Hyperfine structure parametrisation in Maple
In hyperfine structure examinations, routine high resolution spectroscopy methods have to be combined with exact fine structure calculations. The so-called magnetic A and electric B factor of the fine structure levels allow to check for a correct fine structure analysis, to find errors in the level designation, to find new levels and to probe the electron wavefunctions and its mixing coefficients. This is done by parametrisation of these factors into different contributions of the subshell electrons, which are split further into their radial and spin-angular part. Due to the routine with which hyperfine structure measurements are done, a tool for keeping the necessary information together, performing checks online with the experiment and deriving standard quantities is of great help. MAPLE [Maple is a registered trademark of Waterloo Maple Inc.] is a highly developed symbolic programming language, often referred to as the pocket calculator of the future. Packages for theoretical atomic calculation exist (RACAH and JUCYS) and the language meets all the requirements to keep and present information accessible for the user in a fast and practical way. We slightly extended the RACAH package [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] and set up an environment for experimental hyperfine structure calculations, the HFS package. Supplying the fine structure and nuclear data, one is in the position to obtain information about the hyperfine spectrum, the different contributions to the splitting and to perform a least square fit of the radial parameters based on the semiempirical method. Experimentalist as well as theoretical physicist can do a complete hyperfine structure analysis using MAPLE.
hyperfine structure a and b factors complex atom configuration state function electric quadrupole interaction magnetic dipole interaction one-particle operator parametrisation of the a and b factors semiempirical hyperfine structure analysis spin-angular coefficients for hyperfine structure operators relative intensities of hyperfine lines