first forbidden doublet WSII2 - 4 D 5I2.3/2), all I-values were determined using only the metal-absorption tube with 9.44 cm absorption length. We used the pyrex absorption cells also for the first doublet. As for the quadrupole lines of CS,(2) no effect of the windows on the absorption data was found. All integrals of the absorption profiles were obtained by planimetry. Table I presents the measured oscillator strengths. Unfortunately, it was not possible to determine the values of the 52 SI/2 - 52D 512 and 52 S1/2 - 52D3/2 lines. Both values are extremely small. Molecular bands, whose absorptions grow with the square of the particle density, appear at the place where the lines should be situated. They did not allow us to observe these lines. The value given in Table 1 should be an upper limit for the oscillator strengths. This was estimated by measuring the absorption under the molecular band structure. The line profiles of the 52 SII2 - 92D512.3/2 lines (fine structure separation about 69 mA) are strongly blended at particle densities where they can be observed (pressure broadening). Therefore the individual data for these lines have higher uncertainty than for the other lines. But the sums of both oscillator strengths are within the normal limits of error. The errors cited in Table 1 are given by the experimental accuracy. The total estimated error should not greatly exceed 20%. Here the error in the vapour-pressure data(6) is included. In addition to the present data, the theoretical oscillator strengths of WARNER(I) and the experimental values of HERTEL and Ross(3) and of PROKOF'Ey(4) are presented in the table. A comparison with the I-values of Warner, which is also given graphically (see Fig. 1), shows good quantitative agreement for the first quadrupole doublet. For higher members of the forbidden series, the course of the series is qualitatively the same. Especially the minimum in the radial part of the dipole-moment matrix for the second quadrupole doublet is verified. Furthermore, the measured ratios of the oscillator strengths 1(5' SII2 - n2 D 512 )11(5 2S 112 - n2 D 3/2 ) are, except for the third doublet, in agreement with the Burger-Dorgelo rule which demands a ratio of 1.5. The reason for the discrepancy in the case of the third doublet is not known. A comparison with the experimental values of HERTEL and Ross(3) (electron impact technique) and PROKOF'EV(4) (hook method) shows that the values for the first doublet given in the present work are smaller by a factor
749
Oscillator strengths of Rb quadrupole lines 10- 5
f
~
Rb: 5 251/2 - n 2D5/2.3/2
10- 6
•
\
WORK
3
0
II II II II
10- 7
-n 2Ds/ 2} ___ THIS - n 2° /2
\ \
-
"
n 20
-n
} 2 5/2 -WARNER 03/2
II
/ ___ -
,'i
1\( II
II
10- 8
//
A_
-e-
-
-A_ _
...
/I~
<.
\, \ II
~U ~
10- 9
"
~I
1O-10'--L--+--t-----t---+---t----j--' 6 8 9
n -----£=0 Fig. I. Plots of the quadrupole oscillator strengths against the principal quantum number.
Table I. Comparison of experimental and theoretical oscillator strengths
()I)
5 2 51 /2-
LINE
4 2°5/2
5165.2
4 2°3/2
5165.1
5 2°5/2
3889.4
?
WARNER (1)
THIS WORK
( 1 . 35
:.1 )-6
(8.98 :.81-
~2
.0
7
1.94- 10
6 2"5/2
3484.6
6 2°3/2
3484.9
(1. 64 ::.2)
7 2°5/2
3301.4
(2.11 :.2) -8
-8
-8
3301.5
(1. 4
:.2)
8 2°5/2
3201.9
(1. 6
::.2)-8
'3202.0
(1. 05 ::.21- 8
3141.5
(7.96 :1.5)-9
3141.6
(5.2
::
1.5
4.08- 6
1.5
<2.72- 7
.0)-9
PROKOF' EV (4)
7.87- 6
9.45- 9
(2.11 ::.2)-8
7 2°3/2
?
6.85- 7
2.91- 10
3889.9
9 -°5/2 2 9 °3/2
1.03- 6 1.5
-9
5 -°3/2
8 2°3/2
HERTEL (3)
1. 29 6.3
1.1 1. 51 7.3
9.0 1. 52 6.0
6.9 1. 53
-9
1.5
-8 -9
1.5
-9 -9
1.5
-9
3.65- 9
1. 89
of about 1.8 and 3.5, respectively. Here the relative transition probability given by Prokof'ev is calibrated with the absolute oscillator strengths for the resonance lines obtained by GALLAGHER and LEWIS(8) from Hanle-effect measurements. The estimate for the oscillator strength of the second doublet given by Hertel and Ross can be reduced by at least two orders of magnitude. In conclusion, it should be noted that the Coulomb approximation including spin-orbit interaction(l) is a useful tool for calculating oscillator strengths of S-D transitions. This conclusion follows also from the recent work on the S-D series of Cs.(2) Acknowledgement-I would like to thank Prof. Dr. J. lJSRT Vol. 17. No. 6-E
RICHTER
for helpful discussions of this work.
750
I. 2. 3. 4. 5. 6. 7. 8.
K. NIEMAX
REFERENCES B. WARNER, Mon. Not. R. Astr. Soc. 139, 115 (1968). K. NIEMAX, JQSRT in press. 1. V. HERTEL and K. J. Ross, 1. Phys. B: Atom. Molec. Phys. 2, 484 (1969). V. K. PROKOP'EV, Z. Phys. 57, 387 (1929); Zhur. eksptl. teoret. Fiz. I, 123 (1931). G. PICHLER, JQSRT 16, 147 (1976). A. GALLAGHER and E. L. LEWIS, J. Opt. Soc. Am. 63, 864 (1973). A. N. NESMEYANOV, Vapour Pressure of the Chemical Elements, p. 445. Elsevier, Amsterdam (1963). A. GALLAGHER and E. L. LEWIS, Phys. Rev. AIO, 231 (1974).