This paper presents for the first time effective collision strengths for
fine-structure
forbidden transitions in the ground configurations of the 4p
ions
KrIII, IV, V obtained with the
BP R-matrix approach. The comparison with the semi-relativistic
TCC method, essentially an algebraic recoupling technique using
term-coupling coefficients, reveals that the effects of full intermediate
coupling manifest themselves most strongly at low electron temperatures
where the two methods differ by up to a factor of 2.
However, for higher temperatures (
) both methods
generally agree to within 20%. Considering analyses of collisionally
excited lines of krypton ions in PNe with high nebular temperatures
these deviations are comparable with other uncertainties, e.g. due to
the determination of ionization equilibria for heavy elements. Thus
we conclude that for present diagnostics of nebular spectra
the semi-relativistic method can be an adequate alternative to the
computationally expensive BP calculations.
We have reanalysed the spectroscopic data of PB94 for NGC 7027 using our calculated collision strengths for the krypton ions. Our results confirm, although to a lesser extent, the enrichment of krypton in the nebula. The question concerning the mechanisms of the effective enhancement of the heavy element in the atmosphere of the progenitor of NGC 7027 is still open for discussion and will stimulate new strategies in the models of nucleosynthesis and stellar evolution. We note that our data will also be very useful for spectral analyses of other PNe and probably HII regions where lines of krypton ions may be detected with improved observational equipment.
Our future efforts will focus on the application of the Dirac R-matrix method to the calculation of collision strengths for at least one of the krypton ions. This investigation will make possible further checks of the accuracy of the present data. Collision strengths for other ions of astrophysical interest (Xe, Ba, Ni) will be available in the near future.
Acknowledgements
I would like to thank Dr. K. Butler for his continued support of this work and Dr. W. Eissner for making his RAL version of the Breit-Pauli R-matrix package available to us. I am also indebted to the Deutsche Forschungsgemeinschaft for financial support under grant Bu 703/2-1. The calculations were performed on the Cray Y-MP and HP 735 cluster of the Bayerische Akademie der Wissenschaften at the Leibniz Rechenzentrum, München. We gratefully acknowledge a grant of computer time by Cray Research Inc. in cooperation with the Leibniz Rechenzentrum.