1 Introduction

Because of their nuclear stability, iron group elements (especially the even-Z ones without nuclear spin) are frequently encountered in stellar spectra. The lower, I and II, ionization states can be observed in the photosphere, while higher ionization is seen in the emission lines of the chromosphere with its steep rise of ionic temperature, A-type stars constitute important examples of this. Moreover, forbidden transitions are observed in various astronomical objects, where their study is important for diagnostic purposes. For highly charged ions, transitions from metastable levels occur at much longer wavelengths than other transitions in the same ion. This can provide information on the thermal Doppler effect.

Emission lines arising from transitions in Ni XVIII are frequently observed in the spectra of astrophysical objects, such as the solar transition region, Corona (Vernazza & Reeves 1978; Sandlin et al. 1986) and in fusion plasmas (Janev 1991). They may be used to derive electron temperatures of the emitting region through diagnostic line ratios, as first pointed out by Flower & Nussbaumer (1975). A knowledge of the nickel spectrum is also required for the study of impurities injected into Tokamak plasmas (Breton et al. 1979) of fusion research which originate from the nickel alloy liner currently often chosen for these devices.

Ni XVIII belongs to the sodium isolectronic sequence, with a [Ne]3s configuration for the ground state. Experimentally, a resonant photo-pumping scheme for driving lasing action in Ni XVIII and other heavier ions (Cu XIX, Zn XX, etc.) has been proposed by Nielsen (1992). However, to calculate reliable electron temperatures through sensitive equation line ratios for Ni XVIII, accurate atomic data must be employed (Keenan 1992). Theoretically, many calculations have been done for the ions isoelectronic with Na, most of them corresponding to allowed transitions. Theoretical E2 S and f-values are available in the literature: for the three ions with Z = 26, 27 and 28, S-values have been calculated by Tull et al. (1972); along the sodium sequence up to Z = 26, oscillator strengths have been publised by Biemont & Godefroid (1978); and later, Godefroid et al. (1985) have reported values for ${\rm 3s\,^2S-3d\,^2D}$ forbidden transitions along the sodium sequence up to Z = 26. Recently, theoretical results about electric quadrupole transition probabilities for the Na-like ions Ba⁴⁵⁺ through U⁸¹⁺ have been reported (Baik et al. 1991).

Zhang et al. (1989) have reported collision strengths for several Na-like ions with nuclear charge Z = 22, 26, 30 and 34, etc., using the distorted wave method. More recently, the R-matrix method has been used to calculate electron collision strengths for the forbidden and allowed transitions among the seven lowest states of Ni XVIII (Mohan et al. 1996).

Exploring the web pages, excellent databases containing wavelengths and transition probabilities for allowed and forbidden lines in atoms and ions - see p.e. CHIANTI (http://wwwsolar.nlr.navy.mil/chianti.html) can be found. However, data on E2 transition probabilities of Ni XVIII have not been found.

The most extensive data available in the literature are the multiplet S-values calculated by Tull et al. (1972) using Hartree-Fock orbital wavefunctions of frozen-core type, and a critical compilation by Fuhr et al. (1988) of transition probability data and S-values for forbidden lines of Ni XVIII among other ions. The references given by Fuhr et al. (1988) are calculations dating from 1965 (Krueger & Czyzak) and 1972 (Tull et al.). This critical compilation is also available at the NIST database (http://www.physics.nist.gov/fvalbib).

To our knowledge, there are no recent calculations of transition probability data for forbidden lines in relation with this ion, Ni XVIII. On this basis, we have considered that there is room for new calculations on E2 forbidden lines of Ni XVIII.

For many years we have applied the Quantum Defect Orbital method, both in its non-relativistic (QDO) (Simons 1974; Martín & Simons 1975, 1976) and its relativistic (RQDO) (Martín $\&$ Karwowski 1991; Karwowski & Martín 1991) versions, to the calculation of oscillator strengths and photoionization cross sections of a rather large number of atomic species, of different degree of complexity (Biémont et al. 1998; Charro et al. 1999; Charro $\&$ Martín 1999a, 1999b, 2000a, 2000b), including several isoelectronic sequences (see, e.g. Martín et al. 1993; Martín et al. 1994; Charro et al. 1996, 1997, 2000; Charro & Martín 1998 and references therein).

The RQDO formalism, as opposed to sophisticated and costly self-consistent-field procedures, is a simple but reliable analytical method based on a model Hamiltonian that has the great advantage of the computational effort not being increased as the atomic system dealt with becomes heavier. It has been found that the RQDO orbitals behave rather well at intermediate and, in particular, large radial distances. These are, in most cases, the regions that contribute more strongly to the transition moment. The convenience of employing exactly solvable model potentials for calculating atomic transition probabilities manifest itself not only from a practical point of view but also because of the involved physical implications, when they are capable of achieving a good balance between computational effort and accuracy of results.

In the present work, electric quadrupole line strengths for several multiplets as well as their lines corresponding to transitions of Ni XVIII have been computed with the RQDO formalism. The S-values have been calculated on an individual basis, not from the application of the LS-coupling rules within multiplets. We find the direct calculation of fine-structure line strengths to be interesting from a spectroscopic point of view, given their usefulness in the spectral analysis in astrophysics and fusion plasma research. A general good agreement has been found between our data and other results. It is worth pointing out that this is the second time the RQDO procedure is applied to E2 transitions, which required the elaboration of the pertinent computer code.