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Oscillator strengths of the first forbidden lines of rubidium
Quant. Spectros¢. Radiat. Transfer VoL 20, pp. 327-329 © Pergamon Press Ltd., 1978. Printed in Great Britain
0022-.4073f7810901-0Y271$02.00/0
OSCILLATOR STRENGTHS OF THE FIRST FORBIDDEN LINES OF RUBIDIUM? JOSEPH NIt.SEN and JACK ~RLING University of California Lawrence Livermore Laboratory, Livermore, CA 94550, U.S.A. (Received 23 March 1978)
Abstract--The oscillator strengths of the 5s-4d first forbidden lines of rubidium at 5165.~ were determined by performing CW tunable dye laser absorption measurements. Measured oscillator strengths of 8.06+ 0.48 × 10.7 and 5.38-+0.31 × 10-~ for the 2D5/2and ~D~/2states, respectively, are compared with previously published values. 1. INTRODUCTION
OSCILLATORstrengths of the forbidden lines of the alkali metals provide important checks on the validity of various theoretical models in atomic physics. Considerable discrepancy presently exists between experimental values and theoretical oscillator strengths. The advent of tunable dye lasers has provided a powerful technique for studying the weak quadrupole transitions of the alkali metals. Work is presented on the first forbidden lines (5s2Sj/2- 4d2Ds/2,3/2)of rubidium, which yields oscillator strengths somewhat lower than previous experimental measurements by NIE~O~x,°> but in reasonable a~eement with theoretical calculations by WARNER..2~ 2. EXPERIMENTAL RESULTS
The optical system is shown schematically in Fig. 1. The output of a tunable dye laser was split into two beams which were modulated at different frequencies by a chopper wheel. One beam, whose intensity was reduced well below the saturation intensity of the system, was transmitted through the absorption cell. The other beam served as a reference signal. Both signals were detected by a photodiode and amplified by lock-in amplifiers. These signals were divided in a ratiometer to correct for any small variations in the laser output during a measurement and were then recorded on a strip chart recorder. The absorption cell was made of pyrex glass (length 15.95 cm). The cell was evacuated to 8 × 10-6 torr, filled with Rb in a glove box backfilled with argon, and re-evacuated.
Argon pumplaser
Ratio- L meter J I
recorder / Fig. i. Diagrams of the experimental setup for measurements of rubidium absorption at 5165 ~,. tWork performed under the auspices of the U.S. Department of Energy, Contract No. W-7405-Eng-48. 327
328
J. NILSEN and J. MARLING
The heating system consisted of a tubular oven with four separate heating elements. The absorption cell was maintained at a slightly higher temperature than the Rb bath in order to inhibit condensation on the windows. The temperatures of both the cell and the Rb bath were carefully monitored with seven precision thermocouples to an accuracy of I*K. The equilibrium vapor pressure p above the liquid Rb was calculated from a formula verified by GALLAGHERand LEWIS,(3) namely log p = 15.8825
4529.6
Tb
2.991 log To + 5.9(10-4)Tb,
where Tb is the absolute temperature of the Rb bath and p is in torr. The Rb2 molecular density is small compared to the Rb atom density in the 275-303*C temperature interval used in this experiment; for example, Rb2 = 0.6% Rb at 300"C,<4)thus permitting absorption due to Rbz to be neglected. The Rb-atom density N can be calculated from N = 9.66 x 10t8 (p]To), where Tc is the average temperature in the absorption cell. During the course of any measurements, the temperatures were kept constant to within I°K. The CW dye laser was tuned through the Rb resonances by slowly rotating a 0.5 mm thick intracavity solid etalon. The laser bandwidth was 40 m~. A typical absorption spectrum obtained by this procedure is shown in Fig. 2, which illustrates Rb absorption at 5165 A at 303°C on its two fine structure lines. 3. RESULTS The absolute oscillator strengths were measured for the 5s 2S112-4d2Dm and 5s ZSl124d2Dsi2transitions. The absorption coefficient k(•) is determined for the measured line from the relation k ( X ) = 1 In
-
[Io(X)lI(X)],
Reference signal
- Transmitted intensity divided by reference [ signal I-Line assumed to be ~100% transmission
1.00
•-~ 0.75 ._= 0.50 E rr
0.25
5165.30
5165.20
5165.10
5165.00
5164.90
Wavelength - A (A)
Fig. 2. Typicalexample of experimentaldata for the determinationof rubidium oscillator strengths. The upper trace is the dye-laser signal as it is tuned near 5165~. The lower trace is the transmitted signal through 15.95cm of rubidium vaporat 319.5°C cell temperature,303.3°Cside-armtemperature.
