Examples

In order to demonstrate how the data is used a brief example is presented.

Consider the line of neutral magnesium at 8806.76Å. The first step is to identify the levels involved in the transition. Moore's multiplet tables (1972) show this line is from multiplet 7, with level designations -. Moore's energy level tables (1971) are now consulted to determine the type of transition and the energies of the levels. The level has an electron configuration of and the has an electron configuration of . The transition therefore is p-d. The p- and d-state energies are quoted in wavenumber units as 35051.36 cm and 46403.14 cm respectively. The effective principal quantum numbers can then be calculated from the formula
 
with all energies in cm.

For magnesium the series limit is 61669.14 cm. Hence the effective principal quantum numbers for the p- and d-states are 2.030 and 2.680 respectively. Using the fortran code previously mentioned the cross-section for a relative collision speed of ms is found to be 530 atomic units and the velocity parameter is 0.277. The program calculates a width per unit hydrogen atom density of 1.5010cmrad s for the hydrogen broadening of the line at 5000 K. Barklem (1998) has shown that this cross-section leads to a solar abundance of magnesium in accord with the meteoritic value to within the uncertainty in the f-value for the line.

Two Electron Excitations

On some rare occasions, one may have to deal with a transition involving states in which two electrons are excited. What this means in essence, is that one of the core electrons is also in an excited state during the transition and that our simple model of a single electron outside a singly charged core is no longer strictly applicable. However as the line broadening cross-section is largely determined by the tail of the wave function for the optical electron, useful results can still be obtained provided one is careful in the determination of the appropriate binding energy for the optical electron. As an example we choose the E-line of Fe I at 5269.34 Å first observed by Fraünhofer in the solar spectrum. From Moore's multiplet tables (1972) this transition is from multiplet 15, with level designations - with corresponding electron configurations -. The parent configuration for the upper state corresponds to the ground state of Fe II and therefore the effective principal quantum number is calculated in the usual way. However the lower state parent configuration corresponds to the first excited state of Fe II at an energy of 1872.60cm and consequently this energy must be added to the series limit prior to calculating the effective principal quantum number. This leads to an effective principal quantum number for the lower s-state of the transition of 1.368 and an effective principal quantum number of 1.703 for the upper p-state. From the fortran code the cross section for a perturber velocity of 10 ms is 237 atomic units and the velocity parameter is 0.249. Anstee, O'Mara and Ross (1997) have shown that this cross-section leads to a solar abundance of iron in excellent agreement with the meteoritic value.

© Copyright Astronomical Society of Australia 1997