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Absolute oscillator strengths of CrII-lines from combined phase shift and emission measurements
J. Quant. Spectrosc. Radiat. Trans/er Vol. 51, No. 5, pp. 779-785. 1994 Copyright 0 1994ElsevierScienceLtd 00224073(93)EOO63-X Printedin Great Britain. All rights reserved 0022-4073/94 57.00 + 0.00
Pergamon
ABSOLUTE OSCILLATOR STRENGTHS OF CrII-LINES FROM COMBINED PHASE SHIFT AND EMISSION MEASUREMENTS R. SPERGER,?
B. SCHELM,~ M. KOCK,$
T. NEGER,f’§
and M. ULBELt
tlnstitut fiir Experimentalphysik, Technische Universitit Graz, Petersgasse 16, A-8010 Graz, Austria and JInstitut fiir Plasmaphysik, Universitat Hannover, CallinstraBe 38, D-3000 Hannover I, Germany (Received 22 July 1993)
Abstract-Oscillator strengths of lines of singly ionized chromium have been obtained by a combination of emission and spectra-interferometric measurements. A hollow cathode is used as a light source for the emission measurements, where relative oscillator strengths of lines with the upper level in common are determined by measuring branching ratios. The determination of relative oscillator strengths of lines having the lower level in common is based on a phase shift method, which employs a Fourier analysis of the spectral interferograms. A modified wallstabilized arc serves as the light source here. Large sets of relative oscillator strengths are
obtained by linking the results of the two types of measurements. With known lifetimes the relative f-values are connected to an absolute scale where the overall uncertainty is between 10 and 30%.
INTRODUCTION In the last years there has been an increased interest in absolute oscillator strengths of singly ionized elements of the iron group. The data are not only needed for a quantitative analysis of laboratory plasmas and in fusion research, but also for abundance studies in astrophysics. In principle, there are three classical methods of optical plasmadiagnostics used for the determination of oscillator strengths: emission, absorption, and dispersion methods.’ Each method requires different experimental conditions in order to minimize systematic and statistical errors. A combination of level lifetimes with branching ratio measurements delivers reliable but small sets of absolute f-values. Such sets of f-values can be enlarged successfully by linking relative f-values of lines with a common lower level via transitions which exist in both sets.* The latter measurements can be done in absorption or with dispersive methods such as being reported in this paper. In this work a phase shift measurement including a Fourier analysis of the interferograms is preferred, since it can be considered generally as more accurate and more objective than spectra-interferometric methods based on simple fringe-peak-detection. By using the two different techniques mentioned above the data are combined in consistent sets of oscillator strengths. The linking of sets off-values measured in emission and dispersion requires at least one transition in common. If more than one transition is in common, there are several ways of possible linkage, thus increasing the redundance. This method utilizes closed loops 3 and has already been applied to some elements.2.4-6 For a conversion of the data to an absolute scale the lifetime of at least one upper level must be known. Together with the branching fraction of this level the absolute scale can be found. It should be pointed out that neither the technique of branching ratios nor the phase shift method requires any assumptions on the plasma state. The independent measurement of lines is a useful tool for a consistency check for both emission and spectra-interferometric data.
§To whom all correspondence
should be addressed. 779
780
R.
