The present work deals with an ab initio calculation of total energies of the doubly excited np 2 , nd 2 and nf 2 states in the helium-like systems. These total energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. In the present work, a new correlated wave function is presented to express analytically the total energies of the doubly np 2 , nd 2 and nf 2 excited states in the He-like systems. The present results obtained up to Z = 10 and n = 4 agree very well with various computational methods.

We report accurate high-lying energy resonances of the Br 3+ ions. Rydberg series of resonances due to 4p→nd and 4s→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.