Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions

G.V. Shpatakovskaya M.V. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russian Federation

The orbital binding energies, obtained in the experiments or in the quantum-mechanical calculations, are studied in the ground state of many-electron elements. Their dependences on the atomic number and on the degree of ionization are analyzed. The semiclassical quantization condition of Bohr—Sommerfield is used and a filled shell orbital binding energy scaling is shown approximately. The scaling is similar to one in the Thomas—Fermi model, but with other two coefficient functions. The effective method of the demonstration of binding energies in a large number of atoms through these two functions is proposed. In addition the special features of the elements of main and intermediate groups and the influence of relativistic effects are visually manifested. The simple interpolation expressions are built for the two functions. One can use them to estimate orbital binding energies in the filled shells of many-electron atoms and ions to within 10% for the average elements and from 10% to 30% for the heavy ones. The estimation can be used as the initial approximation in precessional atomic computations and also for the rough calculations of the ionization cross sections of many-electron atoms and ions by electrons and heavy particles failing more precise data.

Keywords: periodic system, semiclassic approximation, electron-binding energy, atomic number scaling, ionization state, orbital angular momentum PACS:03.65.−w, 31.10.+z, 31.15.bt (all) DOI:10.3367/UFNe.2018.02.038289 URL: https://ufn.ru/en/articles/2019/2/e/ Citation: Shpatakovskaya G V "Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions" Phys. Usp.62 186–197 (2019)

@article{Shpatakovskaya:2019,author = {G. V. Shpatakovskaya},title = {Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions},publisher = {Physics-Uspekhi},year = {2019},journal = {Phys. Usp.},volume = {62},number = {2},pages = {186-197},url = {https://ufn.ru/en/articles/2019/2/e/},doi = {10.3367/UFNe.2018.02.038289}}

Received: 18th, October 2017, revised: 20th, January 2018, accepted: 9th, February 2018