SPERCER
et al
EXPERIMENTAL
Emission
measurements
Figure 1 shows schematically the setup for the emission measurements. The line intensities were recorded photoelectrically using a photomultiplier in connection with a photon counting system. A 2-m-scanning-monochromator in Czerny-Turner configuration with a plane grating of 2400 lines/mm and a slit width of 10pm was used. For the calibration of the line intensities a mini-arc’ and a current-stabilized carbon arc’ were applied as radiation standards. A hollow cathode discharge served as light source.’ It consisted of three watercooled electrodes: two anodes and a cylindrical tube cathode made of chromium~nickelLstee1 having a length of about 60 mm. In addition, the inner part of the cylinder was hard-chromium-plated to provide a longer period of working. Glass tubes ensured the electrical insulation of the electrodes. The discharge was observed end-on through one anode. It was operated with stationary currents between 0.5 and 2 A. Either neon with pressures between 2 and 4 mbar or argon with pressures between 1 and 2 mbar were used as buffer gases. Current, pressure and buffer gas were varied in order to avoid the risk of blends and misinterpretation of lines. To meet the assumption that the lines were emitted from an optically thin layer, strong lines were checked in relation to weak lines with regard to self-absorption effects by varying the current of the discharge. Phase shft
measurements
The optical arrangement for the phase shift measurements is shown in Fig. 2. The main part of the optical setup is a Mach-Zehnder interferometer illuminated by a “white light” source (a pulsed capillary discharge, CD). In order to avoid a diminishing of the contrast of the interferograms because of too strong illumination by the radiation of the arc plasma (A). a fast shutter (FS) is used. The exposure time is adjusted to match the time interval of emission of the background light source (~440 psec). Two spectrographs (Jobin Yvon HR 1000, focal length m. grating 2000 lines/mm; GH, focal I .6 m, grating with 2 160 lines/mm) were used to record simultaneously
I I I
SCM --------
--l---____z~’
t-----, TM
I
’
D
SM
PM
PCS
tl
RS
PC
Fig. I. Sketch of the optical setup for the emission measurements. SM, spherical plane mirror; D, diaphragm; H. hollow cathode; SCM, scanning monochromator; PCS, photon counting system: RS, radiation standard; PC. personal
mirror; TM. turnable PM, photomultiplier; computer.
Absolute
BS
oscillator
W
strengths
781
of CrII-lines
W
M
Fig. 2. The optical setup for the phase shift measurements. CD, capillary discharge; L, lense; BS, beamsplitter; M, plane mirror; W, window; CP, compensation plate; A. test zone with arc; FS. fast shutter; D, diaphragm; ES, entrance slit of spectrograph.
interferograms in widely separated spectral regions at wavelengths of transitions which have the same lower level in common but have rather different upper levels on the energy scale. For the dispersion measurements a modified cascaded wall-stabilized arc was used.’ The cascade consisted of rings of graphite which were insulated from one another by beads of aluminium oxide ceramic. Sintered rings of chromium oxide were placed concentrically within the graphite rings. This arrangement was inserted into a tube of aluminium oxide ceramic. The whole assembly was fitted inside a vacuum sealed hard glass tube. Due to the radiation of the plasma column, particles are evaporated from inner wall of the rings of metal oxide to provide a dense plasma with a sufficient population of CrII levels necessary for a successful application of dispersion methods. Since the central part of the arc was not water-cooled, the tendency to condensation of the vapour could be diminished. The arc-plasma was prepared at stationary currents of about 25 A. The spectral interferograms, however, were recorded during a superposed current pulse (maximum being 250 A). Its duration and the delay between start of the current pulse and opening of the fast shutter could be adjusted, in order to optimize the population number densities of the excited CrII states as desired.
DATA
REDUCTION
AND
RESULTS
From the emission measurements sets of relative oscillator strengths have been obtained. The relativef-values are found by comparing the measured line intensities. If a transition from an upper level u to a lower level I, is compared with a transition from level u to a lower level L, the relative f-value results from
(I intensity of the line, A wavelength, g statistical weight of the level). The relativef-values converted to an absolute scale by considering the branching fraction BF,, of the transition
can be and the
782
R. SPERCER et al
z 6~0 7/2 (5)
z 6Pg2
z 6D!$2 t
a6D3t2
a6D7/2
(4) a6D512
Fig. 3. An example for two possibilities to link two transitions. The oscillator strength of the transition a 6D,.2-z 6P $,z (274.01 nm) is connected to the transition a 6D,2-; ‘D ‘;,?(265.36 nm). either through the path (4) -+ (2) + (0) - (I) or through (4) + (2) 4 (3) +(I). Phase shift measurements are indicated by solid arrows, emission measurements by dashed ones,
lifetime
T of the upper
level: s,f,, = W,&
The constant
C is a combination
0
-
(2)
‘C =
of natural
constants
and has a value of 1499.2.“’
8
0
--------___________ A
8
AA
A
0
A
0
0” A
0
A
0
A
A A
-0,6 250
300
350
wavelengthhm Fig. 4. Difference between the log(&)-values of this work and those of Younger et al” and Martin et al” [log(gf),,,,,,] as a function of wavelength. (0) correspond to transitions belonging to the a (‘D-multiplet (same values given in Refs 12 and 13), (0) (same values given in Refs 12 and 13, too) and (A) (Ref. 12) to those belonging to the a 4D-multiplet.
