Modeling the wavelength of unresolved transition arrays in the extreme ultraviolet region from Sn to Hf ions by combining theoretical and experimental spectral data

This paper proposes a method to determine the wavelength of unresolved transition arrays (UTAs) in the extreme ultraviolet (EUV) wavelength region from Sn to Hf plasma by combining calculated and experimental data. Based on a computational analysis of the atomic structure, we show that the wavelength of UTAs can be explained using the screening theory by a simple quadratic formula using the effective core charge and the screening constant for 4d electrons as parameters. The results from the model were compared with experiments to reproduce the trend of the spectrum, which has a minimum wavelength with respect to the ion charge. The wavelength is shown to agree with experiment over Pd- to Sr-like ions by applying a small shift that was determined using the spectrum observed in the electron beam ion trap. The present model would allow us to calculate the opacity of Sn plasmas with much smaller computational time than using present large-scale collisional radiative models, with fewer energy levels and parameterized rate coefficients, which will be also useful to investigate the efficiency of the EUV light source.