Oscillator strengths for ${}^{2}P\text{−}{}^{2}S$ transitions in neutral boron

In this study, we perform a set of benchmark variational calculations for the ground state and for the 18 lowest bound excited ${}^{2}S$ and ${}^{2}P$ states of the boron atom. The nonrelativistic wave function of each state is generated in an independent calculation by expanding its wave function in terms of a large number ($10000–16000$) of all-electron explicitly correlated Gaussian functions (ECG). The Hamiltonian used in the calculations explicitly depends on the mass of the boron nucleus. The nonlinear parameters of the ECGs are extensively optimized with a procedure that employs the analytic energy gradient determined with respect to these parameters. These highly accurate nonrelativistic wave functions are used to compute the transition dipole moments and the corresponding oscillator strengths for all allowed transitions between the considered states. These quantities are reported for the transitions of the ${}^{10}\mathrm{B}$ and ${}^{11}\mathrm{B}$ isotopes, as well as for the boron atom with an infinite nuclear mass, ${}^{\infty }\mathrm{B}$, and used to evaluate the isotopic shifts of the oscillator strengths. The results generated in this work are considerably more accurate than the data obtained in the previous theoretical calculations.

Figure 1

Heat-map plot of the ${}^{11}\mathrm{B}$ oscillator strengths (a), (b), as well as of the relative isotopic shifts (c), (d) defined as $[f{(}^{10}\text{B})-f{(}^{11}\text{B})]/f{(}^{11}\text{B})$. Plots (a) and (c) on the left side of the figure show the results obtained using the length formalism, while those on the right side, (b) and (d), correspond to the velocity formalism.