IOP PUBLISHING
PHYSICA SCRIPTA
Phys. Scr. 76 (2007) 577–592
doi:10.1088/0031-8949/76/5/028
Oscillator strength measurements
in Pr II with the fast-ion-beam
laser-induced-fluorescence technique
R Li1 , R Chatelain2 , R A Holt1 , S J Rehse3 , S D Rosner1 and T J Scholl1
1
Department of Physics and Astronomy, University of Western Ontario, London, ON, N6A 3K7, Canada
Department of Physics, McGill University, Montréal, QC, H3A 2T8, Canada
3
Department of Physics and Astronomy, Wayne State University, Detroit, MI, 48202, USA
2
E-mail: rosner@uwo.ca
Received 25 May 2007
Accepted for publication 10 September 2007
Published 16 October 2007
Online at stacks.iop.org/PhysScr/76/577
Abstract
The spontaneous-emission branching fractions of 32 levels of Pr II were measured by the
fast-ion-beam laser-induced-fluorescence technique. The levels studied had energies from
∼21 500 to ∼29 000 cm−1 , and the decay branches detected were in the range from 250 to
850 nm. The experimental uncertainties are within 10%. Using our previously measured
radiative lifetimes, we determined the Einstein A coefficients and oscillator strengths for 260
transitions. The results are important for stellar elemental abundance determinations.
PACS numbers: 32.70.Cs, 32.70.Fw, 95.30.Ky
1. Introduction
The study of lanthanide (rare-earth) elements in stellar
photospheres is important in increasing our understanding of
nucleosynthesis, and the mechanisms which move elements
between the core of a star and its surface. The lanthanides
are particularly useful because they constitute a continuous
sequence of atomic numbers, and their spectra fall in similar
wavelength ranges, yet the nucleosynthesis pathways leading
to the formation of the many different stable isotopes can
be quite different. In his extensive review of the lanthanide
elements in stellar spectra [1], Wahlgren pointed out the
importance of metal-poor galactic halo stars in testing models
of nucleosynthesis that proceed via the r- (rapid) and s- (slow)
neutron capture processes. In a recent study of these stars,
abundances of singly-ionized La, Eu, Dy and Nd were used
to infer an inhomogeneous distribution of neutron-capture
elements in the early interstellar medium [2]. Lanthanide
elements are also found in the Sun, and in chemically
peculiar (CP) stars of the upper main sequence, where their
abundance is high compared to solar values. In CP stars
with measurable magnetic-field effects, the abundances of the
lanthanide elements are among the most enhanced. Strasser
et al [3] have studied the strengths and line profiles of Pr, Nd,
and other elements in the slowly rotating Ap star HD 187474
in order to model their abundance distributions over the stellar
0031-8949/07/050577+16$30.00
surface and test a previously derived magnetic field geometry.
Lanthanides are also important in the comparison of solar and
meteoritic elemental abundances, which have often been taken
to be the same [4].
Laboratory measurement of oscillator strengths
(f -values) is of prime importance in inferring abundances. As
astrophysical models become more detailed, improving the
accuracy of f -values becomes more important. For example,
it is expected that systematic differences between solar and
meteoritic abundances should exist because of selective
diffusion of elements to and from the visible photosphere, but
higher accuracy is required to observe this effect [4].
In the 1930s, Meggers et al began a program of intensity
measurements at the US National Bureau of Standards that
led to a number of monographs listing intensities [5, 6]
and oscillator strengths [7]. The accuracy of the oscillator
strengths was limited by the assumptions about local
thermodynamic equilibrium, rate of entry and exit of atoms
from the discharge, and negligible self-absorption. The overall
uncertainty in log g f (where f is the absorption oscillator
strength and g is the multiplicity 2J + 1 of the lower state)
was estimated as a standard deviation varying from 0.24 to
0.29 as the upper-level term energy varied from 1.5 × 104 to
5.0 × 104 cm−1 , corresponding to a factor of error of 1.7–2.0
in g f .
© 2007 The Royal Swedish Academy of Sciences
Printed in the UK
577
R Li et al
A more accurate approach to determining oscillator
strengths is to combine data on the branching fractions
(BFs) for all transitions from a given level with a
value for the spontaneous emission lifetime of that level.
Lage and Whaling [8] measured BFs in a hollowcathode discharge and incorporated the beam-foil lifetime
measurements of Andersen and Sorensen [9] to obtain
oscillator strengths for transitions from five levels of Pr II.
Kurucz and Bell [10] have compiled experimental oscillator
strengths in a form which is available online (http://cfawww.harvard.edu/amp/ampdata/kurucz23/sekur.html) using
the data of Lage and Whaling, BFs from the intensity
measurements of Meggers et al, together with experimental
lifetime data. Goly et al [11] obtained BF values for 62 Pr
II transitions by measuring the emission from a ferroelectric
plasma source. Using Fourier transform spectrometry and
previously measured lifetimes, Ivarsson et al [12] determined
oscillator strength values for 31 lines of Pr II in
the 280–800 nm range. Biémont et al [13] performed
relativistic Hartree–Fock (HFR) calculations of BFs for
24 levels and combined them with their own timeresolved laser-induced-fluorescence lifetime measurements
to calculate oscillator strengths for ∼150 transitions;
these are available online from the DREAM database
(http://w3.umh.ac.be/∼astro/dream.shtml).
In the present work, we have carried out a measurement
of BFs of Pr II for all levels whose lifetimes we determined
in a previous study [14]. The use of a laser/fast-ion-beam
method enables highly selective excitation of ions to the level
of interest. The resulting uncluttered fluorescence spectrum
contains only transitions that emanate from that common
upper level, so it is impossible to mistakenly include branches
that belong to other upper levels. The combination of the
previously measured lifetimes with the BFs measured here
produces oscillator strengths with experimental uncertainties
of ∼10% arising mainly from the calibration of the
optical response of our detector system as a function of
wavelength.
2. Experimental method
In our apparatus, Pr+ ions are produced by surface ionization
on a hot tungsten filament in a modified Danfysik 911A
source. The ion source contains only Pr vapor produced by
a small, electrically heated oven, and there is no discharge.
Under such conditions, ions can be produced in metastable
states with energies up to several 1000 cm−1 ; in this work
we utilized metastable ions with energies up to 5079 cm−1 .
After acceleration to 10 keV, the ions are focused and massfiltered by a Wien filter before being electrostatically deflected
to merge collinearly with a counter-propagating laser beam.
The collinear geometry creates kinematic compression [15] of
the Doppler width to ∼150 MHz, which increases the signal
size and makes the excitation process more selective. The ion
current, typically ∼100 nA, is detected by a Faraday cup with
secondary-electron suppression.
