Ground-state energy of beryllium atom with parameter perturbation method

Abstract

We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom's Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme, where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.

Parameter Perturbation Method for Helium Ground State Energy Calculation

“…Moreover, since the wavefunctions in different orders of the parameter perturbation method can be easily constructed in a systematic way via considerations of the symmetry and some other properties of the system, it is convenient to attain different levels of precision by adjusting the number of orders involved without too much calculation difficulty [7]. Although this new method is still unknown to many, its desirable advantages have attracted researchers to apply it to various fields such as the calculations of the ground energies of C 4+ , N 5+ , O 6+ , and Be atoms and those of non-linear harmonic oscillators [8,9]. To investigate how well this new method works for the calculation of helium ground state energy, this paper tries to compare the approximated results with the experimental result and find the relationship between the accuracy of the approximation and the orders of perturbation.…”

Penentuan Energi Dasar Atom Berilium (Be) Menggunakan Metode Variasional Dengan Dua Parameter

“…Perluasannya untuk perhitungan keadaan eksitasi juga dapat dilakukan dengan cara interaksi konfigurasi. Dalam studi ini, perhitungan energi dasar menggunakan atom Berilium, karena secara teori konfigurasi elektron atom Berilium adalah 1 2 , 2 2 ., memiliki dua elektron di bagian dalam (Shell K) dan dua elektron di kulit luar (Shell L) sehingga konfigurasi atom Berilium ini cukup menarik untuk dikaji, sebagaimana yang telah dilakukan oleh peneliti sebelumnya (Wu and Meng 2018;Y. Yulianto, R. Ramdani, M.S.…”