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We report accurate high-lying energy resonances of the Br\({}^{3+}\) ions. Rydberg series of resonances due to 4 p\( \to\) n d and 4 s\( \rightarrow\) np  transitions converging respectively to the 4s\({}^{2}\)4p (\({}^{2}\)P\({}_{3/2}\)) and 4s4p\({}^{2}\)(\({}^{4}\)P\({}_{3/2}\), \({}^{2}\)D\({}_{5/2}\)) series limits in Br\({}^{4+}\) are considered. The calculations are performed using the screening constant by unit nuclear charge  (SCUNC) method up to \(n=40\). The results obtained are compared with recent ALS measurements of Macaluso et al ., [ J. Phys. B: At. Mol. Opt. Phys. 52 (2019), 145002]. Analysis of the present results is achieved in the framework of the standard quantum-defect theory and of the SCUNC procedure by calculating the effective charge. It is shown that the SCUNC method reproduces excellently the ALS results up to \(n=27\). Our predicted data up to \(n=40\) may be of great importance for the atomic physics community in connection with the modeling of plasma and astrophysical systems.

Single Photoionization Study of Br3+ via the Screening Constant by Unit Nuclear Charge Method