Absolute
oscillator
strengths
of CrII-lines
783
The relative oscillator strengths for lines with the same lower level are obtained from the spectral interferograms utilizing Fourier algorithms. The Fourier analysis yields the highly resolved phase change in the spectral vicinity of the transition. The so-determined experimental phase change is subject to a linear least-squares-fit procedure from which the NJ-values are obtained. A full description of this type of phase method has recently been published.4 Subsequently, the sets of oscillator strengths found by emission and dispersion methods have been combined using transitions measured in common. Where possible, the lines were linked together by taking different ways. Figure 3 shows an example where thef-value of the transition a 6D,,,-z ‘P yjz with the wavelength 274.009 nm is connected with the f-value of the transition a 6D,,,-z 6D ;);Iand the wavelength 265.357 nm, by using two possible ways. Besides, the transitions between the upper levels z 6P $, z 6D ;),>and the lower levels a 6D,,2, a bD,12establish a closed loop, since the oscillator strengths of the four different lines were measured by both methods (Fig. 3). If the lower levels of a four level system are indicated with (0) and (1) the upper ones with (2)
Table 1. Absolute oscillator strengths of CrII for the a6D-multiplet. The transition a “f$-z ‘D ;,‘2 is the reference transition with log(gf = -0.78. The comparison is made with values given in Refs 12 and 13, which confirmed that of Ref. 12. transition
wavelength
PI
E”
cm-t
cm-r
nm
- Z6Dom
49493
- z4Do siz -
log(gf)
fog(gfI
accuracy
this work
ref. 12/13
%
266.871
- 0.67
- 0.52
20
49352
267.879
- 0.39
20
Ii7
48750
272.275
- 1.002
20
- fiP05,,
48491
274.203
- 0.82
10
- *Pox2
48399
274 898
- 0 52
20
- fiF05,z
47041
285 568
-0 18
15
- +p0si2
49706
266 173
- 1.29
10
- *Do,,2
49646
266.602
-0 10
- 0 30
15
- z6D” 312
49565
267.180
-034
-037
15
- *Do,,2
49352
268.709
- 0.60
15
- 24PO312
49006
271.231
- 0.76
I5
- 26P0712
48632
274.009
- 1.18
- 26P”92
4849 1
275.073
- 0.43
IO
- 26P0312
48399
275.772
-053
15
- tiFO,/z
47228
284.983
- z6FoS/2
4704 1
286.51 I
- 0.12
- z4P0512
49706
267.283
- 0.59
- z6Po7R
48638
275.187
- 0.69
10
- z6PoJL?
48491
276.259
- 0.28
10
- z6Fo912
47465
284.324
0.052
- 0.11
10
- Z6FO712
47228
286.257
- 0.45
- 0.21
10
a6D3,, -
24P
12033
a6D5,2 -
a6DTj2 -
12148
0.13
- 1.00
- 0 05
20
10 10
12304 - 0.45
10
R.
