Calculations of collisional data for heavy trace elements have been stimulated by the recent detection of collisionally excited lines of krypton, xenon and barium ions in the spectrum of the planetary nebula (PN) NGC 7027 (Péquignot & Baluteau 1994, hereafter referred to as PB94). In a previous paper (Schöning 1996, hereafter Paper I) we have presented effective collision strengths for transitions within the 4pk (k=2-4) ground configuration of KrIII, IV, V. The calculations have important implications for analyses of the nebular krypton lines. We have shown that the collision strengths for krypton ions are similar in magnitude to those for homologous transitions in lighter noble gas ions and thus cannot account for the anomalous intensities of the collisionally excited krypton lines in NGC 7027.
Unexpectedly large line intensities have also been measured for the xenon and barium ions identified in NGC 7027. Péquignot & Baluteau have discussed the plausible explanation that the abundances of the heavy elements in the PN are enhanced by roughly an order of magnitude relative to the solar system values. The authors suggest that the process of nucleosynthesis in low-mass stars and the subsequent injection of its by-products into the interstellar medium be carefully reinvestigated using reliable elemental abundances. Thus detailed quantitative analyses of the XeIII, IV, VI and BaII,IV lines are needed which make it necessary to have accurate electron collision strengths available.
We have performed preliminary calculations of effective collision strengths for XeIV (Schöning 1995) using the non-relativistic R-matrix theory (Berrington et al. 1987). In this work fine-structure splitting of the target terms has been approximately included through algebraic transformations of the LS-coupling transmission matrices to intermediate coupling. Since the applicability of the non-relativistic method is restricted to low-Z ions the resulting collision strengths are considered to be only rough estimates. Nevertheless, the data proved to be useful for examining the gross behaviour of the effective collision strengths of heavy noble gas ions.
For heavy ions such as xenon (Z=54) and barium (Z=56) relativistic effects are important. For instance the target structure and, consequently, the target thresholds in the collision strengths as a function of colliding electron energy are significantly affected by fine-structure splitting. Thus, within the framework of the close-coupling approach, these effects have to be consistently included in the target and scattered electron wavefunction from the outset. With regard to the relatively high nuclear charge of the complex ions the Dirac R-matrix theory (see Norrington & Grant 1987) is the state of art for solving the electron scattering problem in a J-J coupling representation. However, since these calculations are extremely demanding in terms of computing time it is impractical to produce large amounts of collisional data with the presently available computing facilities. Hence, as in Paper I we have tackled the electron scattering problem using the low-Z Breit-Pauli formulation of the R-matrix method (Hummer et al. 1993: The IRON Project, hereafter IP93). Here the non-relativistic continuum Hamiltonian is transformed from LS-coupling to a pair coupling scheme and the one-body mass correction, Darwin and spin-orbit terms are additionally included. It is well known that the Breit-Pauli Hamiltonian is applicable to intermediate Z-ions with Z not much beyond Z=30. We expect, however, that with increasing electron temperature (i.e. higher collisional energies) relativistic target effects will play a minor rôle in the scattering process. Thus for selected ions we have compared the Breit-Pauli collision strengths with test calculations using the Dirac R-matrix method in order to estimate the accuracy of our results and to clarify the question as to whether our data can be used to provide reliable diagnostics for highly excited nebular spectra. Furthermore, analogously to the case of krypton ions, we have investigated the applicability of the semi-relativistic R-matrix method, an extension of the non-relativistic R-matrix theory, as an adequate alternative to the costly Breit-Pauli calculations.
In the following section (Sect. 2) we will briefly outline the various approaches for the calculation of effective collision strengths for the ions of xenon and barium under consideration: semi-relativistic (TCC ), Breit-Pauli (BP ) and Dirac (DC ) R-matrix methods. Subsequently the BP results are presented in Sect. 3. For selected transitions a comparison of the different methods is critically discussed (Sect. 4). Finally, concluding remarks are given in Sect. 5.