Weak lines, being unsaturated, are particularly important for the determination of interstellar abundances of elements. From a theoretical point of view, there are several possible causes of an electric dipole transition having a small oscillator strength. In some cases, several contributions to the dipole matrix element substantially cancel (e.g. the 1808 Å line Si II), while in other cases, the oscillator strength would be zero but for the inclusion of small relativistic effects (e.g. the intersystem 1909 Å line in C. II).

For weak lines, the interstellar abundances depend on the oscillator strength (calculated or measured) and the equivalent width (observed). The increased resolution of the Goddard High Resolution Spectrograph on board the Hubble Space Telescope provides for many lines equivalent widths of much greater precision than was previously available. This situation presents a challenge to theorists to improve the quality of their calculations of oscillator strengths.

Such calculations are difficult for weak transitions, especially when the cause is cancellation. Of course, with larger and more powerful computer a vailable, it is possible to undertake more extensive calculations. But the quality of observational data now makes it imperative for theorists not merely to do a better calculation than before, but to give a considered estimate of the accuracy of the results. Since there are no effective theoretical methods for obtaining rigorous bounds to oscillator strengths which could give a useful guide to accuracy, theoretical estimates of accuracy can be achieved only by undertaking a systematic sequence of calculations of increasing complexity, while ensuring that no significant contributions to the calculations are omitted.