- Email: [email protected]
Determination of natural radiative lifetimes for highly excited P states in rubidium
Volume 59A, number 1
PHYSICS LETTERS
1 November 1976
DETERMINATION OF NATURAL RADIATIVE LIFETIMES FOR HIGHLY EXCITED P STATES IN RUBIDIUM F. GOUNAND, P.R. FOURNIER, J. CUVELLIER and J. BERLANDE Centre d’Etudes Nucle’aires de Saclay, Service de Physique Atomique, B.P. no. 2, 911 90, Gif-sur-Yvette, France Received 23 August 1976 The natural radiative lifetimes of highly excited (12 ~ n ~ 22) P states in rubidium have been measured. They exhibit a near-hydrogenic behaviour with, however, some deviation of the absolute values from the available theoretical calculations.
The development of tunable dye-lasers permits numerous studies concerning highly excited states, which are inaccessible when using conventional light sources. In particular, radiative lifetime measurements of some of the Rydberg states of the alkali atoms have been made [1, 2] allowing interesting comparisons with theoretical calculations. Most of these works deal with S and D states, optically pumped using step-wise excitation. We present here an experimental study concerning Rydberg P states of rubidium for which few results are available. The experimental set-up is shown schematically in fig. 1. The P levels are directly populated using a nitrogen-pumped dye laser (Rhodamine B) associated with an extra-cavity frequency doubling device. The U.V. pulses from the dye-laser have a half-width of 3 ns.
~
1)
(106 s-
0.5
,
______
____________
Cell
Dye Laser I
/
.
I____________
II
/
Mono-
chromator
L PM
/ Amplificator Discriminator
/
/
/ /~ p~pis 1
•~f’l(~
fl
Computer
Ll_ MuLtichanneL Analyser
Fig. 2. Experimental plot of the inverse of the observed lifetime versus rubidium pressure for the 14 P level.
The line width is about 0.3 A and the repetition rate usually 30 Hz. The experimental cell is set in an oven (T = 460 K) and connected by a capillary to a vacuum or gas filling system. After a typical baking procedure the residual pressure is about 5 X iO~T. Liquid rubidium arm, the temperature of which canisbelocated variedin bya aside separate heating system. We
uV
I ~A
NRb (1012 cm3)
j
observe the population of a given nP level, after the laser excitation, by looking at the direct fluorescence of the (nP -÷ 4D) transition. A high-speed photon counting system associated with a multichannel analyser (with time resolution variable from 40 ns up to 1 ps) allows the determination of the decay of the cxcited state population as a function of time for a given rubidium pressure. The extrapolation to zero rubidium pressure yields the natural radiative lifetime (fig. 2). The method as well as the results concerning the collisional processes will be discussed elsewhere [3] The working rubidium pressures are in the range 8 X 106 to 1 0—~T. Radiation trapping is absent as the termi.
Fig. 1. Experimental set-up
23
Volume 59A, number 1
PHYSICS LETTERS
Table 1 Experimental and theoretical lifetime values for P-states in rubidium —~
density, which is determined from the temperature of the side-arm containing the liquid rubidium [6]. We verified that density measurements were in agreement
Radiative lifetime (x 106 s)
with
Experiment Theory (ref. (7]) cannot 1.55 ±0.20 2.22 2.60 ±0.40 3.95 6.40 ±1.30 7.93 14.0 ±5.0 19.2
fects (pile-up and statistics). The experimental data are fit using classical least-square procedures. The re-
State
12 P 14 P 17 P 22 P
1 November 1976
-
nal state of the observed transitions is not the ground state. Numerous checks are made to ensure that the following parameters have a negligible influence on the results obtained: laser line-width, power in the excitation pulse [4], polarization [5] diffusion time of the atoms during the observation. A detailed discussion of these checks will be found in ref. [3]. The major uncertainty is in the determination of the rubidium ,
/,
t(10~sl
those obtained by absorption measurements of the resonance line in the cell for pressures greater than 6 X l0~ T. Because of experimental conditions we maice absorption measurements at lower pressures. The other uncertainties are due to counting ef.