The single-frequency laser beam is produced by an argonion-pumped Coherent 699–21 dye laser using Stilbene 3 dye,
which has a nominal single-frequency tuning curve from 415
to 465 nm. Given the metastable energy range of the ions, we
578
can study all excited levels from ∼21 500 to ∼29 000 cm−1
for Pr II, except for some levels whose lifetimes are too
long to provide sufficient signal in our detection apparatus.
The laser wavelength is determined to ∼1 part in 107
with a traveling-mirror Michelson interferometer using a
polarization-stabilized reference helium-neon laser as a
reference [16, 17].
Ion resonance with the counter-propagating laser beam is
confined to a small post-acceleration region. As the ions enter
this region, they are accelerated and brought into resonance
with the Doppler-shifted laser beam. The excitation occurs
primarily in a central cylindrical volume in which the potential
is nearly uniform over ∼3 cm length. The background light
from scattered laser light is reduced by focusing the laser
beam and the use of apertures, while the light arising from ionneutral collisions is kept at an acceptable level by maintaining
the vacuum at 10−6 –10−7 Torr. The light background is further
suppressed by modulating the post-acceleration potential at
2 kHz, providing an ac component to the LIF that is detected
with a lock-in amplifier.
Two bundles of optical fibers are positioned around the
post-acceleration region to collect the LIF. The LIF from
one bundle is used for branching-fraction data while the
other provides a ‘normalization’ signal that is used to correct
the branching-fraction signal for variations in the excitation
rate due to drifts in the properties of the laser and ion
beams. This normalization signal is obtained from a relatively
strong transition in the LIF spectrum, and is divided into
the branching-fraction signal before relative intensities are
calculated. The fibers of each bundle are mounted in specific
angular arrays chosen to minimize systematic error in the BFs
arising from anisotropic excitation and detection [18].
The two fiber bundles are connected to two identical
f /3.8 scanning monochromators. Each monochromator
has three gratings on a rotating carousel to provide
complete spectral coverage: their reciprocal linear dispersions
and spectral ranges are as follows: (1.0 nm mm−1 , 250–
500 nm), (1.5 nm mm−1 , 250–750 nm), and (3.0 nm mm−1 ,
250–1500 nm). The light detector for the normalization
monochromator is a bialkali-photocathode blue-sensitive
photomultiplier (PMT), while that for the branchingratio monochromator is a trialkali-photocathode PMT with
extended red response useful in practice to ∼850 nm. In
order to eliminate second-order diffraction lines, a long-pass
filter (91.5% flat transmission for wavelength λ > 550 nm) is
inserted for scans above ∼600 nm. The PMTs were operated
in current mode to allow the use of lock-in detection for
background suppression and wavelength stabilization (see
below).
To calibrate the wavelength-dependent response of the
complete detector system (fibre array + monochromator
+ PMT), a 200-W NIST-traceable quartz-tungsten-halogen
(QTH) lamp (Oriel model 63355) is used as a standard
illumination source. The uncertainty of the response
calibration was estimated as 7.1% systematic and 1.5%
statistical. For a detailed discussion see [18].
The signal from the normalization monochromator is
connected to two lock-in amplifiers. One operating in ‘2 f ’
mode provides the background-suppressed normalization
signal, while the second, operating in ‘1 f ’ mode, provides an
Oscillator strength measurements in Pr II
Figure 1. Partial fluorescence spectrum in Pr II from the upper
level with energy 22675.439 cm−1 . This level was laser-excited
using the transition at 440.88 nm from the ground state of the ion.
The laser power was 115 mW and the ion current is 75 nA. Dwell
time was 4s per 1-nm step.
error signal for dye-laser wavelength stabilization. With the
laser wavelength locked to the peak of the pump-transition
resonance, the branching-fraction monochromator is scanned
to record the spontaneous emission lines from 250 to 850 nm.
During a scan, the computer also records the normalization
signal, the laser power transmitted through the apparatus, and
the ion-beam current. A sample decay-branch partial spectrum
for the upper level 22 675.44 cm−1 is shown in figure 1.
3. Data analysis
BFs are obtained from a spectrum such as that shown in
figure 1 by determining the relative intensities of all observed
transitions from an excited state. For transitions from an
upper state u to a set of lower states l, the relative intensities
Iul are obtained by dividing the areas Sul of the observed
spectral lines by the wavelength-dependent detection sensitivity of our apparatus. The latter is determined in a separate
calibration procedure employing our QTH irradiance standard
as r (λul )/i(λul ), where r (λul ) is the measured response of
our fibre/monochromator/PMT system, and i(λul ) is the value
of the manufacturer’s spectral irradiance data for our lamp.
Altogether,
Sul
Iul =
.
(1)
[r (λul ) /i (λul )]
BFs Rul are then obtained as
Iul λul
Rul = P
,
Iul λul
(2)
l
in which the λul factors are needed to convert relative
intensities into relative photon emission rates.
The areas Sul are found by least-squares fitting the
emission lines with a symmetric Gaussian function, chosen
after a systematic study to optimize goodness of fit and
robustness [18]. The uncertainties associated with the areas
obtained from the fitting procedure ranged from 0.2% for the
strongest lines to 5% for the weakest. Due to the wavelengthdependent dispersion of a Czerny–Turner monochromator,
2
a linewidth function w(λ) = A λ − λ̄ + B λ − λ̄ + C was
employed in the fitting, where λ̄ is the mean wavelength of
the scanned range (introduced merely to reduce correlation
between the fitted parameters and minimize truncation
errors). This quadratic parameterization was a satisfactory
representation of the true wavelength dependence over the
range of interest, and provided a robust fit for small peaks
common in the infrared region for Pr II.
In some cases it is necessary to combine partial spectra
taken with different gratings in order to obtain complete
spectral coverage with adequate resolution. The relative
normalization of the spectra being combined is determined
from spectral lines in the overlap regions common to both
spectra. The procedure employs a least-squares adjustment of
n − 1 multiplicative normalization constants when the fitted
areas from n spectra are being merged.
4. Results
The data required for the BF calculation are the relative
intensities of all measured branches from a given upper state.
These data are presented in table 1. Obtaining BFs from
relative intensities assumes that all radiative transitions that
contribute to the decay of the level have been measured. This
is practically impossible due to the limited spectral region of
detectors and poor signal-to-noise ratio (SNR) for a number of
weak lines, predominantly in the near infrared region. (In both
tables 1 and 2, lines labeled as ‘w’ were reproducible to the
eye but could not be fit because of a poor SNR.) In our work,
only the transitions between 250 and 850 nm were observed,
and the g A and log g f values derived from them are presented
in table 2, along with g A values from [8, 11–13] where
available. To assess the error in our g A values arising from
unseen branches, it is interesting to compare our data with that
of Ivarsson et al [12], who also measured both lifetimes and
BFs but made a theoretical correction for missed branches.
