Challenges of Theoretical Spectroscopy of Heavy and Superheavy Atoms and Ions

A review of methods of efficient accounting for correlation and relativistic effects is presented. A considerable part of efforts for these approaches must be devoted to coping with integrations over spin‐angular variables, occurring in the matrix elements of the operators under consideration. Efficient methods to find the abovementioned quantities are described, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), on second quantization in coupled tensorial form, and on graphical technique. This allows to study and to generate fairly accurate their spectroscopic data practically for any atom and ion of periodical table.