784
and (3) a combination
of the,f-values
SPERGER
et
al
like (3)
should yield the value 1 for R, provided statistical errors do not contribute. (P indicates phase shift measurements and E emission measurements.) Taking the above mentioned levels as an example, a value of 0.82 had been obtained with an uncertainty of 25%. The lifetimes are taken from Ref. 11. In Tables 1 and 2 absolute oscillator strengths of singly ionized chromium for transitions with the lower levels belonging to the a 6D-- and u “D-multiplets are listed. Thef-values are converted to an absolute scale via the transition a 6D,s2--z‘D ; z. For the lifetime of the upper level z 6D (;,?a value of 4.5 nsec is given. The log(&)-value used as reference is - 0.78 with an assumed uncertainty of 6%. Younger et al’* and Martin et alI3 report an absolute log(&)-value of -0.65 for the mentioned transition, with an uncertainty of < 50%. The values of this work are compared with those of Younger et al” and Martin et alI3 in Tables 1 and 2. The values of the later published compilation of Martin et alI3 equal those of Ref. 12. where they
Table 2. Absolute oscillator strengths of CrII for the u’D-multiplet. The transition a “&-z ‘0 ;,> is the reference transition with log(g&r = -0.78. The comparison is made with values given in Refs 12 and 13. Where values are given in both references they are the same and those given only in Ref. 12 are put in parenthesis. ansition
wavelength
fog(gf)
log(gf)
accuracy
Et
E”
cm-t
cm-r
nm
this work
ref 12/13
%
- PD”,,,
54626
285.677
- 0.71
- 0 50
20
- ~~FOY,
51670
312.036
-0.19
0 12
20
- z4F03/z
51585
312.869
- 0.82
- 0 32
20
- Z6DOJ/Z
49706
332.406
- 121
- fiD”,/,
49565
333 981
- 1 03
(-048)
20
- Z6DOIn
49493
334.783
- 1.24
(-076)
20
- ~~D’J/z
54626
287 043
-0 14
- z4F0712
51789
312.494
0.44
- z4F”
51670
313.668
- 0 29
49706
334 257
- 0.51
(-041)
15
- #D”s,z
49565
335.849
- 0.44
(- 0.13)
15
- z4Do
49352
338.268
- 0.70
(- 0.33)
15
49006
342.273
- 0.15
(-0.01)
15
)3R -
19631
‘J/Z -
-
z4P
15
19798
512 92
512
- z4P” 312
- 0.02
15 15
- 0 25
15
Absolute oscillator strengths of CrII-lines
785
096
092o,.
0
OO
_--------A~-___*____________ 00A
A
-0,2 -
0
0
0 A
-0,4 -
0
A
0
A A
0
A
-0.6 i5000
50000
55000
upper level energy/cm’ l Fig. 5. Log(&)-difference
plot as a function of the upper level energy (for further explanation see text of Fig. 4).
are considered by Martin et al” for the spectral range discussed here. Values reported only in the older compilation of Younger et al’* are put into parenthesis (Table 2). In Fig. 4 the d-values of this work are compared graphically to those of other authors depending on the wavelength, corresponding to the Tables 1 and 2. This comparison shows a systematical tendency in the deviations of log(&)-values with the wavelength. At higher wavelengths especially the values of Ref. 12 were found to be larger than our values. Besides a large spread, no clear systematic tendency can be recognized from Fig. 5, in which the log(&)-difference plot shows the dependence on the upper level energy. Since LTE is not required for the evaluation of oscillator strengths as performed in this work and two completely different kinds of measurements have been combined too, the values found should be superior to those, which are based on LTE assumptions in principle. Figure 4 might suggest possible discrepancies in the calibration of the spectral sensitivity of the detectors between the measurements cited in Ref. 12 and our measurements. REFERENCES 1. M. C. E. Huber and R. J. Sandeman, Rep. Prog. Phys. 49, 397 (1986). 2. K. Danzmann and M. Kock, J. Phys. B: Atom. Molec. Whys. 13, 2051 (1980). 3. B. L. Cardon, P. L. Smith and W. Whaling, Phys. Rev. 20, 2411 (1979). 4. R. Sperger and T. Neger, Opt. Commun. 80, 401 (1991). 5. R. Sperger, Thesis, Technische Universitat Graz (1990). 6. H. JHger, T. Neger, and R. Sperger, Opt. Commun. 61, 252 (1986). 7. J. M. Bridges and W. R. Ott, Appl. Opt. 16, 367 (1977). 8. H. Magdeburg and U. Schley, Z. Angew. Phys. 20, 465 (1966). 9. K. Danzmann, M. Gunther, J. Fischer, M. Kock and M. Ktihne, Appl. Opt. 27, 4974 (1988). IO. A. P. Thorne, Spectrophysics, Chapman and Hall (1974). 1I. W. Schade, B. Mundt and V. Helbig, Phys. Rev. A 42, 1 (1990). 12. S. M. Younger, J. R. Fuhr, G. A. Martin and W. L. Wiese, J. Phys. Chem. RejT Data 7, 565 (1978). 13. G. A. Martin, J. R. Fuhr and W. L. Wiese, J. Phys. Chem. Re$ Data 17, 336 (1988).