Except for the upper level at 22675.44 cm−1 , the agreement
is almost always excellent, implying that the contribution
of missed branches is comparable with the experimental
uncertainties. For the same 22675.44 cm−1 upper level, the
agreement between the data of Goly et al [11] and our work
is excellent (except for one branch where they took data from
elsewhere), and our spectrum has a very good SNR, so the
disagreement with Ivarsson et al on this level is puzzling. It is
interesting to note that for the upper level at 26860.44 cm−1 ,
three branches are in excellent agreement (difference <1
standard deviation), while the branch at 426.179 nm gives
very poor agreement (difference >6 standard deviations).
Since this line is listed as ‘complex’ by Meggers et al [6],
it is likely that Ivarsson et al measured a blend in their hollow
cathode discharge, while we observed a single line because of
our selective laser excitation of the upper level.
In table 3, we make an overall numerical comparison
of our results for gu Aul to those of [11, 12], both of whom
used measured lifetimes and measured BFs, and gave error
estimates. For these references we list the average quantity
579
R Li et al
Table 1. Relative intensities of branches from a given upper level of Pr II. The intensities of branches that were observed but too weak to
analyze are indicated by ‘w’.
Wavelength in airb
(nm)
Relative
intensity
0.00
441.95
1649.01
1743.72
3403.21
3893.46
4097.60
7438.23
7446.43
453.592c
462.874
490.275d
492.563d
536.423
550.915
557.183
684.659d
685.046d
1
0.69(8)
0.17(2)
0.00
441.95
1649.01
1743.72
3403.21
3893.46
4097.60
442.913c
451.758
477.822d
479.994d
521.551
535.240
541.154
22675.44
0.00
441.95
3893.46
4097.60
7438.23
7446.43
440.882c
449.646
532.276
538.126
656.107d
656.462d
1
0.36(4)
0.36(4)
0.16(2)
0.05(1)
22885.59
0.00
441.95
1649.01
1743.72
3403.21
3893.46
4097.60
7438.23
7446.43
436.833c
445.436
470.754
472.863
513.142
526.388
532.107
647.181d
647.526d
1
0.13(1)
0.10(1)
0.11(1)
0.031(5)
0.32(3)
0.13(1)
0.032(8)
23261.36
0.00
441.95
1743.72
3403.21
3893.46
4097.60
7438.23
8099.72
429.777c
438.101
464.605
503.432
516.174
521.673
631.813
659.374e
1
0.036(5)
0.15(2)
0.023(5)
0.30(3)
0.08(1)
w
0.008
23660.20
0.00
441.95
4097.60
7438.23
7446.43
7744.27
422.535c
430.576
511.038
616.278
616.594
628.128
1
0.34(4)
0.14(2)
w
w
w
23977.83
441.95
1649.01
1743.72
2998.36
3403.21
5108.40
5226.52
8489.87
10030.31
424.763c
447.726
449.634
476.523
485.900
529.809
533.148
645.484
716.777
1
0.45(6)
0.52(7)
0.20(3)
0.13(2)
0.66(8)
0.23(3)
w
w
24115.50
441.95
1649.01
1743.72
2998.36
3403.21
422.293c
444.983
446.866
473.42
482.670
1
0.27(5)
0.47(8)
0.11(2)
w
Upper level energya
(cm−1 )
22040.05
22571.48
580
Lower level energya
(cm−1 )
0.011(5)
0.36(4)
0.16(2)
0.05(2)
1
0.27(3)
0.072(8)
0.034(5)
0.32(3)
0.14(1)
Oscillator strength measurements in Pr II
Table 1. Continued.
Wavelength in airb
(nm)
Relative
intensity
3893.46
5079.35
5108.40
5226.52
6413.93
8489.87
494.372
525.17d
525.973d
529.262
564.765
639.796
w
0.36(4)
1743.72
3403.21
4097.60
5108.40
5226.52
8465.04
8489.87
10163.47
11418.52
441.377c
476.272
492.567
518.385
521.580
627.625d
628.605d
702.534
770.498
1
0.27(3)
w
0.20(2)
0.048(7)
0.008(3)
24716.04
0
441.95
1649.01
1743.72
3893.46
5226.52
7438.23
7446.43
8099.72
8489.87
9128.67
404.481
411.846
433.397
435.184c
480.114
512.952
578.617
578.892
601.648
616.118
641.368
0.36(4)
1
0.4(1)
0.6(2)
w
0.25(3)
w
w
w
0.13(3)
w
24835.03
441.95
1743.72
2998.36
3403.21
5079.35
5108.40
6413.93
9646.67
10163.47
10535.83
11418.52
11447.73
409.840
432.941c
457.817
466.465
506.043d
506.788d
542.705
658.218
681.404
699.147
745.145d
746.771d
0.18(2)
1
0.32(3)
0.76(8)
0.12(2)
25248.69
1649.01
2998.36
3403.21
4437.15
5079.35
6417.83
11749.49
11794.38
12243.49
13029.09
423.615c
449.306
457.632
480.369
495.664
530.896
740.581
743.052
768.712
818.134
1
0.19(2)
0.34(4)
0.055(7)
0.62(6)
0.17(2)
0.04(3)
0.05(1)
0.03(1)
0.04(3)
25467.47
0.00
441.95
1743.72
4097.60
7438.23
7446.43
8099.72
9045.00
392.547
399.479
421.400c
467.818
554.501d
554.753d
575.617
608.752
0.53(6)
1
0.022(3)
0.031(4)
0.074(8)
0
441.95
1649.01
392.053
398.968
419.160
0.25(4)
1
0.68(9)
Upper level energy
(cm−1 )
24393.73
25499.52
a
Lower level energya
(cm −1 )
0.16(2)
w
w
0.028(5)
0.047(9)
0.05(1)
0.034(6)
0.10(1)
0.031(6)
0.041(8)
0.11(1)
0.09(1)
581
R Li et al
Table 1. Continued.
