Semiclassical method of analysis and estimation of the orbital binding energies in manyelectron 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 quantummechanical calculations, are studied in the ground state of manyelectron 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 manyelectron 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 manyelectron atoms and ions by electrons and heavy particles failing more precise data.