Pergamon
ABSOLUTE OSCILLATOR STRENGTHS OF CrII-LINES FROM COMBINED PHASE SHIFT AND EMISSION MEASUREMENTS R. SPERGER,?
B. SCHELM,~ M. KOCK,$
T. NEGER,f’§
and M. ULBELt
tlnstitut fiir Experimentalphysik, Technische Universitit Graz, Petersgasse 16, A-8010 Graz, Austria and JInstitut fiir Plasmaphysik, Universitat Hannover, CallinstraBe 38, D-3000 Hannover I, Germany (Received 22 July 1993)
Abstract-Oscillator strengths of lines of singly ionized chromium have been obtained by a combination of emission and spectra-interferometric measurements. A hollow cathode is used as a light source for the emission measurements, where relative oscillator strengths of lines with the upper level in common are determined by measuring branching ratios. The determination of relative oscillator strengths of lines having the lower level in common is based on a phase shift method, which employs a Fourier analysis of the spectral interferograms. A modified wallstabilized arc serves as the light source here. Large sets of relative oscillator strengths are
obtained by linking the results of the two types of measurements. With known lifetimes the relative f-values are connected to an absolute scale where the overall uncertainty is between 10 and 30%.
INTRODUCTION In the last years there has been an increased interest in absolute oscillator strengths of singly ionized elements of the iron group. The data are not only needed for a quantitative analysis of laboratory plasmas and in fusion research, but also for abundance studies in astrophysics. In principle, there are three classical methods of optical plasmadiagnostics used for the determination of oscillator strengths: emission, absorption, and dispersion methods.’ Each method requires different experimental conditions in order to minimize systematic and statistical errors. A combination of level lifetimes with branching ratio measurements delivers reliable but small sets of absolute f-values. Such sets of f-values can be enlarged successfully by linking relative f-values of lines with a common lower level via transitions which exist in both sets.* The latter measurements can be done in absorption or with dispersive methods such as being reported in this paper. In this work a phase shift measurement including a Fourier analysis of the interferograms is preferred, since it can be considered generally as more accurate and more objective than spectra-interferometric methods based on simple fringe-peak-detection. By using the two different techniques mentioned above the data are combined in consistent sets of oscillator strengths. The linking of sets off-values measured in emission and dispersion requires at least one transition in common. If more than one transition is in common, there are several ways of possible linkage, thus increasing the redundance. This method utilizes closed loops 3 and has already been applied to some elements.2.4-6 For a conversion of the data to an absolute scale the lifetime of at least one upper level must be known. Together with the branching fraction of this level the absolute scale can be found. It should be pointed out that neither the technique of branching ratios nor the phase shift method requires any assumptions on the plasma state. The independent measurement of lines is a useful tool for a consistency check for both emission and spectra-interferometric data.
§To whom all correspondence
should be addressed. 779
780
R.