Upper level energy
(cm−1 )
25569.19
25610.20
25656.69
26146.01
582
a
Wavelength in airb
(nm)
Relative
intensity
1743.72
3403.21
3893.46
5226.52
7438.12
7446.43
8099.72
8465.04
9128.67
10116.63
10163.47
420.832c
452.438
462.704
493.130
553.517d
553.768d
574.560
586.883
610.672
649.893
651.879
0.47(6)
0.025(4)
0.034(5)
0.017(3)
0.13(2)
1649.01
2998.36
3403.21
5079.35
5108.4
5226.52
6413.93
6417.83
7659.76
9646.67
417.939
442.925c
451.015
487.91d
488.60d
491.440
521.905d
522.011d
558.210
627.868
1
0.26(3)
0.27(3)
0.020(6)
441.95
1649.01
1649.01
2998.36
3403.21
5079.35
5108.4
6413.93
8465.04
8489.87
9378.63
9646.67
10535.83
11418.52
397.214
417.225
417.225
442.122c
450.182
486.936d
487.626d
520.790
583.094d
583.939d
615.910
626.255
663.195
704.445
0.79(8)
1
1
0.23(2)
0.047(6)
0.056(6)
441.95
1649.01
1743.72
2998.36
3403.21
5079.35
5108.4
6413.93
7438.23
8465.05
8489.87
9378.63
9646.67
11418.52
396.481
416.416
418.065e
441.215c
449.242
485.836d
486.523d
519.531
548.742
581.517d
582.358d
614.151
624.435
702.151
0.9(1)
1
0.038
0.08(2)
0.025(5)
0.043(7)
0
441.95
1649.01
1743.72
3403.21
3893.46
7438.23
7446.43
8465.04
8489.87
9128.67
382.359
388.934
408.098
409.682
439.576c
449.261
534.388d
534.623d
565.423
566.219
587.474
0.08(1)
0.49(5)
0.65(7)
1
0.06(1)
0.020(5)
0.08(1)
Lower level energya
(cm−1 )
0.022(4)
0.10(1)
0.035(5)
0.03(1)
0.04(2)
w
0.45(5)
w
w
0.19(2)
0.065(7)
0.030(3)
0.046(5)
0.011(2)
0.021(3)
0.19(2)
0.010(3)
0.07(1)
0.018(3)
0.035(5)
0.036(6)
0.07(2)
0.02(1)
0.037(6)
Oscillator strength measurements in Pr II
Table 1. Continued.
Wavelength in airb
(nm)
Relative
intensity
10163.47
10729.75
625.510
648.487
0.045(7)
0.011(3)
441.95
1649.01
1743.72
2998.36
3403.21
6413.93
7438.23
8465.04
8489.87
9378.63
9646.67
10163.47
10535.83
11418.52
11794.38
385.155
403.934
405.488
427.227
434.749c
500.246
527.271
557.461d
558.235d
587.383
596.782
615.782
630.236
667.378
684.547
0.24(3)
0.29(3)
1
0.35(4)
0.24(3)
0.044(8)
w
0.005(2)
1649.01
2998.36
3403.21
4437.15
5079.35
5108.4
6413.93
6417.83
7659.76
9646.67
10030.31
11005.57
11749.49
11794.38
13029.09
403.175
426.378
433.870c
454.254
467.908d
468.545d
499.083d
499.180d
532.182
595.127
609.038
647.509
680.287d
682.372d
745.174
1
0.33(3)
0.44(5)
0.048(6)
0.13(1)
441.95
1743.72
2998.36
3403.21
6413.93
8465.04
8489.87
9646.67
10535.83
11418.52
383.296
403.433
424.948c
432.390
497.125
553.588d
554.350d
592.346
625.289
661.834
0.42(4)
1
0.39(4)
0.23(2)
0.038(5)
0.026(5)
26640.86
1649.01
1743.72
3403.21
9378.63
9646.67
10116.63
10163.47
400.017
401.539
430.215c
579.136
588.274
605.004
606.727
0.71(8)
1
0.12(2)
0.13(2)
0.04(1)
0.10(3)
0.07(2)
26707.31
0
441.95
1743.72
3403.21
5226.52
7438.23
7446.43
8099.72
8465.04
8489.87
9821.67
374.323
380.622
400.470
428.988c
465.402
518.822d
519.043d
537.266
548.026d
548.772d
568.717
0.020(3)
0.028(4)
1
0.14(2)
0.029(3)
0.048(5)
Upper level energy
(cm−1 )
26398.52
26445.11
26524.02
a
Lower level energya
(cm−1 )
0.009(3)
0.046(8)
0.008(3)
0.014(4)
0.06(1)
w
0.075(8)
0.13(1)
0.010(3)
0.07(1)
0.014(4)
0.025(6)
0.08(1)
0.066(8)
0.031(7)
0.16(2)
0.005(2)
0.033(4)
0.011(3)
583
R Li et al
Table 1. Continued.
Wavelength in airb
(nm)
Relative
intensity
9378.63
10163.47
576.916
604.287
0.051(6)
0.09(1)
1649.01
2998.36
3403.21
4437.15
5108.40
6413.93
6417.83
7659.76
8140.67
9646.67
10030.31
10163.47
10729.75
11005.57
13029.09
396.525
418.948c
426.179
445.830
459.588
488.933d
489.026d
520.655
534.032
580.752
593.990
598.729
619.745
630.523
722.770
0.66(7)
1
0.037(5)
0.047(6)
w
0.043(5)
441.95
1649.01
1743.72
2998.36
3403.21
5079.35
6413.93
8465.04
8489.87
9378.63
10030.31
10163.47
10535.83
11418.52
11447.73
376.967
394.943
396.426
417.182
424.351c
456.856
486.529
540.480d
541.207d
568.560
590.445
595.127
608.616
643.184d
644.391d
w
1
0.85(9)
0.93(10)
0.33(4)
w
w
0.026(9)
2998.36
4437.15
5079.35
5108.40
6413.93
6417.83
7659.76
7805.61
8958.49
10030.31
11005.57
11611.05
414.311
440.583c
453.415d
454.014d
482.629
482.720
513.514
517.390
550.220
584.713
620.081
644.278
1
0.18(2)
0.10(1)
w
w
0.11(1)
0.29(3)
w
0.05(1)
w
w
27781.69
2998.36
4437.15
5079.35
7805.61
8958.49
11611.05
14705.96
403.383
428.242c
440.360
500.459
531.112
618.234
764.566
1
0.72(7)
0.31(3)
0.08(1)
0.14(2)
0.08(1)
0.013(8)
28009.80
1649.01
2998.36
3403.21
4437.15
5079.35
5108.40
7659.76
11005.57
379.244
399.704
406.281
424.101c
435.979d
436.532d
491.26
587.925
0.11(2)
0.30(3)
1
0.45(5)
0.17(2)
Upper level energy
(cm−1 )
26860.95
26961.96
27128.00
584
a
Lower level energya
(cm−1 )
0.17(2)
w
0.009(2)
0.08(1)
w
0.019(3)
0.014(2)
0.017(3)
0.023(8)
0.09(2)
0.10(2)
0.04(1)
0.11(3)
0.06(1)
0.09(1)
Oscillator strength measurements in Pr II
Table 1. Continued.