329
Oscillator strengths of the first forbidden lines of rubidium Table 1. The oscillator strengths listed in this table have been multiplied by 107. Lower Energy State
Line Ce ter, ~
4d 2D5/2
5165.18
8.065.48
4d 2D3/2
5]65.06
5.38±.31
Present Work
Warner(21 Niemax(]) 10.3
Hertel(5] Prokof,ev(6~
13.5±.I 40.8
6.85
78.7
8.98±.8
where Io(A) and I(A) are the wavelength-dependent intensities of the incident and transmitted light a n d L is the absorption length. After integrating for line absorption, the Ladenburg relation f k(A) dA = (¢re2/mc2)Ao2N(T)f is used to determine the oscillator strength/. A dozen measurements were made over the temperature range 275-303°C for each line and averaged to determine /. There was no observed dependence of / on temperature. The measured oscillator strengths are presented in Table 1. In addition to the present results, the theoretical oscillator strength of W~NF,R(2~ and the experimental results of NIE~X, ") HERTEL and Ross, (5) and PROKOF'EV(6) are also shown. The errors cited in Table 1 are given as the standard deviations for the total number of measurements made during the experiments. The total experimental error is ~ 10%. Comparisons with the experimental values of NIEMAX(t) (who used a scanning monochromator), HF~TEL and Ross(s) (inelastic electron scattering), and PROKOF'EV~6) (hook method) show that the oscillator strengths given in the present work are smaller by a factor of 1.7, 3.0 and 5.9, respectively. The theoretical calculations of W ~ E R t2~ are in excellent agreement with the present work. The new results presented in this paper are a strong indication that the Coulomb approximation, including spin-orbit interaction, is a valid method for calculating oscillator strengths of S - D transitions. Acknowledgement--Oneof the authors (J.N.) wishes to thank KAYNiEM.~Xfor helpful conversations. REFERENCES I. K. NIEI~/AX,JQSRT 17, 747 0977). 2. B. WARNER,Mon. Not. R. Astr. Soc. 139, 115 (1968). 3. A. GALLAGHERand E. L. LEws, Phys. Rev. AI0, 231 (1974). 4. AN. N. NESMEYANOV,VaporPressureof the Elements, p. 443. AcademicPress, New York (1963). 5. I. V. HERTELand K. J. Ross, J. Phys. B: Atom. Molec. Phys. 2, 484 (1969). 6. V. K. PROKOF'~,Z. Phys. $7, 387 (1929); Zhur. eksptl, theoret, lqz. 1, 123 (1931).
0022-.4073f7810901-0Y271$02.00/0
OSCILLATOR STRENGTHS OF THE FIRST FORBIDDEN LINES OF RUBIDIUM? JOSEPH NIt.SEN and JACK ~RLING University of California Lawrence Livermore Laboratory, Livermore, CA 94550, U.S.A. (Received 23 March 1978)
Abstract--The oscillator strengths of the 5s-4d first forbidden lines of rubidium at 5165.~ were determined by performing CW tunable dye laser absorption measurements. Measured oscillator strengths of 8.06+ 0.48 × 10.7 and 5.38-+0.31 × 10-~ for the 2D5/2and ~D~/2states, respectively, are compared with previously published values. 1. INTRODUCTION
OSCILLATORstrengths of the forbidden lines of the alkali metals provide important checks on the validity of various theoretical models in atomic physics. Considerable discrepancy presently exists between experimental values and theoretical oscillator strengths. The advent of tunable dye lasers has provided a powerful technique for studying the weak quadrupole transitions of the alkali metals. Work is presented on the first forbidden lines (5s2Sj/2- 4d2Ds/2,3/2)of rubidium, which yields oscillator strengths somewhat lower than previous experimental measurements by NIE~O~x,°> but in reasonable a~eement with theoretical calculations by WARNER..2~ 2. EXPERIMENTAL RESULTS
The optical system is shown schematically in Fig. 1. The output of a tunable dye laser was split into two beams which were modulated at different frequencies by a chopper wheel. One beam, whose intensity was reduced well below the saturation intensity of the system, was transmitted through the absorption cell. The other beam served as a reference signal. Both signals were detected by a photodiode and amplified by lock-in amplifiers. These signals were divided in a ratiometer to correct for any small variations in the laser output during a measurement and were then recorded on a strip chart recorder. The absorption cell was made of pyrex glass (length 15.95 cm). The cell was evacuated to 8 × 10-6 torr, filled with Rb in a glove box backfilled with argon, and re-evacuated.
