Fortunately, there is a continuing increase and improvement of astrophysical observational possibilities, both by satellite and by ground based observatories. Technically advanced telescopes are used to search for faint objects and to detect the emitted light with highly dispersive equipment such as the Hubble Space Telescope (HST) and the International Ultraviolet Explorer (IUE). The vacuum ultra-violet region will be observed by FUSE-LYMAN at high resolution down to the Lyman continuum at 912 Å.
At the same time, this progress underlines the need for more and more accurate atomic and molecular transition probabilities. Most stellar spectra are affected with broad features or blends. Therefore, to investigate stellar objects in a state of the art way, transition probabilities (either from theoretical calculations or from laboratory observations) should necessarily be accurate to about 10% or better.
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 stages 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.
To start our calculations of transition probabilities, we choose Titanium and Vanadium which are cases of intermediate complexity and allow for comparison with other work; for the near future, the study of iron and nickel which are of even greater astrophysical importance, is planned.
Ti and V are observed in a variety of stellar objects. In the sun,
Ti figures in third place in terms of numbers of lines (Jaschek & Jaschek
1995). Hundreds of Ti I and Ti II lines are observed in the solar
photospheric spectrum (Moore et al. 1966; Biémont
1976). Ti II appears in mid-B-type stars, slowly increases towards
F-type, and persists up to type M. Ti has been found overabundant (with
respect to Fe) in extreme halo dwarfs (Magain 1989). Due to
the lack of accurate transition probabilities of higher ionization, one was
forced here to use the weaker Ti I lines to determine the abundance. Ti II
is used to determine the radial velocity of A-type shell stars (Levato
et al.\
1995). Ti III is less frequently observed but has been
seen in Ap stars (Bidelman 1966) as well as by the IUE in 
Orionis.
(Rogerson & Upson 1982).
Similarly, V I and V II show several hundreds of lines in the solar photospheric spectrum. Knowledge of accurate transition probabilities is therefore vital for the determination of the solar abundance of V and refining the chemical composition of the sun (Whaling et al. 1985). V II has been seen in late B-type stars and is also observed in A stars (Jaschek & Jaschek 1995). In non-normal stars, V shows a behaviour similar to that of Fe and consequently is considered as "typical metal". V is slightly overabundant with respect to iron in globular cluster stars (Wheeler et al.\ 1989). V IV is seen in the balloon UV spectrum of the sun (Samain 1995).
Although the orthogonal operator method has been used for more than a decade now to describe energy levels of iron group elements, the present work is the first to calculate transition probabilities in this framework. It has been shown (Raassen & Uylings 1996) to give reliable results for complex atoms, i.e. atoms with Z > 20 and more than one electron outside closed shells. What are the advantages and disadvantages of the new orthogonal operator method? In Sect. 2, a short introduction of the method itself in relation to other current methods of producing gf- or A-values is given; similarities as well as differences are discussed. In Sect. 3, details of the actual calculation as well as the numerical results are given.