Upper level energy a
(cm−1 )
Wavelength in air b
(nm)
Relative
intensity
11749.49
11794.38
12826.94
13029.09
13373.61
614.824d
616.527d
658.456
667.341
683.050
0.05(1)
2998.36
3403.21
5079.35
5108.40
5226.52
10729.75
399.316
405.880
435.518c
436.070d
438.328d
577.729
0.18(2)
1
0.29(4)
0.05(2)
28172.96
2998.36
3403.21
4437.15
5079.35
11749.49
11794.38
397.116
403.605
421.186
432.899c
608.717d
610.385d
0.35(4)
0.20(3)
1
0.67(7)
0.18(4)
28201.95
2998.36
4437.15
5079.35
5108.40
6413.93
6417.83
7805.61
8958.49
11005.57
11611.05
11794.38
12243.49
14705.96
396.657
420.672
432.355c,d
432.900d
458.840d
458.922d
490.147
519.511
581.355
602.572
609.306
626.454
740.757
0.43(5)
1
0.11(2)
28034.08
28577.79
Lower level energy a
(cm−1 )
2998.36
3403.21
4437.15
5079.35
5108.40
7659.76
10729.75
11005.57
11611.05
11749.49
11794.38
12826.94
13029.09
390.829
397.116
414.122
425.440c,d
425.967d
477.923
560.130d
568.921d
589.225
594.072d
595.660d
634.711d
642.963d
w
0.09(2)
w
0.11(2)
0.04(2)
0.05(1)
0.17(2)
0.024(8)
0.10(2)
0.023(9)
w
0.41(5)
0.32(4)
1
0.16(2)
w
0.04(2)
w
0.16(4)
0.09(2)
a
NIST Atomic Spectroscopy Database
(http://physics.nist.gov/PhysRefData/ASD/index.html).
b
Wavelength sources in order of decreasing priority:
1. NIST Atomic Spectroscopy Database (see footnote a);
2. Kurucz R L and Bell B 1995 Atomic Line Data, Kurucz CD-ROM no. 23
(Cambridge, MA.: Smithsonian Astrophysical Observatory). Online at
http://cfa-www.harvard.edu/amdata/ampdata/kurucz23/sekur.html;
3. Ritz wavelengths calculated from NIST energy levels.
c
Transition used to excite the upper level.
d
Blended line in this work.
e
Transition observed by [6], but not in this work. The relative intensity is
calculated from data in that reference.
585
R Li et al
Table 2. Transition probabilities and oscillator strengths for Pr II derived from branching-fraction and lifetime data. Values of gu Aul from
this work are compared with those of [8, 11–13]. Branches that were observed but were too weak to fit are indicated by ‘w’.
Upper level
energy
(cm−1 )a
J
Lifetime
(ns)b
22040.05
5
67.5(1.7)
22571.48
586
5
51.8(6)
Transition
wavelength
(nm)
Branching
fraction
This work
BLQSXc
gu Aul
(106 s−1 )
ILWd
GKNWe
LWf
loggl flu
This work
453.592
462.874
490.275g
492.563g
536.423
550.915
557.183
684.659g
685.046g
0.38(2)
0.27(2)
0.070(7)
62(4)
44(3)
11(1)
−0.715
−0.849
−1.382
0.005(2)
0.17(1)
0.073(8)
0.03(1)
0.8(3)
27(2)
12(1)
5(1)
−2.465
−0.903
−1.255
−1.469
442.913
451.758
477.822g
479.994g
521.551
535.240
541.154
0.51(2)
0.14(1)
0.040(4)
109(5)
30(2)
8.5(8)
−0.495
−1.032
−1.532
0.021(2)
0.20(1)
0.085(7)
4.4(5)
42(3)
18(1)
−1.750
−0.739
−1.100
22675.44
5
13.5(2)
440.882
449.646
532.276
538.126
656.107g
656.462g
0.48(2)
0.18(1)
0.21(1)
0.096(8)
0.036(8)
394(18)
144(11)
170(12)
78(7)
29(6)
22885.59
5
35.0(7)
436.833
445.436
470.754
472.863
513.142
526.388
532.107
647.181g
647.526g
0.50(2)
0.068(6)
0.057(7)
0.059(7)
0.018(3)
0.20(1)
0.077(7)
0.024(6)
158(7)
21(2)
18(2)
19(2)
5.8(8)
62(5)
24(2)
7(2)
23261.36
5
48.8(1.6)
429.777
438.101
464.605
503.432
516.174
521.673
631.813
659.374
0.60(2)
0.022(3)
0.099(9)
0.016(3)
0.21(2)
0.056(6)
w
w
134(7)
5.0(6)
22(2)
3.6(7)
48(4)
13(1)
518(41)
178(18)
113(12)
18(2.3)
358(89)
164(41)
207(52)
4(1)
0.053
−0.368
−0.123
−0.461
−0.723
−0.346
−1.199
−1.227
−1.206
−1.639
−0.592
−0.988
−1.329
96.4
41.7
15.2
7.22
25.2
−0.429
−1.845
−1.142
−1.858
−0.720
−1.292
7.85
3.62
23660.20
4
7.57(15)
422.535
430.576
511.038
616.278
616.594
628.128
0.66(2)
0.23(2)
0.11(1)
w
w
w
786(29)
269(21)
134(13)
23977.83
6
36.0(9)
424.763
447.726
449.634
476.523
485.900
529.809
533.148
645.484
716.777
0.28(2)
0.13(1)
0.16(1)
0.063(6)
0.041(4)
0.24(2)
0.083(8)
w
w
103(8)
49(4)
57(4)
23(2)
15(2)
85(6)
30(3)
24115.50
6
7.92(15)
422.293
444.983
446.866
0.39(2)
0.11(2)
0.20(2)
642(41)
185(31)
321(40)
494(123)
153(38)
98(24)
0.323
−0.125
−0.280
−0.280
−0.555
−0.834
−0.762
−1.109
−1.282
−0.446
−0.895
735
181
299
698(49)
225(18)
270(22)
445(111)
122(31)
135(34)
508
161
200
0.235
−0.261
−0.017
Oscillator strength measurements in Pr II
Table 2. Continued.
