Lowest Excitation Energy ofBe9

Abstract

Variational calculations employing explicitly correlated Gaussian functions and explicitly including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation] have been performed to determine the lowest singlet transition energy in the 9Be atom. The non-BO wave functions were used to calculate the alpha2 relativistic corrections (alpha=1/137.035,999,679). With those corrections and with the alpha3 and alpha4 QED corrections determined previously by others, we obtained 54,677.35 cm(-1) for the 3(1)S-->2(1)S transition energy. This result falls within the error bracket for the experimental transition of 54,677.26(10) cm(-1). This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.

Lower Rydberg2Dstates of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions

“…It shows the convergence of the total energies of the 7 Li states with the number of basis functions. In the table, we also show the energies of 6 Li and ∞ Li calculated with 4000 ECGs, that is, the largest basis sets used in the calculations. One can see that the energies of all five states are very well converged.…”

“…The optimization of the ECG basis sets for these states have been performed for the 7 Li isotope and then used to also calculate the 2 D energy levels of the 6 Li isotope, as well as of the lithium atom with an infinite nuclear mass ( ∞ Li). The ∞ Li are shown because they can be compared with the results obtained in the standard way that involves the BO approximation.…”

“…Very accurate results for three-, four-, and five-electron atoms (with all electrons in s states or one electron in a p state and the rest in s states) have been obtained with those functions [6][7][8][9][10][11][12][13]. The main advantage of using Gaussians in atomic calculations is due to the simplicity of the Hamiltonian and overlap integrals with those functions, which can be evaluated analytically in a compact form for an arbitrary number of electrons.…”

“…where n = N − 1, r i is the distance between the ith electron and the nucleus, m 0 is the nucleus mass (12 786.3933m e for 7 Li and 10 961.898m e for 6 …”

“…These deficiencies cause a certain slowdown of the convergence to the exact nonrelativistic wave function. Fortunately, as the calculations have shown [6][7][8][9][10][11][12][13], they can be effectively remedied by using longer expansions and by performing extensive optimization of the Gaussian nonlinear parameters using the variational energy minimization.…”