The recent detection of
heavy trace elements with nuclear charge numbers Z > 30 in the
planetary nebula (PN) NGC 7027 (Péquignot & Baluteau
1994, hereafter referred to as PB94) has opened
up interesting scientific possibilities in astrophysics.
In particular, several relatively strong collisionally excited forbidden
lines in the [KrIII, IV, V] spectra were unambigously
identified. Using crude estimates for the collision strengths of krypton ions
Péquignot & Baluteau found that krypton could be overabundant by a
factor of 
compared to the solar system value. This unexpected
result is a clear indication that PNe can play a much more important rôle
in the overall process of element synthesis than has previously been
recognized. Since the noble gas emerges from the neutron capture
process in the interior of the progenitor of NGC 7027 and has obviously been
injected into the interstellar medium it is very interesting with a view to
testing models for the final stages of stellar evolution and the
chemical evolution of galaxies.
We have tackled the problem of calculating collisional data for krypton ions.
In a previous paper (Schöning & Butler 1995, hereafter
referred to as Paper I) we have provided for the first time effective
collision strengths for fine-structure forbidden transitions in the 4p
ground configuration of KrIV . Since this ion was considered as a
test case for the computation of collisional data for heavy elements
the scattering problem was solved using a semi-relativistic R-matrix
approach, i.e. the method approximately allows for relativistic effects in
the target through transformations of the LS-coupling transmission matrices
calculated with the non-relativistic R-matrix technique (Berrington et al.\
1987) to intermediate coupling. Nevertheless, we have argued
that this method yields reliable results which lead us
to conclude that the krypton overabundance reported by Péquignot &
Baluteau is probably real.
However, convincing quantitative analyses of the observed lines make it necessary to employ the most accurate collisional data currently achievable. Thus the aim of this paper is to apply recently developed electron scattering techniques to the calculation of collision strengths for krypton ions such that relativistic effects in both the target and scattered electron wave function are consistently included from the outset. Within the context of the R-matrix method two approaches are available. In the low-Z Breit-Pauli (BP ) formulation (see Hummer et al. 1993, hereafter IP93) 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. However, since it is well known that the BP\ Hamiltonian is applicable to intermediate Z-ions with Z not much beyond Z=30 test calculations are desirable for at least one of the krypton (Z=36) ions using the Dirac R-matrix theory (see Norrington & Grant 1987) which is the state of art for the heavy-atom case. These calculations are currently underway and will be the subject of a future paper (Schöning, in preparation).
The plan of this paper is as follows. In Sect. 2 we outline the calculation of effective collision strengths for the ions of krypton under consideration. The results are presented in Sect. 3 and critically discussed in Sect. 4. Finally, concluding remarks are given in Sect. 5.