Upper level
energy
(cm−1 )
J
Lifetime
(ns) b
Transition
wavelength
(nm)
473.420
482.670
494.372
525.171g
525.973g
529.262
564.765
639.796
24393.73
24716.04
24835.03
6
5
6
80.9(1.3)
6.4(11)
92.7(1.2)
Branching
fraction
33
13
8
291
−0.571
121
9
25
−0.269
0.049(8)
80(13)
2.20
0.17(2)
286(26)
12.0
365
314(25)
23(6)
10(5)
9(5)
204(51)
0.08(1)
w
w
128(17)
122
132(13)
100(50)
17.3
loggl flu
This work
0.072
441.377
476.272
492.567
518.385
521.580
627.625g
628.605g
702.534
770.489
0.58(2)
0.17(1)
w
0.13(1)
0.033(4)
0.007(2)
94(4)
27(2)
−0.563
−1.034
22(2)
5.3(7)
1.1(3)
−1.062
−1.664
−2.178
0.026(4)
0.048(8)
4.2(7)
8(1)
−1.508
−1.164
404.481
411.846
433.397
435.184
480.114
512.952
578.617
578.892
601.648
616.118
641.368
0.12(1)
0.34(3)
0.15(4)
0.22(5)
207(23)
588(57)
251(71)
374(89)
0.11(1)
w
w
w
0.07(2)
w
186(23)
409.840
432.941
457.817
466.465
506.043g
506.788g
542.705
658.218
681.404
699.147
745.145g
746.771g
201(50)
475(119)
301(75)
157(39)
33(8)
141(35)
−0.293
0.175
−0.150
0.027
−0.134
112(26)
−0.196
0.058(5)
0.35(2)
0.12(1)
0.29(2)
0.050(5)
8.2(7)
49(3)
17(1)
40(2)
7.0(7)
−1.686
−0.861
−1.280
−0.884
−1.570
0.023(5)
0.018(3)
0.055(6)
0.018(3)
0.025(4)
3.2(7)
2.6(4)
7.7(8)
2.5(4)
3.4(6)
−1.851
−1.778
−1.273
−1.742
−1.543
−0.835
−1.490
−1.202
−1.933
−0.837
−1.315
−1.478
−1.401
−1.656
−1.336
96.6(2.0)
423.615
449.306
457.632
480.369
495.664
530.896
740.581
743.052
768.712
818.134
0.35(2)
0.069(6)
0.13(1)
0.022(2)
0.25(2)
0.074(6)
0.03(2)
0.031(7)
0.016(9)
0.03(2)
54(3)
10.7(9)
20(2)
3.4(4)
40(3)
11(1)
4(3)
5(1)
2(1)
5(3)
25467.47
4
11.6(9)
392.547
399.479
421.400
467.818
554.501g
554.753g
575.617
608.752
0.26(2)
0.51(2)
0.012(2)
0.018(2)
0.052(5)
206(21)
392(35)
9(1)
14(2)
40(5)
0.078(7)
0.070(7)
61(7)
54(7)
392.053
0.08(1)
54(7)
16.2(4)
LW c
BLQSX c
7
5
GKNW e
This work
25248.69
25499.52
gu Aul
(106 s−1 )
ILW a
202(50)
458(114)
15.3(2.8)
−0.323
−0.028
−1.624
−1.330
−0.730
−0.521
−0.521
64(16)
−0.907
587
R Li et al
Table 2. Continued.
Upper level
energy
(cm−1 )
25569.19
25610.20
25656.69
26146.01
588
J
7
6
6
5
Lifetime
(ns) b
6.32(39)
21.1(5)
9.05(21)
18.8(1.4)
Transition
wavelength
(nm)
Branching
fraction
This work
BLQSX c
221(16)
398.968
419.160
420.832
452.438
462.704
493.130
553.517g
553.768g
574.560
586.883
610.672
649.893
651.879
0.08(1)
0.23(2)
0.16(1)
0.009(1)
0.013(1)
0.007(1)
0.057(5)
0.33(2)
158(14)
110(9)
6.2(7)
8.7(9)
4.6(7)
39(3)
0.010(2)
0.050(4)
0.017(2)
0.015(5)
0.02(1)
7(1)
34(3)
12(1)
10(3)
15(9)
417.939
442.925
451.015
487.910g
488.600g
491.440
521.905g
522.011g
558.210
627.868
0.46(2)
0.13(1)
0.14(1)
0.011(3)
1099(84)
305(30)
323(32)
26(8)
397.214
417.225
418.880
442.122
450.182
486.936g
487.626g
520.790
583.094g
583.939g
615.910
626.255
663.195
704.445
0.29(2)
0.38(2)
396.481
416.416g
418.065g
441.215
449.242
485.836g
486.523g
519.531
548.742
581.517g
582.358g
614.151
624.435
702.151
0.35(2)
0.40(2)
382.359
388.934
408.098
409.682
439.576
449.261
534.388g
534.623g
565.423
w
0.26(2)
621(56)
w
w
gu Aul
(106 s−1 )
ILW a
GKNW e
286(29)
110(11)
110(11)
loggl flu
This work
−0.277
−0.379
−0.535
−1.718
−1.554
−1.776
−0.752
−1.463
−0.759
−1.181
−1.198
−1.011
1240
162
302
7.07
18.3
9.42
170
508
1146(69)
268(21)
311(25)
809(202)
306(76)
128(32)
12.8(3.2)
217(20)
486(34)
150(37)
363(91)
21
179(12)
237(13)
LW c
786
342
174
27
20
10
143
353
< 1.5
39
24.5
0.459
−0.048
−0.007
−1.030
0.405
−0.374
−0.209
350
8.40
117
23.1
0.094(7)
0.020(2)
0.025(2)
58(5)
12(1)
15(1)
0.089(7)
0.035(3)
55(4)
21(2)
−0.651
−0.962
0.017(2)
0.026(2)
0.007(1)
0.014(2)
11(1)
16(1)
4.0(7)
8(1)
−1.221
−1.022
−1.578
−1.200
−0.770
−1.437
−1.258
4.35
13.0
498(34)
569(36)
560(39)
523(131)
555(44)
0.033(6)
0.010(2)
0.020(3)
47(9)
15(3)
29(4)
48(5.3)
44(11)
−0.859
−1.341
−0.989
0.092(8)
0.005(2)
0.041(4)
132(12)
8(2)
59(6)
125(10)
176(44)
−0.272
−1.454
−0.520
0.010(2)
0.021(3)
0.024(4)
15(3)
30(4)
34(5)
−1.075
−0.760
−0.596
0.028(3)
0.17(1)
0.25(2)
0.38(2)
0.026(4)
0.008(2)
0.039(5)
16(2)
102(11)
144(14)
221(20)
15(2)
5(1)
23(3)
−1.449
−0.634
−0.445
−0.255
−1.361
−1.844
−1.011
0.037(7)
21(5)
−0.988
540(135)
0.069
0.170
Oscillator strength measurements in Pr II
Table 2. Continued.