sults are given in table 1. The lifetimes plotted against the effective quantum number n~are shown in a loglog plot in fig. 3. The variation predicted by the quanturn defect theory r = r0(n*)3 is quite well satisfied; we obtain r = TO(n*)x with r 0 = 1 .5 ±0.2 ns and x = 3.1 ±0.2. However, substantial deviation is found between our lifetimes and the available theoretical results [7, 8] Similar deviations were recently observed for the S and D states of rubidium and cesium [9] which, on the other hand, are not observed in the sodium case. It seems therefore that more sophisticated calculations, probably including spin-orbit and core polarization effects, would be needed to permit .
a valuable comparison with the observed results.
/~/
References
/‘I
10
[1] S. Svanberg and P. Tsekeris, Phys. Rev. A 11(1975)1125 and references therein. [2] T.F. Gallagher, S.A. Edelstein and R.M. Hill, Phys. Rev. A 11(1975)1504. [3] 1. Gounand, P.R. Fournier and J. Berlande, to be published. [4] M. Gross, C. Fabre, P. Pillet and S. Haroche, Phys. Rev. Lett. 36(1976)1035. [5] J.S. Deech, R. Luypaert and G.W. Series, 1. Phys. B 8 (1975) 1406.
/
/
5
/
r
/
/_~,/
/4 /9 /
/~/ I,
1
1 -/
10
15
20
25
—
Fig. 3. Log-log plot of the P-state lifetimes for rubidium versus the effective quantum number. The broken line represents the experimental results, the solid one the theoretical results of ref. [7] (which are closed to those obtained from ref. [8]).
24
[6] A.N. Nesmeyanov, Vapor pressure of the elements (Academic Press, New York, 1963). [7] F.M. Anderson and V.A. Zilitis, Opt. Spectrosc. 16 (1964) 211. [8] D.R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) 242 (1949) 101. [9] H. Lundberg and S. Svanberg, Phys. Lett. 56A (1976) 31.
PHYSICS LETTERS
1 November 1976
DETERMINATION OF NATURAL RADIATIVE LIFETIMES FOR HIGHLY EXCITED P STATES IN RUBIDIUM F. GOUNAND, P.R. FOURNIER, J. CUVELLIER and J. BERLANDE Centre d’Etudes Nucle’aires de Saclay, Service de Physique Atomique, B.P. no. 2, 911 90, Gif-sur-Yvette, France Received 23 August 1976 The natural radiative lifetimes of highly excited (12 ~ n ~ 22) P states in rubidium have been measured. They exhibit a near-hydrogenic behaviour with, however, some deviation of the absolute values from the available theoretical calculations.
The development of tunable dye-lasers permits numerous studies concerning highly excited states, which are inaccessible when using conventional light sources. In particular, radiative lifetime measurements of some of the Rydberg states of the alkali atoms have been made [1, 2] allowing interesting comparisons with theoretical calculations. Most of these works deal with S and D states, optically pumped using step-wise excitation. We present here an experimental study concerning Rydberg P states of rubidium for which few results are available. The experimental set-up is shown schematically in fig. 1. The P levels are directly populated using a nitrogen-pumped dye laser (Rhodamine B) associated with an extra-cavity frequency doubling device. The U.V. pulses from the dye-laser have a half-width of 3 ns.
~
1)
(106 s-
0.5
,
______
____________
Cell
Dye Laser I
/
.
I____________
II
/
Mono-
chromator
L PM
/ Amplificator Discriminator
/
/
/ /~ p~pis 1
•~f’l(~
fl
Computer
Ll_ MuLtichanneL Analyser
Fig. 2. Experimental plot of the inverse of the observed lifetime versus rubidium pressure for the 14 P level.
