* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Semiclassical calculation of electron spectra in atoms through two
History of quantum field theory wikipedia , lookup
Matter wave wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Hartree–Fock method wikipedia , lookup
Chemical bond wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Molecular orbital wikipedia , lookup
Wave–particle duality wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Particle in a box wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Electron scattering wikipedia , lookup
Canonical quantization wikipedia , lookup
Renormalization group wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Atomic orbital wikipedia , lookup
Electron configuration wikipedia , lookup
Hydrogen atom wikipedia , lookup
43th international conference on plasma physics and CF, February 8 – 12, 2016, Zvenigorod SEMICLASSICAL CALCULATION OF ELECTRON SPECTRA IN ATOMS THROUGH TWO UNIVERSAL FUNCTIONS V.Ya. Karpov1 and G.V. Shpatakovskaya2 1 2 Bruk Institute of Electronic Controlling Machines, Moscow, Russia, [email protected] Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia, [email protected] The features of the one-electron spectra in the spherically symmetric self-consistent attraction potentials have been under study in the paper [1] (also, reviews [2, 3]). Specifically, the potentials with the Coulomb singularity have been there considered. As is well known, the screening of the Coulomb potential leads to the lift of the degeneracy in the orbital momentum l . It has been shown in [1], that the corresponding splitting E nl E nl E n 0 quadratically depends on the orbital momentum l 1/ 2 (here n is a principal quantum number). In addition an analysis of the energy levels calculated in the nonrelativistic Hartree-Fock model for some heavy elements has confirmed the dependence even for not small orbital momentum l 1, 2, 3 . That was a basis of the proposed method to calculate the electron spectra in atoms. The semiclassical approach is applied to calculate one-electron spectrum in a free atom. The atomic number scaling in the Thomas-Fermi model and Bohr-Zommerfeld quantization condition are used. Then on the assumption of the square dependence on the orbital momentum it is possible to calculate a spectrum of any element through the two universal functions, computed for the hydrogen (atomic number Z 1). One of the functions is the classical electron action ( ) for the s-state ( l 0 ). (Z ) At first the s- level energy En 0 is calculated from the quantization condition Z 1/ 3 ( n ) n, En( Z0 ) Z 4 / 3 n (1) Then one can use the square-law equation Enl( Z ) En( Z0 ) Z 2 / 3 ( n ) 2 to calculate the other levels E nl(Z ) . The algorithm to define the second universal function (2) ( ) , the tables and plots of the both functions are given. It is demonstrated the comparison with the results of E nl - computation from the Bohr-Zommerfeld condition and with the nonrelativistic Hartree-Fock model. This work was supported in part by the Russian Foundation for Basic Research (project no. 1401-00828). References [1]. Shpatakovskaya G.V. JETP Lett., 2001, 73, 268. [2]. Shpatakovskaya G.V. Phys. Usp., 2012, 55, 429. [3]. Shpatakovskaya Galina, Quasiclassical Method in Quantum Physics Problems (LAP LAMBERT Academic Publishing GmbH, 2012) , ISBN 978-3-8465-2681-1 (in Russian) 1