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Astron. Astrophys. 328, 752-755 (1997)

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3. Discussion

A typical P II emission spectrum, acquired with 0.006nm full-width half-maximum spectral resolution, is shown in Figure 1. The measured intensity ratio of the [FORMULA] transtion at 221.0nm to the [FORMULA] transition at 219.6nm is [FORMULA]. Because the two lines can be observed simultaneously, there are no errors due to drifts of the source. Therefore, long integration times can be used to reduce photon statistical noise. Depending upon source conditions, integration times range from 1 to 10 minutes, resulting in statistical uncertainties in the final measurement of less than 2%. The spectrum shown in Figure 1 has already been divided by the radiometric curve obtained with the deuterium lamp, and so exhibits the true signal-to-noise arising from both the measurement and the radiometric correction.

[FIGURE] Fig. 1. P II spectrum showing the [FORMULA] branch at 221.033nm and the [FORMULA] branch at 219.556nm. The spectral resolution is .006nm.

Although the echelle grating gives greatly improved dispersion and resolution over a standard grating, it has the difficulty that many spectral orders overlap.

Unwanted orders can be very effectively eliminated with the use of a pre-monochromator with a suitably narrow bandpass, such as the Seya-Namioka instrument used here. However, when extremely weak lines are being observed, as in the present case, a small amount of leakage from other orders can sometimes be observed. In Figure 1, an off-order Ar line can be seen on the short wavelength side of the 219.6nm line. The relative intensity of the Ar line is only about 10% and it is almost completely resolved from the 219.6nm line. The two lines are separated by 0.012nm and the spectral resolution is 0.006nm. The line appearing at 220.7nm is actually a He I line at 318.77nm in [FORMULA] order.

Possible systematic effects at the 5% level and below are difficult to identify. We can say, however, that because of the small transition probabilities of these lines it is certain that radiation trapping does not occur. In addition, both lines originate from a common upper level, so collisional processes do not influence their relative intensities. A check for errors in the radiometric correction is made by changing the position of the lines relative to the pre-monochromator bandpass and to the photodiode array, independently. Although we have used a resolving power of 35,000, there is also the possibility of a weak unresolved blend.

Difficulties in calculating parameters such as branching ratios, fine-structure splitting, and lifetimes for weak inter-system lines have been noted (Brage 1997, Ellis 1989, Martinson and Ellis 1985). Several calculations of the [FORMULA] multiplet branching ratio in P II have been presented in recent years which have varied by as much as a factor of two (see Table 1), although most are in the range 2.81-2.94. Many of the efforts have focussed on the lifetime of the [FORMULA] level which was measured by Calamai (1992). However, Brage (1997) has shown that the lifetime and branching ratio are influenced by different physical effects.

Recent ab initio calculations by Brage (1997) have given a ratio in the range 2.82-2.94 depending on the number of terms mixing with the [FORMULA] level and the exact form of the Hamiltonian used. The present measurement confirms the upper end of this range, although the experimental uncertainty is not yet small enough to differentiate between some of the theoretical fine-tuning that has been attempted recently.

No precise measurements for this branching ratio have been made previously. An early laboratory observation by Martin (1959) yielded an estimated ratio of 2.5, with no experimental uncertainty given. Svendinius (1983) observed a ratio of 0.5, but this anomalous result was later shown to be caused by a contaminating P IV line (Smith et al. 1984b). A measurement of the same ratio in iso-electronic S III (the branching ratio is expected to vary slowly along an iso-electronuc sequence) yielded a value of 2.7 (Moos et al. 1983). This latter result is in agreement with Brage's (1997) calculations for S III.

The P II 219.6nm and 221.0nm lines are the only significant decay branches of the [FORMULA] metastable level, so absolute transition probabilities for these transitions can be obtained by combining our measured branching ratio with the previously measured lifetime of the [FORMULA] level (Calamai et al. 1992). Using [FORMULA] sec, the absolute transition probabilities are [FORMULA] s-1 and [FORMULA] s-1.

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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998