An explicit empirical formula for fine-structure separations of2P0and2D terms for ions in the Cu isoelectronic sequence

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Abstract
A screened hydrogen-like model has been used to re-express available measurements of fine-structure separations for 2P0 and 2D terms in the Cu isoelectronic sequence as screening parameters, which are found to be very regular and slowly varying as functions of Z, n and l. These regularities have been quantified by empirical searches for linearising mapping functions, which indicate that the screening parameter S is very well represented by a linear function of the reciprocal screened charge S=a+b/(Z-S), with a slope a and intercept b which follow the relationships a varies as (n-3)k and a+2 square root b=constant. This yields an explicit empirical formula for the fine structure for any value of Z and n for the isoelectronic sequence of these Rydberg series. Predictions for the fine-structure separations for the n=4-8 2P0 and n=4-6 2D terms for all ions from As V to U LXIV are presented.