1 Introduction

The present calculation is a contribution to the international IRON Project (Hummer et al. 1993; Paper I) whose members are working to obtain reliable rate coefficients for collisional excitation of fine-structure transitions in positive ions induced by electron impact. Other papers in the series are given in the section References, while a complete list of IRON Project published papers and those in press is available at the Internet address http://www.am.qub.ac.uk. The present paper is devoted to the beryllium-like iron ion $\rm Fe^{+22}$.

The temperature dependent rate coefficient $q(i \to j)$ for a transition between atomic levels with indices i and j and energy separation E_ij is given in terms of the effective, or thermally averaged, collision strength ${\sl \Upsilon}(i - j)$ by

$$q(i \to j) = 2 \pi^{1/2} a_0\, \hbar\, m_{\rm e}^{-1}\, ({\rm Ry}/kT)^{1/2}\,$$

$${\rm exp}(-E_{ij}/kT)\,{\sl \Upsilon}(i - j)/(2J_i+1)$$ (1)

where $2 \pi^{1/2} a_0\, \hbar\, m_{\rm e}^{-1} = 3.610 \ 10^{-24}\,\,{\rm m^3\,\,s^{-1}}$. For energies we use the Rydberg unit, which has the value ${\rm Ry} = 13.6058$ eV, while the Boltzmann constant is given by $k = 8.617 \ 10^{-5}\,\,~{\rm eV\,\,deg^{-1}}$, the temperature T being in degrees Kelvin. The factor (2J_i+1) is the statistical weight of level i.

  

Table 1: Chronological list of work on electron excitation of Fe XXIII

Following Seaton (1953) we define the effective collision strength $\sl \Upsilon$ as follows:

$$\begin{eqnarray} {\sl \Upsilon}(i - j) = \int_0^{\infty} {\sl \Omega}(i - j) \, {\rm exp}(-E_j/kT)\, {\rm d}(E_j/kT)\end{eqnarray}$$ (2)

where E_j is the energy of the colliding electron after excitation has occurred. The energy dependent collision strength ${\sl \Omega}(i - j)$ and cross section $Q(i \to j)$ are related as follows:

$$\begin{eqnarray} Q(i \to j) = {{\pi\, {\sl \Omega}(i - j)} \over {(2J_i+1) k_i^2}}\end{eqnarray}$$ (3)

where k_i is the wave number of the colliding electron incident on the target ion in level i.

Eighteen years ago Bhatia & Mason (1981) used W.B. Eissner's distorted wave collision code, which originated at University College London, to calculate collision strengths for many transitions in $\rm Fe^{+22}$. Five years later Bhatia & Mason (1986) extended their work to energies both below and above those they considered in 1981; they gave a comprehensive tabulation covering the interval from 15 to 350 Ry. In order to carry out thermal averaging Bhatia & Mason (1986) linearly interpolated their data and integrated the resulting function ${\sl \Omega} \times {\rm exp}(-E_j/kT)$ analytically (Mason 1998, private communication) in order to obtain $\sl \Upsilon(T)$. Corliss & Sugar (1982) estimate the ionization energy of the ground state to be 15797000 $\rm cm^{-1}$ (143.95 Ry), which means that three of Bhatia & Mason's (1986) energies lie above the ionization threshold while the rest are below. Since Bhatia & Mason (1981) include a thorough discussion of collision calculations devoted to $\rm Fe^{+22}$ up to the time of their own investigation, the reader is encouraged to consult their paper for information on this ion and we shall refrain from giving further details here except for a list of relevant papers in Table 1.