Upper level
energy
(cm−1 )
26398.52
26445.11
26524.02
J
6
7
6
Lifetime
(ns) b
8.19(8)
26.4(1.4)
77(7)
Transition
wavelength
(nm)
Branching
fraction
This work
BLQSX c
gu Aul
(106 s−1 )
ILW a
GKNW e
LW c
loggl flu
This work
566.219
587.474
625.510
648.487
385.155
403.934
405.488
427.227
434.749
500.246
527.271
557.461g
558.235g
587.383
596.782
615.782
630.236
667.378
684.547
0.012(5)
0.020(3)
0.026(4)
0.007(2)
0.095(9)
0.12(1)
0.41(2)
0.15(1)
0.10(1)
0.023(4)
7(3)
12(2)
15(2)
4(1)
151(20)
188(24)
657(72)
244(32)
167(23)
36(7)
−1.458
−1.217
−1.046
−1.618
−0.475
−0.336
0.209
−0.175
−0.326
−0.871
0.003(1)
4(2)
−1.696
0.005(2)
0.028(4)
0.005(2)
0.009(2)
0.041(6)
w
8(3)
45(8)
8(3)
14(4)
65(12)
−1.369
−0.621
−1.337
−1.076
−0.360
403.175
426.378
433.870
454.254
467.908g
468.545g
499.083g
499.180g
532.182
595.127
609.038
647.509
680.287g
682.372g
745.174
0.38(2)
0.132(9)
0.18(1)
0.021(2)
0.056(5)
217(16)
75(7)
103(9)
12(1)
32(3)
−0.276
−0.688
−0.538
−1.439
−0.984
0.035(3)
20(2)
−1.126
0.068(5)
0.006(2)
0.041(5)
0.009(2)
0.016(3)
38(4)
3.4(9)
24(3)
5(1)
9(2)
−0787
−1.748
−0.883
−1.516
−1.200
0.054(8)
31(5)
−0.593
383.296
403.433
424.948
432.390
497.125
553.588g
554.350g
592.346
625.289
661.834
0.16(1)
0.39(2)
0.16(1)
0.095(7)
0.018(2)
0.014(2)
26(3)
66(7)
27(3)
16(2)
3.1(4)
2.4(5)
0.038(4)
0.019(4)
0.11(1)
6.4(9)
3.1(7)
18(2)
−1.473
−1.734
−0.932
34.0
28.7
24.8
−1.238
−0.790
−1.130
−1.346
−1.944
−1.965
26640.86
5
26.2(2)
400.017
401.539
430.215
579.136
588.274
605.004
606.727
0.30(2)
0.43(2)
0.054(6)
0.08(1)
0.026(8)
0.06(2)
0.04(1)
127(9)
180(10)
23(2)
34(5)
11(3)
27(6)
18(5)
−0.515
−0.362
−1.199
−0.768
−1.241
−0.836
−0.993
26707.31
5
30.0(1.4)
374.323
380.622
400.470
428.988
465.402
518.822g
519.043g
537.266
548.026g
0.012(2)
0.017(2)
0.64(2)
0.099(8)
0.021(2)
0.040(4)
4.4(6)
6.2(8)
234(13)
36(3)
7.7(9)
15(2)
−2.037
−1.872
−0.250
−1.000
−1.599
−1.231
1.6(7)
10(1)
−2.157
−1.326
0.004(2)
0.029(3)
589
R Li et al
Table 2. Continued.
Upper level
energy
(cm−1 )
26860.95
26961.96
27128.00
590
J
7
6
8
Lifetime
(ns) b
6.69(52)
11.7(5)
5.79(13)
Transition
wavelength
(nm)
548.772g
568.717
576.916
604.287
396.525
418.948
426.179
445.830
459.588
488.933g
489.026g
520.655
534.032
580.752
593.990
598.729
619.745
630.523
722.770
376.967
394.943
396.426
417.182
424.351
456.856
486.529
540.480g
541.207g
568.560
590.445
595.127
608.616
643.184g
644.391g
Branching
fraction
This work
0.010(2)
0.046(5)
0.085(8)
0.29(2)
0.46(2)
0.017(2)
0.023(2)
3.7(9)
17(2)
31(3)
643(64)
1025(93)
39(5)
51(7)
0.023(2)
51(6)
0.098(8)
220(25)
0.005(1)
0.053(7)
12(3)
120(19)
0.013(2)
0.010(1)
0.014(2)
29(5)
29(5)
31(6)
w
0.26(2)
0.22(1)
0.26(2)
0.093(8)
w
w
0.009(3)
BLQSX c
gu Aul
(106 s−1 )
ILW a
GKNW e
LW c
loggl flu
This work
34.9
−1.751
−1.070
−0.766
0.181
0.431
−0.978
−0.817
23.6
227
−0.739
−0.739
−0.048
307
1410
579(41)
917(64)
155(17)
214(17)
315(78)
452(113)
41(20)
119(30)
8.13
93.8
15.9
34.5
15.8
3.31
−1.211
−0.198
−0.198
−0.779
−0.889
−0.616
293(22)
250(20)
288(22)
104(10)
−0.164
−0.230
−0.123
−0.553
10(4)
−1.344
0.009(3)
0.034(7)
0.041(8)
0.018(5)
0.05(1)
10(3)
38(8)
46(9)
20(6)
52(12)
−1.319
−0.702
−0.612
−0.950
−0.494
0.53(2)
0.10(1)
0.060(5)
1561(71)
297(25)
175(16)
1910
124
103
10.4
10.4
18.7
214
616
414.311
440.583
453.415
454.014
482.629
482.629
482.720
513.514
517.390
550.220
584.713
620.081
644.278
0.076(7)
0.19(1)
222(22)
569(44)
0.038(9)
w
w
112(25)
w
27781.69
8
18.4(6)
403.383
428.242
440.360
500.459
531.112
618.234
764.566
0.40(2)
0.30(2)
0.13(1)
0.038(4)
0.075(8)
0.048(6)
0.010(6)
366(23)
278(19)
122(10)
35(4)
70(8)
44(6)
9(5)
28009.80
7
6.97(21)
379.244
399.704
406.281
424.101
435.979g
0.042(6)
0.12(1)
0.40(2)
0.19(1)
0.073(8)
91(13)
256(23)
871(53)
408(33)
157(17)
1579(95)
315(25)
232(25)
6.8(3.4)
38(4.9)
38(4.9)
921(230)
156(39)
109(54)
991
153
83
7
7
7
258(28)
604(48)
145(36)
345(86)
212
541
< 10
16.8
9.61
0.604
−0.062
−0.268
0.359
−0.240
31
−0.049
−0.116
−0.449
−0.881
−0.531
−0.595
−1.104
< 15
333(83)
506(126)
174(44)
63(16)
1500
345
159
−0.706
−0.213
−0.334
−0.041
−0.350
Oscillator strength measurements in Pr II
Table 2. Continued.
