**7. Conclusions**

With the help of the developed ATOM software, a huge number of calculations of various atomic processes have been carried out, in most of which multielectron processes play a decisive role. These calculations can be considered the result of a computational experiment in which many-particle effects are studied for a well-defined and well-known pair interaction between electrons. Naturally, in this short review of the obtained results and the possibilities of applying the presented experiment, not all processes associated with the reaction of the electronic system of atoms to external influences are discussed.

In the processes mentioned above, relativistic effects that have little impact on the partial photoionization cross sections of individual shells were neglected. However, when describing photoprocesses in atoms, such characteristics that are directly related to relativistic corrections to the interaction are also determined. One of them is the parameter called the *"branching ratio"* [18], which characterizes the relative probability of the ionization of shell sublevels with different total angular momenta j. The presence of a spin in an electron leads to the fact that during the photoionization of shells, the remaining ion can be in states that differ in the total momentum *j* = *l* ± 1/2.

In the process of the photoionization of internal atomic shells with a total moment *j* > 1/2 (*l* > 0), the resulting ions have a certain alignment (the predominant orientation of the total moment *j*) along the direction of the incident photon beam. This alignment, which arises as a result of the uneven population of states with different projections of the total momentum of the ion *M*, manifests itself in the anisotropy of the angular distribution of emission photons or Auger electrons emitted during the decay of a vacancy. The alignment of ions depends on the squares of the dipole amplitudes in a different way than the photoionization cross section, and the measurement of the angular anisotropy of electrons or photons therefore also provides additional independent information about the photoionization process.

The final stage of the computational experiment is the analysis of the results and their comparison with the experimental data. The ATOM system has turned out to be very effective in solving a wide class of problems in the study of atomic processes, including processes involving atomic ions, endohedral fullerenes, diatomic molecules, and atomic clusters, as well as processes in a number of problems in solid state physics.

The ATOM system was created on the initiative and with the active participation of Prof. Miron Ya. Amusia. It was his ideas that led to the creation of the self-consistent RPAE approximation, which was the next step in many-body theory after the HF approximation. The development of the proposed approach and the creation of the ATOM complex of computational programs continued for more than a year of research in the field of physics of multielectron atoms. The development of such systems will make it possible to carry out mass molecular calculations, as well as calculations of atoms placed in strong electric or magnetic fields. The obtained results will become the theoretical base, the starting point for comparing theory and experiment. Thus, the area of applicability of the approach that a group of theoretical physicists under the leadership of Miron Ya. Amusia developed in the theory of the atom will be significantly expanded, providing experimenters with theoretical results of initial approximations that have a relatively high accuracy "on average".

The results of a computational experiment using the ATOM system can be found in supplementary materials and in a number of our monographs [7–11,16,17,19,43].

**Supplementary Materials:** The following supporting information can be downloaded at https: //www.mdpi.com/article/10.3390/atoms10020052/s1. List of main publications in which the results were obtained using the ATOM program system.

**Author Contributions:** Conceptualization, L.V.C. and V.K.I.; methodology, V.K.I.; software, L.V.C.; writing—original draft preparation, L.V.C. and V.K.I.; writing—review and editing, L.V.C. and V.K.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We consider it our duty to thank Kheifetz A. for his advice and help in preparing our manuscript for publication.

**Conflicts of Interest:** The authors declare no conflict of interest.