SPERCER
et al
EXPERIMENTAL
Emission
measurements
Figure 1 shows schematically the setup for the emission measurements. The line intensities were recorded photoelectrically using a photomultiplier in connection with a photon counting system. A 2-m-scanning-monochromator in Czerny-Turner configuration with a plane grating of 2400 lines/mm and a slit width of 10pm was used. For the calibration of the line intensities a mini-arc’ and a current-stabilized carbon arc’ were applied as radiation standards. A hollow cathode discharge served as light source.’ It consisted of three watercooled electrodes: two anodes and a cylindrical tube cathode made of chromium~nickelLstee1 having a length of about 60 mm. In addition, the inner part of the cylinder was hard-chromium-plated to provide a longer period of working. Glass tubes ensured the electrical insulation of the electrodes. The discharge was observed end-on through one anode. It was operated with stationary currents between 0.5 and 2 A. Either neon with pressures between 2 and 4 mbar or argon with pressures between 1 and 2 mbar were used as buffer gases. Current, pressure and buffer gas were varied in order to avoid the risk of blends and misinterpretation of lines. To meet the assumption that the lines were emitted from an optically thin layer, strong lines were checked in relation to weak lines with regard to self-absorption effects by varying the current of the discharge. Phase shft
measurements
The optical arrangement for the phase shift measurements is shown in Fig. 2. The main part of the optical setup is a Mach-Zehnder interferometer illuminated by a “white light” source (a pulsed capillary discharge, CD). In order to avoid a diminishing of the contrast of the interferograms because of too strong illumination by the radiation of the arc plasma (A). a fast shutter (FS) is used. The exposure time is adjusted to match the time interval of emission of the background light source (~440 psec). Two spectrographs (Jobin Yvon HR 1000, focal length m. grating 2000 lines/mm; GH, focal I .6 m, grating with 2 160 lines/mm) were used to record simultaneously
I I I
SCM --------
--l---____z~’
t-----, TM
I
’
D
SM
PM
PCS
tl
RS
PC
Fig. I. Sketch of the optical setup for the emission measurements. SM, spherical plane mirror; D, diaphragm; H. hollow cathode; SCM, scanning monochromator; PCS, photon counting system: RS, radiation standard; PC. personal
mirror; TM. turnable PM, photomultiplier; computer.
Absolute
BS
oscillator
W
strengths
781
of CrII-lines
W
M
Fig. 2. The optical setup for the phase shift measurements. CD, capillary discharge; L, lense; BS, beamsplitter; M, plane mirror; W, window; CP, compensation plate; A. test zone with arc; FS. fast shutter; D, diaphragm; ES, entrance slit of spectrograph.
interferograms in widely separated spectral regions at wavelengths of transitions which have the same lower level in common but have rather different upper levels on the energy scale. For the dispersion measurements a modified cascaded wall-stabilized arc was used.’ The cascade consisted of rings of graphite which were insulated from one another by beads of aluminium oxide ceramic. Sintered rings of chromium oxide were placed concentrically within the graphite rings. This arrangement was inserted into a tube of aluminium oxide ceramic. The whole assembly was fitted inside a vacuum sealed hard glass tube. Due to the radiation of the plasma column, particles are evaporated from inner wall of the rings of metal oxide to provide a dense plasma with a sufficient population of CrII levels necessary for a successful application of dispersion methods. Since the central part of the arc was not water-cooled, the tendency to condensation of the vapour could be diminished. The arc-plasma was prepared at stationary currents of about 25 A. The spectral interferograms, however, were recorded during a superposed current pulse (maximum being 250 A). Its duration and the delay between start of the current pulse and opening of the fast shutter could be adjusted, in order to optimize the population number densities of the excited CrII states as desired.
DATA
REDUCTION
AND
RESULTS
From the emission measurements sets of relative oscillator strengths have been obtained. The relativef-values are found by comparing the measured line intensities. If a transition from an upper level u to a lower level I, is compared with a transition from level u to a lower level L, the relative f-value results from
(I intensity of the line, A wavelength, g statistical weight of the level). The relativef-values converted to an absolute scale by considering the branching fraction BF,, of the transition
can be and the
782
R. SPERCER et al
z 6~0 7/2 (5)
z 6Pg2
z 6D!$2 t
a6D3t2
a6D7/2
(4) a6D512
Fig. 3. An example for two possibilities to link two transitions. The oscillator strength of the transition a 6D,.2-z 6P $,z (274.01 nm) is connected to the transition a 6D,2-; ‘D ‘;,?(265.36 nm). either through the path (4) -+ (2) + (0) - (I) or through (4) + (2) 4 (3) +(I). Phase shift measurements are indicated by solid arrows, emission measurements by dashed ones,
lifetime
T of the upper
level: s,f,, = W,&
The constant
C is a combination
0
-
(2)
‘C =
of natural
constants
and has a value of 1499.2.“’
8
0
--------___________ A
8
AA
A
0
A
0
0” A
0
A
0
A
A A
-0,6 250
300
350
wavelengthhm Fig. 4. Difference between the log(&)-values of this work and those of Younger et al” and Martin et al” [log(gf),,,,,,] as a function of wavelength. (0) correspond to transitions belonging to the a (‘D-multiplet (same values given in Refs 12 and 13), (0) (same values given in Refs 12 and 13, too) and (A) (Ref. 12) to those belonging to the a 4D-multiplet.
