4 Results and conclusions

 

 

Table 2: A_ki-values obtained in this work and the comparison with the existing literature. Next to the data from this work, statistical deviation in percentage is indicated in parentheses. Relative data from Miller et al. (1972) are rescaled to the value of Fuhr & Wiese (1998) at $\lambda =435.5$ nm.

$\lambda$	Transition	Multiplet	Aki	Ref.	Aki	Ref.
(nm)			(108 s-1)	(exp)	(108 s-1)	(th)
457.720	5s'-5p'	2D5/2-2F $^{\rm o}_{7/2}$	0.741 (12)	This work	1.415	Spector & Garpman (1977)
			6.9	Levchenko (1971)
			1.54	Miller et al. (1972)
			0.961	Keil (1973)
			1.05	Baessler et al. (1979)
			1.23	Fonseca & Campos (1982)
			0.795	Brandt et al. (1982)	1.15	Brandt et al. (1982)
			2.76	Bertuccelli & Di Rocco (1991)
			0.73	Samoilov et al. (1975)
			0.831	Castro et al. (2001)
			0.96	Fuhr & Wiese (1998)
458.285	5p-6s	4D $^{\rm o}_{5/2}$-4P3/2	0.811 (2)	This work
			0.812	Castro et al. (2001)
			0.76	Fuhr & Wiese (1998)
459.280	5p'-4d''	2P $^{\rm o}_{3/2}$-2D5/2	0.293 (6)	This work
459.849	5p-6s	2P $^{\rm o}_{3/2}$-4P1/2	0.232 (9)	This work
460.402	5p-6s	4D $^{\rm o}_{1/2}$-4P1/2	0.420 (11)	This work
461.528	5s-5p	2P3/2-2P $^{\rm o}_{3/2}$	0.499 (2)	This work	0.7898	Koozekanani & Trusty (1969)
			0.87	Miller et al. (1972)	0.732	Spector & Garpman (1977)
			0.99	Podbiralina et al. (1973)	0.125	El Sherbini (1976)
			0.23	Samoilov et al. (1975)
			1.55	Bertuccelli & Di Rocco (1991)
			0.509	Castro et al. (2001)
			0.54	Fuhr & Wiese (1998)
461.915	5s-5p	2P3/2-2D $^{\rm o}_{5/2}$	0.74 (12)	This work	0.771	Koozekanani & Trusty (1969)
			1.47	Miller et al. (1972)	0.325	El Sherbini (1976)
			0.808	Keil (1973)	1.24	Spector & Garpman (1977)
			0.45	Samoilov et al. (1975)
			0.817	Brandt et al. (1982)	1.24	Brandt et al. (1982)
			1.62	Bertuccelli & Di Rocco (1991)
			0.748	Castro et al. (2001)
			0.81	Fuhr & Wiese (1998)
479.633	5p-6s	4S $^{\rm o}_{3/2}$-2P1/2	0.180 (9)	This work
480.297	4d-5p'	4P5/2-2D $^{\rm o}_{3/2}$	0.006 (12)	This work
481.176	5s-5p	4P1/2-4D $^{\rm o}_{3/2}$	0.133 (4)	This work	0.412	Koozekanani & Trusty (1969)
			0.9	Levchenko (1971)	0.166	Spector & Garpman (1977)
			0.46	Miller et al. (1972)	0.005	El Sherbini (1976)
			0.32	Bertuccelli & Di Rocco (1991)
			0.17	Fuhr & Wiese (1998)
482.518	5s-5p	2P1/2-4S $^{\rm o}_{3/2}$	0.246 (5)	This work	0.073	Koozekanani & Trusty (1969)
			0.08	Levchenko (1971)	0.388	Spector & Garpman (1977)
			0.5	Miller et al. (1972)	0.153	El Sherbini (1976)
			0.33	Podbiralina et al. (1973)
			0.54	Bertuccelli & Di Rocco (1991)
			0.208	Castro et al. (2001)
			0.19	Fuhr & Wiese (1998)

 

Table 2: continued.