Argon pumplaser
Ratio- L meter J I
recorder / Fig. i. Diagrams of the experimental setup for measurements of rubidium absorption at 5165 ~,. tWork performed under the auspices of the U.S. Department of Energy, Contract No. W-7405-Eng-48. 327
328
J. NILSEN and J. MARLING
The heating system consisted of a tubular oven with four separate heating elements. The absorption cell was maintained at a slightly higher temperature than the Rb bath in order to inhibit condensation on the windows. The temperatures of both the cell and the Rb bath were carefully monitored with seven precision thermocouples to an accuracy of I*K. The equilibrium vapor pressure p above the liquid Rb was calculated from a formula verified by GALLAGHERand LEWIS,(3) namely log p = 15.8825
4529.6
Tb
2.991 log To + 5.9(10-4)Tb,
where Tb is the absolute temperature of the Rb bath and p is in torr. The Rb2 molecular density is small compared to the Rb atom density in the 275-303*C temperature interval used in this experiment; for example, Rb2 = 0.6% Rb at 300"C,<4)thus permitting absorption due to Rbz to be neglected. The Rb-atom density N can be calculated from N = 9.66 x 10t8 (p]To), where Tc is the average temperature in the absorption cell. During the course of any measurements, the temperatures were kept constant to within I°K. The CW dye laser was tuned through the Rb resonances by slowly rotating a 0.5 mm thick intracavity solid etalon. The laser bandwidth was 40 m~. A typical absorption spectrum obtained by this procedure is shown in Fig. 2, which illustrates Rb absorption at 5165 A at 303°C on its two fine structure lines. 3. RESULTS The absolute oscillator strengths were measured for the 5s 2S112-4d2Dm and 5s ZSl124d2Dsi2transitions. The absorption coefficient k(•) is determined for the measured line from the relation k ( X ) = 1 In
-
[Io(X)lI(X)],
Reference signal
- Transmitted intensity divided by reference [ signal I-Line assumed to be ~100% transmission
1.00
•-~ 0.75 ._= 0.50 E rr
0.25
5165.30
5165.20
5165.10
5165.00
5164.90
Wavelength - A (A)
Fig. 2. Typicalexample of experimentaldata for the determinationof rubidium oscillator strengths. The upper trace is the dye-laser signal as it is tuned near 5165~. The lower trace is the transmitted signal through 15.95cm of rubidium vaporat 319.5°C cell temperature,303.3°Cside-armtemperature.
329
Oscillator strengths of the first forbidden lines of rubidium Table 1. The oscillator strengths listed in this table have been multiplied by 107. Lower Energy State
Line Ce ter, ~
4d 2D5/2
5165.18
8.065.48
4d 2D3/2
5]65.06
5.38±.31
Present Work
Warner(21 Niemax(]) 10.3
Hertel(5] Prokof,ev(6~
13.5±.I 40.8
6.85
78.7
8.98±.8
where Io(A) and I(A) are the wavelength-dependent intensities of the incident and transmitted light a n d L is the absorption length. After integrating for line absorption, the Ladenburg relation f k(A) dA = (¢re2/mc2)Ao2N(T)f is used to determine the oscillator strength/. A dozen measurements were made over the temperature range 275-303°C for each line and averaged to determine /. There was no observed dependence of / on temperature. The measured oscillator strengths are presented in Table 1. In addition to the present results, the theoretical oscillator strength of W~NF,R(2~ and the experimental results of NIE~X, ") HERTEL and Ross, (5) and PROKOF'EV(6) are also shown. The errors cited in Table 1 are given as the standard deviations for the total number of measurements made during the experiments. The total experimental error is ~ 10%. Comparisons with the experimental values of NIEMAX(t) (who used a scanning monochromator), HF~TEL and Ross(s) (inelastic electron scattering), and PROKOF'EV~6) (hook method) show that the oscillator strengths given in the present work are smaller by a factor of 1.7, 3.0 and 5.9, respectively. The theoretical calculations of W ~ E R t2~ are in excellent agreement with the present work. The new results presented in this paper are a strong indication that the Coulomb approximation, including spin-orbit interaction, is a valid method for calculating oscillator strengths of S - D transitions. Acknowledgement--Oneof the authors (J.N.) wishes to thank KAYNiEM.~Xfor helpful conversations. REFERENCES I. K. NIEI~/AX,JQSRT 17, 747 0977). 2. B. WARNER,Mon. Not. R. Astr. Soc. 139, 115 (1968). 3. A. GALLAGHERand E. L. LEws, Phys. Rev. AI0, 231 (1974). 4. AN. N. NESMEYANOV,VaporPressureof the Elements, p. 443. AcademicPress, New York (1963). 5. I. V. HERTELand K. J. Ross, J. Phys. B: Atom. Molec. Phys. 2, 484 (1969). 6. V. K. PROKOF'~,Z. Phys. $7, 387 (1929); Zhur. eksptl, theoret, lqz. 1, 123 (1931).