Theoretical Investigation On The Energy Structure Of Beryllium-like Atoms

Based on tensor expression of the Breit-Pauli Hamiltonian of many-electron atoms, and with the help of irreducible tensor theory and the angular momentum coupling theory, practical formula for the non-relativistic energy, for the relativistic correction, which include mass correction, one- and two-body Darwin correction, spin-spin contact interaction and orbit-orbit interaction; and for the fine-structure energy, which include the spin-orbit interaction, spin-other orbit interaction and the spin-spin interaction, of Beryllium-like atoms has been derived. All the angular interactions and spin sums involved in problem have been worked out analytically; the corresponding energies are expressed in a combination of several radial integrations.A Mathematica program is developed to calculate the energy levels of the Beryllium-like atoms. The program includes three sub-programs: (1) representation transformation from Slater representation to Racah representation; (2) calculation of non-relativistic energy levels and their relativistic corrections; (3) calculation of the fine-structure energies.Aided by the program, the non-relativistic energy levels and their relativistic corrections, and the fine-structure energies of Beryllium-like atoms in the configurations 1s22s2 and 1s22snp(n=2-6,Z=4-8) have been investigated. The results of the calculations are compared to the experimental data.In order to improve the calculations, two methods have been taken to study the low-excited energy levels and the high Rydberg energy levels of Beryllium atoms. The first is to construct new radial wave functions, in which the key point is to modify hydrogen-like radial wave functions, the new function is constructed by adding variational parameters to each terms of the general Laguerre polynomials in the hydrogen-like radial wave functions. Wavefunctions and energies of beryllium atoms in 1s~22snd (n=3-6) configuration are calculated. The results are in good agreement with experimental data. The second is utilizing the WBEPM theory to investigate the Rydberg energy levels of Beryllium atom. The Rydberg energy levels and quantum defects of 1s~22snd 1S0 (n=3-50), 1s~22snd 1Po1 (n=3-50) and 1s~22snd 1D2(n=3-50) spectrum series for Beryllium atom are calculated. The calculated results are in excellent agreement with the known experimental data and many energy levels for highly excited states are predicted.