Absolute
oscillator
strengths
of CrII-lines
783
The relative oscillator strengths for lines with the same lower level are obtained from the spectral interferograms utilizing Fourier algorithms. The Fourier analysis yields the highly resolved phase change in the spectral vicinity of the transition. The so-determined experimental phase change is subject to a linear least-squares-fit procedure from which the NJ-values are obtained. A full description of this type of phase method has recently been published.4 Subsequently, the sets of oscillator strengths found by emission and dispersion methods have been combined using transitions measured in common. Where possible, the lines were linked together by taking different ways. Figure 3 shows an example where thef-value of the transition a 6D,,,-z ‘P yjz with the wavelength 274.009 nm is connected with the f-value of the transition a 6D,,,-z 6D ;);Iand the wavelength 265.357 nm, by using two possible ways. Besides, the transitions between the upper levels z 6P $, z 6D ;),>and the lower levels a 6D,,2, a bD,12establish a closed loop, since the oscillator strengths of the four different lines were measured by both methods (Fig. 3). If the lower levels of a four level system are indicated with (0) and (1) the upper ones with (2)
Table 1. Absolute oscillator strengths of CrII for the a6D-multiplet. The transition a “f$-z ‘D ;,‘2 is the reference transition with log(gf = -0.78. The comparison is made with values given in Refs 12 and 13, which confirmed that of Ref. 12. transition
wavelength
PI
E”
cm-t
cm-r
nm
- Z6Dom
49493
- z4Do siz -
log(gf)
fog(gfI
accuracy
this work
ref. 12/13
%
266.871
- 0.67
- 0.52
20
49352
267.879
- 0.39
20
Ii7
48750
272.275
- 1.002
20
- fiP05,,
48491
274.203
- 0.82
10
- *Pox2
48399
274 898
- 0 52
20
- fiF05,z
47041
285 568
-0 18
15
- +p0si2
49706
266 173
- 1.29
10
- *Do,,2
49646
266.602
-0 10
- 0 30
15
- z6D” 312
49565
267.180
-034
-037
15
- *Do,,2
49352
268.709
- 0.60
15
- 24PO312
49006
271.231
- 0.76
I5
- 26P0712
48632
274.009
- 1.18
- 26P”92
4849 1
275.073
- 0.43
IO
- 26P0312
48399
275.772
-053
15
- tiFO,/z
47228
284.983
- z6FoS/2
4704 1
286.51 I
- 0.12
- z4P0512
49706
267.283
- 0.59
- z6Po7R
48638
275.187
- 0.69
10
- z6PoJL?
48491
276.259
- 0.28
10
- z6Fo912
47465
284.324
0.052
- 0.11
10
- Z6FO712
47228
286.257
- 0.45
- 0.21
10
a6D3,, -
24P
12033
a6D5,2 -
a6DTj2 -
12148
0.13
- 1.00
- 0 05
20
10 10
12304 - 0.45
10
R.