Upper level
energy
(cm−1 )
J
Lifetime
(ns) b
Transition
wavelength
(nm)
436.532g
491.260
587.925
614.824g
616.527g
658.456
667.341
683.050
28034.08
6
48.4(3.0)
Branching
fraction
This work
BLQSX c
gu Aul
(106 s−1 )
ILW a
GKNW e
LW c
33(8)
15
86
114
loggl flu
This work
0.030(4)
0.052(7)
0.029(6)
65(10)
111(15)
63(13)
0.631
−0.240
−0.444
w
0.061(9)
w
131(19)
0.059
399.316
405.880
435.518
436.070g
438.328g
577.729
0.10(1)
0.59(2)
0.19(2)
0.03(1)
28(3)
158(12)
50(6)
8(3)
−1.172
−0.408
−0.850
−1.642
0.09(2)
25(5)
−0.909
−1.169
−1.401
−0.640
−0.778
−0.909
28172.96
7
70.6(1.9)
397.116
403.605
421.186
432.899
608.717g
610.385g
0.13(1)
0.076(8)
0.41(2)
0.28(2)
0.10(2)
29(3)
16(2)
86(5)
59(4)
22(4)
28201.95
8
10.7(6)
396.657
420.672
432.355g
432.900g
458.840g
458.922g
490.147
519.511
581.355
602.572g
609.306g
626.454
740.757
0.20(2)
0.49(2)
0.055(9)
314(30)
779(57)
87(15)
0.021(8)
33(13)
0.027(8)
0.10(1)
0.016(5)
0.07(1)
43(12)
163(20)
25(8)
117(17)
0.017(6)
w
26(10)
−0.808
390.829
397.116
414.122
425.440g
425.967g
477.923
560.130g
568.921g
589.225
594.072g
595.660g
634.711g
642.963g
0.17(1)
0.13(1)
0.44(2)
0.071(9)
361(35)
285(29)
935(64)
151(19)
−0.082
−0.171
−0.381
−0.386
w
0.02(1)
51(23)
−0.622
0.10(2)
219(49)
0.064
0.06(1)
131(22)
−0.101
28577.79
7
7.03(28)
419(42)
967(77)
98(12)
235(59)
770(77)
83(21)
−0.130
−0.315
−0.613
−0.980
39(10)
190(19)
−0.806
−0.180
−0.892
−0.195
a
NIST Atomic Spectra Database [Ver. 3.0] available online at http://physics.nist.gov/PhysRefData/ASD.
All lifetimes taken from [14] except that for level 26524.02 cm−1 [13].
c
Biémont et al [13].
d
Ivarsson et al [12].
e
Goly et al [11].
f
Lage and Whaling et al [8].
g
Blended line in this work.
b
1̄g A and its standard deviation, where
1gul Aul ≡
(gul Aul )ref − (gul Aul )this work
p
.
(σul 2 )ref + (σul 2 )this work
(3)
Since the measured lifetimes used in these references can
be quite different, we have also listed the same statistics
using (gul Aul )ref calculated with our own measured lifetimes,
effectively providing a comparison of measured BFs. Table
3 shows very good overall agreement, especially when the
591
R Li et al
Table 3. Overall comparisons of g A data with other work that used
both measured lifetimes and measured BFs.
Reference
Ivarsson et al [12]
Goly et al [11]
1ag A
1bg A
0.30(48)
−1.46(30)
−0.08(48)
−0.11(28)
a
Calculated using lifetimes from the
reference of column 1
b
Calculated using our lifetimes from [14].
same lifetimes are used for the comparison. There are however
individual exceptions, as described above. In a comparison
of our results with those of Lage and Whaling [8], where
only general statements about error are given, we find that
the percentage difference ranges from +39 to −178%, with
a standard deviation of 51%. Comparison of our results
with those of Biémont et al [13] is difficult because their
data depends on theoretical branching ratios for which no
uncertainty estimates are given. If we take an uncertainty of
50%, based on an upper limit in earlier work [19] by this
group, and eliminate three cases where we report blended
lines, we find seven cases out of 40 where the 1 parameter
(defined above) is greater than 2. In five of these transitions,
the lines are weak, and for the transition at 396.525 nm, 1
is only slightly more than 2. The large disagreement for the
transition at 397.214 nm is puzzling since weaker transitions
from the same upper level (25610.20 cm−1 ) are in much better
agreement.
The Einstein coefficients Aul and absorption oscillator
strengths flu were calculated using our previously determined
radiative lifetimes [14] and well-known formulae [20] for
electric dipole transitions,
Aul = Rul /τu ,
gl flu =
1
gu Aul ,
0.66702σul2
(4)
(5)
where τu is the upper-state lifetime, gu = 2Ju + 1 and gl =
2Jl + 1 are the statistical weights of the upper and lower levels
respectively and σul is the transition wave number (cm−1 ).
5. Conclusions
We have measured 260 oscillator strengths for Pr II transitions
over the wavelength range 250–850 nm, originating from 32
levels in the range ∼21 500–29 000 cm−1 . Highly selective
laser excitation of only a single upper level produces an
uncluttered fluorescence spectrum, removing any ambiguity
in the assignment of a transition to a pair of energy
592
levels. The oscillator strengths were obtained by combining
measured relative intensities with previously measured
radiative lifetimes. Of the 260 measured oscillator strengths,
183 have been determined accurately for the first time.
The uncertainties arose principally from systematics of the
efficiency calibration of the optical detection system (7.1%),
with smaller statistical contributions (1.5%). The measured
values were compared with prior measurements using both
our lifetimes and lifetimes measured by others.
Acknowledgment
We are grateful to the Natural Sciences and Engineering
Research Council of Canada for financial support.
References
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[7] Corliss C H and Bozman W R 1962 Experimental Transition
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[9] Andersen T and Sorensen G 1974 Sol. Phys. 38 343
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[13] Biémont E, Lefèbvre P-H, Quinet P, Svanberg S and Xu H L
2003 Eur. Phys. J. D 27 33
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[16] Hall J L and Lee S A 1976 Appl. Phys. Lett. 29 367
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R A and Rosner S D 2006 Can J. Phys. 84 723
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2003 J. Phys. B: At. Mol. Opt. Phys. 36 4773
[20] Martin W C and Wiese W L 1996 Atomic, Molecular,
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