The line width is about 0.3 A and the repetition rate usually 30 Hz. The experimental cell is set in an oven (T = 460 K) and connected by a capillary to a vacuum or gas filling system. After a typical baking procedure the residual pressure is about 5 X iO~T. Liquid rubidium arm, the temperature of which canisbelocated variedin bya aside separate heating system. We
uV
I ~A
NRb (1012 cm3)
j
observe the population of a given nP level, after the laser excitation, by looking at the direct fluorescence of the (nP -÷ 4D) transition. A high-speed photon counting system associated with a multichannel analyser (with time resolution variable from 40 ns up to 1 ps) allows the determination of the decay of the cxcited state population as a function of time for a given rubidium pressure. The extrapolation to zero rubidium pressure yields the natural radiative lifetime (fig. 2). The method as well as the results concerning the collisional processes will be discussed elsewhere [3] The working rubidium pressures are in the range 8 X 106 to 1 0—~T. Radiation trapping is absent as the termi.
Fig. 1. Experimental set-up
23
Volume 59A, number 1
PHYSICS LETTERS
Table 1 Experimental and theoretical lifetime values for P-states in rubidium —~
density, which is determined from the temperature of the side-arm containing the liquid rubidium [6]. We verified that density measurements were in agreement
Radiative lifetime (x 106 s)
with
Experiment Theory (ref. (7]) cannot 1.55 ±0.20 2.22 2.60 ±0.40 3.95 6.40 ±1.30 7.93 14.0 ±5.0 19.2
fects (pile-up and statistics). The experimental data are fit using classical least-square procedures. The re-
State
12 P 14 P 17 P 22 P
1 November 1976
-
nal state of the observed transitions is not the ground state. Numerous checks are made to ensure that the following parameters have a negligible influence on the results obtained: laser line-width, power in the excitation pulse [4], polarization [5] diffusion time of the atoms during the observation. A detailed discussion of these checks will be found in ref. [3]. The major uncertainty is in the determination of the rubidium ,
/,
t(10~sl
those obtained by absorption measurements of the resonance line in the cell for pressures greater than 6 X l0~ T. Because of experimental conditions we maice absorption measurements at lower pressures. The other uncertainties are due to counting ef.
sults are given in table 1. The lifetimes plotted against the effective quantum number n~are shown in a loglog plot in fig. 3. The variation predicted by the quanturn defect theory r = r0(n*)3 is quite well satisfied; we obtain r = TO(n*)x with r 0 = 1 .5 ±0.2 ns and x = 3.1 ±0.2. However, substantial deviation is found between our lifetimes and the available theoretical results [7, 8] Similar deviations were recently observed for the S and D states of rubidium and cesium [9] which, on the other hand, are not observed in the sodium case. It seems therefore that more sophisticated calculations, probably including spin-orbit and core polarization effects, would be needed to permit .
a valuable comparison with the observed results.
/~/
References
/‘I
10
[1] S. Svanberg and P. Tsekeris, Phys. Rev. A 11(1975)1125 and references therein. [2] T.F. Gallagher, S.A. Edelstein and R.M. Hill, Phys. Rev. A 11(1975)1504. [3] 1. Gounand, P.R. Fournier and J. Berlande, to be published. [4] M. Gross, C. Fabre, P. Pillet and S. Haroche, Phys. Rev. Lett. 36(1976)1035. [5] J.S. Deech, R. Luypaert and G.W. Series, 1. Phys. B 8 (1975) 1406.
/
/
5
/
r
/
/_~,/
/4 /9 /
/~/ I,
1
1 -/
10
15
20
25
—
Fig. 3. Log-log plot of the P-state lifetimes for rubidium versus the effective quantum number. The broken line represents the experimental results, the solid one the theoretical results of ref. [7] (which are closed to those obtained from ref. [8]).
24
[6] A.N. Nesmeyanov, Vapor pressure of the elements (Academic Press, New York, 1963). [7] F.M. Anderson and V.A. Zilitis, Opt. Spectrosc. 16 (1964) 211. [8] D.R. Bates and A. Damgaard, Phil. Trans. Roy. Soc. (London) 242 (1949) 101. [9] H. Lundberg and S. Svanberg, Phys. Lett. 56A (1976) 31.