784
and (3) a combination
of the,f-values
SPERGER
et
al
like (3)
should yield the value 1 for R, provided statistical errors do not contribute. (P indicates phase shift measurements and E emission measurements.) Taking the above mentioned levels as an example, a value of 0.82 had been obtained with an uncertainty of 25%. The lifetimes are taken from Ref. 11. In Tables 1 and 2 absolute oscillator strengths of singly ionized chromium for transitions with the lower levels belonging to the a 6D-- and u “D-multiplets are listed. Thef-values are converted to an absolute scale via the transition a 6D,s2--z‘D ; z. For the lifetime of the upper level z 6D (;,?a value of 4.5 nsec is given. The log(&)-value used as reference is - 0.78 with an assumed uncertainty of 6%. Younger et al’* and Martin et alI3 report an absolute log(&)-value of -0.65 for the mentioned transition, with an uncertainty of < 50%. The values of this work are compared with those of Younger et al” and Martin et alI3 in Tables 1 and 2. The values of the later published compilation of Martin et alI3 equal those of Ref. 12. where they
Table 2. Absolute oscillator strengths of CrII for the u’D-multiplet. The transition a “&-z ‘0 ;,> is the reference transition with log(g&r = -0.78. The comparison is made with values given in Refs 12 and 13. Where values are given in both references they are the same and those given only in Ref. 12 are put in parenthesis. ansition
wavelength
fog(gf)
log(gf)
accuracy
Et
E”
cm-t
cm-r
nm
this work
ref 12/13
%
- PD”,,,
54626
285.677
- 0.71
- 0 50
20
- ~~FOY,
51670
312.036
-0.19
0 12
20
- z4F03/z
51585
312.869
- 0.82
- 0 32
20
- Z6DOJ/Z
49706
332.406
- 121
- fiD”,/,
49565
333 981
- 1 03
(-048)
20
- Z6DOIn
49493
334.783
- 1.24
(-076)
20
- ~~D’J/z
54626
287 043
-0 14
- z4F0712
51789
312.494
0.44
- z4F”
51670
313.668
- 0 29
49706
334 257
- 0.51
(-041)
15
- #D”s,z
49565
335.849
- 0.44
(- 0.13)
15
- z4Do
49352
338.268
- 0.70
(- 0.33)
15
49006
342.273
- 0.15
(-0.01)
15
)3R -
19631
‘J/Z -
-
z4P
15
19798
512 92
512
- z4P” 312
- 0.02
15 15
- 0 25
15
Absolute oscillator strengths of CrII-lines
785
096
092o,.
0
OO
_--------A~-___*____________ 00A
A
-0,2 -
0
0
0 A
-0,4 -
0
A
0
A A
0
A
-0.6 i5000
50000
55000
upper level energy/cm’ l Fig. 5. Log(&)-difference
plot as a function of the upper level energy (for further explanation see text of Fig. 4).
are considered by Martin et al” for the spectral range discussed here. Values reported only in the older compilation of Younger et al’* are put into parenthesis (Table 2). In Fig. 4 the d-values of this work are compared graphically to those of other authors depending on the wavelength, corresponding to the Tables 1 and 2. This comparison shows a systematical tendency in the deviations of log(&)-values with the wavelength. At higher wavelengths especially the values of Ref. 12 were found to be larger than our values. Besides a large spread, no clear systematic tendency can be recognized from Fig. 5, in which the log(&)-difference plot shows the dependence on the upper level energy. Since LTE is not required for the evaluation of oscillator strengths as performed in this work and two completely different kinds of measurements have been combined too, the values found should be superior to those, which are based on LTE assumptions in principle. Figure 4 might suggest possible discrepancies in the calibration of the spectral sensitivity of the detectors between the measurements cited in Ref. 12 and our measurements. REFERENCES 1. M. C. E. Huber and R. J. Sandeman, Rep. Prog. Phys. 49, 397 (1986). 2. K. Danzmann and M. Kock, J. Phys. B: Atom. Molec. Whys. 13, 2051 (1980). 3. B. L. Cardon, P. L. Smith and W. Whaling, Phys. Rev. 20, 2411 (1979). 4. R. Sperger and T. Neger, Opt. Commun. 80, 401 (1991). 5. R. Sperger, Thesis, Technische Universitat Graz (1990). 6. H. JHger, T. Neger, and R. Sperger, Opt. Commun. 61, 252 (1986). 7. J. M. Bridges and W. R. Ott, Appl. Opt. 16, 367 (1977). 8. H. Magdeburg and U. Schley, Z. Angew. Phys. 20, 465 (1966). 9. K. Danzmann, M. Gunther, J. Fischer, M. Kock and M. Ktihne, Appl. Opt. 27, 4974 (1988). IO. A. P. Thorne, Spectrophysics, Chapman and Hall (1974). 1I. W. Schade, B. Mundt and V. Helbig, Phys. Rev. A 42, 1 (1990). 12. S. M. Younger, J. R. Fuhr, G. A. Martin and W. L. Wiese, J. Phys. Chem. RejT Data 7, 565 (1978). 13. G. A. Martin, J. R. Fuhr and W. L. Wiese, J. Phys. Chem. Re$ Data 17, 336 (1988).