$\lambda$	Transition	Multiplet	Aki	Ref.	Aki	Ref.
(nm)			(108 s-1)	(exp)	(108 s-1)	(th)
483.207	5s-5p	4P3/2-4P $^{\rm o}_{1/2}$	0.896 (12)	This work	1.061	Koozekanani & Trusty (1969)
			4.98	Levchenko (1971)	1.127	Spector & Garpman (1977)
			1.46	Miller et al. (1972)	0.584	El Sherbini (1976)
			1.67	Bertuccelli & Di Rocco (1991)
			0.787	Castro et al. (2001)
			0.73	Fuhr & Wiese (1998)
483.656	5p-5d	2S $^{\rm o}_{1/2}$-4D1/2	0.372 (6)	This work
484.660	5s-5p	2P3/2-2P $^{\rm o}_{1/2}$	0.796 (9)	This work	1.053	Spector & Garpman (1977)
			1.75	Miller et al. (1972)
			2.54	Podbiralina et al. (1973)	<0.0009	El Sherbini (1976)
			0.898	Brandt et al. (1982)	0.36	Brandt et al. (1982)
			2.4	Bertuccelli & Di Rocco (1991)
			0.762	Castro et al. (2001)
530.866	5s-5p	4P3/2-4P $^{\rm o}_{5/2}$	0.025 (5)	This work	0.043	Koozekanani & Trusty (1969)
			0.024	Fuhr & Wiese (1998)	0.071	El Sherbini (1976)
531.741	5p-5d	2D $^{\rm o}_{3/2}$-4P1/2	0.038 (9)	This work
532.277	5p-6s	2P $^{\rm o}_{1/2}$-4P3/2	0.042 (5)	This work
533.341	4d'-5f	2D5/2-2F $^{\rm o}_{7/2}$	0.494 (1)	This work
			0.49	Castro et al. (2001)
534.676	5p-6s	4D $^{\rm o}_{3/2}$-4P5/2	0.028 (6)	This work
535.545	4d-5f	2D5/2-4F $^{\rm o}_{5/2}$	0.018 (9)	This work
541.843	4d'-5f	2D3/2-2D $^{\rm o}_{3/2}$	0.079 (16)	This work
543.863	4d-5p	4D1/2-4D $^{\rm o}_{1/2}$	0.058 (29)	This work
544.634	4d-5p	4D1/2-2P $^{\rm o}_{3/2}$	0.027(9)	This work
546.817	4d'-5f	2D3/2-2F $^{\rm o}_{5/2}$	0.332(13)	This work
549.954	5s-5p	4P1/2-4P $^{\rm o}_{1/2}$	0.014 (11)	This work	0.030	Koozekanani & Trusty (1969)
					0.021	El Sherbini (1976)
553.229	4d-5p'	2F7/2-2F $^{\rm o}_{7/2}$	0.001 (20)	This work
555.299	4d'-5f	2D3/2-4F $^{\rm o}_{5/2}$	0.109 (6)	This work
556.865	4d-5p	4D5/2-4D $^{\rm o}_{3/2}$	0.034 (3)	This work
			0.025	Podbiralina et al. (1973)
			0.025	Samoilov et al. (1975)
565.037	4d-5p'	2P3/2-2D $^{\rm o}_{5/2}$	0.006 (38)	This work
568.189	5s-5p	2P3/2-4D $^{\rm o}_{5/2}$	0.100 (8)	This work	0.314	Koozekanani & Trusty (1969)
					0.358	El Sherbini (1976)
569.035	4d-5p'	2P3/2-2D $^{\rm o}_{3/2}$	0.246 (7)	This work
			0.082	Samoilov et al. (1975)
574.927	5p'-5d	2D $^{\rm o}_{5/2}$-2D5/2	0.018 (36)	This work
575.298	5s-5p	2P1/2-4D $^{\rm o}_{3/2}$	0.014 (8)	This work	0.037	Koozekanani & Trusty (1969)
					0.013	El Sherbini (1976)
577.141	4d-5p	4D1/2-2P $^{\rm o}_{1/2}$	0.086 (8)	This work
577.772	4d'-5f	2F5/2-4F $^{\rm o}_{7/2}$	0.020 (39)	This work

Once an A_ki-value has been obtained for each line and at each instant where this line was measured, plots representing all these values along the plasma life have been made. One of them, showing the measured transitions probabilities for the KrII 459.28 and 555.299 nm is shown in Fig. 6. As can be seen, no systematic trends are observed in any of the lines. The random distribution around the mean value is a typical behaviour in these measurements. From now on, we will assign the mean value as the A_ki-value and the standard deviation as a quality indicator of the mean value. In this sense, it is significant that 28 of the 35 measured KrII lines have uncertainties lower than 15% and only the 7 weakest lines show greater uncertainties. This result shows the quality of the measurements performed.

Figure 6: Two examples of the evolution of the measured transition probabilities measured in this work along the plasma life. No systematic trends are detected.

In Table 2, all measured transitions have been indicated. They have been ordered by increasing wavelength (first column). The second and third columns indicate the transition array and multiplet respectively, in all cases according to the notation suggested by Striganov & Sventitskii (1968). The fourth and fifth columns contain all the experimental works considered, indicating in the case of data coming from this work the calculated standard deviation (in percentage) in parentheses. It is important to remark that, in the case of the work from Miller et al. (1972), this work offers relative transition probabilities but, since the value for $\lambda =435.5$ nm is coincident with that recommended by Fuhr & Wiese (1998), both sets of data are comparable between them and of course, with our data. The sixth and seventh columns contain the A_ki-values obtained from theoretical calculations.

When taking a look at the comparisons among data in Table 2, the first noticeable point is the great scatter in the data. This is a very old problem in KrII transition probabilities, with two different aspects: the absolute scale of the A_ki-values compared and the quality of the relative ones. In this work, as explained in Sect. 3.3, the scale selected by us to transform our relative measurements to absolute ones corresponds to that of Castro et al. (2001), which is really the same as that of Fuhr & Wiese (1998). In this last publication, the authors maintain as a reference the same data published by NIST from 1978 (Wiese & Martin 1978, 1980; Fuhr & Wiese 1990, 1996). If we re-examine Fig. 4, we see the nice linear behaviour of the KrII excited states population, a situation always present with our plasma source (e.g. Gigosos et al. 1994; Aparicio et al. 1997; del Val et al. 2000; Mar et al. 2000) and a first result can be guessed. The data from Castro et al. (2001), from Fuhr & Wiese (1998) and therefore, from ourselves, might not be a good absolute scale, but at least does seem to represent a good relative one. Small differences between the data from Castro et al. (2001) and ours, corresponding to measurements performed in the same plasma source, arise from the uncertainty in intensity measurements and statistical deviations of the fits in the Boltzmann plots.

If we compare our data with other experimental ones, we find a curious agreement with those from Brandt et al. (1982) and Keil (1973). Both works correspond to measurements performed in wall-stabilized arcs at atmospheric pressure by assuming total LTE. Although there are only three data points to compare with Brandt et al. (1982), the mean ratio between our data and theirs is 0.91 with only 2% statistical deviation. The arc at atmospheric pressure is probably one of the plasma sources closest to LTE and the two-wavelength interferometry technique employed by them in $N_{\rm e}$ diagnostics is one of the most accurate ones used to determine this parameter. The plasma generated in our work has been demonstrated to be well described by a pLTE model and other plasmas generated by this source have been shown to be very close to LTE (Aparicio et al. 1999). As a conclusion, we can say that the scale from Brandt et al. (1982) is probably near to the absolute scale. In relation to data from Miller et al. (1972), very frequently considered as a good reference in a relative scale, we do not find good coincidence with our data. In fact, even assuming that $\lambda =435.5$ nm is not a good line to use as the reference to rescale their work (this is one of the most prominent lines in KrII visible spectra and is very sensitive to self-absorption), we find that the ratio between their data and ours is $2.11 \pm 25$%. We can conclude that data from Miller et al. (1972) must be taken with care as a relative scale of KrII transition probabilities. These comparisons can be shown in Fig. 7. If we try comparisons with Bertuccelli & Di Rocco (1991), the mean ratio between their data and ours is $2.64 \pm 23$%. Comparisons with other experimental works reveal greater differences between their relative scales and ours.

Figure 7: Comparisons between the ratios of data taken from the bibliography (bib) and ours (Tw). Data taken from Table 1 correspond with those labelled with an asterisk there, that is to say, those employed in the Boltzmann plots. For the ratios with these data, 15% error bars have been considered for our results.

Relative to theoretical works, comparisons with data from Koozekanani & Trusty (1969), based on intermediate coupling calculations with the absolute values obtained from Hartree-Fock functions, are very poor. Their data are on average 1.87 times greater than ours, with a deviation around 49%. Discrepancies are even greater when compared to calculations from El Sherbini (1976). However, we note the very good coincidence between the conclusions extracted by Brandt et al. (1982) and ours in relation to calculations performed by Spector & Garpman (1977), on the basis of intermediate coupling coefficients with the radial integral obtained from relativistic self-consistent-field wavefunctions. They found a mean ratio between their data and those from this theoretical reference of around $1.5 \pm 14$%. Certainly, the present work contains only three lines measured by Brandt et al. (1982) as stated before, and four other ones not measured by them but calculated by Spector & Garpman (1977), but curiously the mean ratio between this theoretical work and our data is $1.493 \pm 15$%, almost the same as that found by Brandt et al. (1982) with a systematic but reasonable deviation. We think this result reinforces the idea of a good placing of our data in a relative scale and is probably not far from an absolute one.

As a final conclusion, this work offers transition probabilities of a set of 35 KrII lines in the spectral region from 450 to 580 nm. For 20 of them, there are no previous data. We can estimate an error of 15% for more than 80% of them and 40% for the rest, always on a relative scale. Many of them will be useful in refining new calculation models. Furthermore, this work sheds some light what are probably the most significant theoretical and experimental works, those of Spector & Garpman (1977) and Brandt et al. (1982) respectively. However, new and more precise calculations and measurements are still required in order to clarify the uncertainties remaining in KrII transition probabilities.

Acknowledgements

The authors thank S. González for his collaboration in the experimental arrangement, and the Spanish Dirección General de Investigación Científica y Técnica (Ministerio de Educación y Ciencia) and the Consejería de Educación y Cultura de Castilla y León for their financial support under contracts No. PB98-0356 and VA23-99 respectively. Dr. J. A. Aparicio wants to express his personal acknowledgement to the Organización Nacional de Ciegos de España (ONCE) for help.