Variational calculations employing explicitly correlated Gaussian functions have been performed for the ground states of ${}^9\mathrm{Be}$ and ${}^9\mathrm{Be}^{+}$ including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation]. An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed, leading to energies of the two systems noticeably improved over those found in the recent paper of Pachucki and Komasa [Phys. Rev. A 73, 052502 (2006)]. The non-BO wave functions were used to calculate the ${\alpha }^2$ relativistic corrections $(\alpha =e^2∕\hslash c)$. With those corrections and the ${\alpha }^3$ and ${\alpha }^4$ corrections taken from Pachucki and Komasa, a new value of the ionization potential (IP) of ${}^9\mathrm{Be}$ was determined. It agrees very well with the most recent experimental IP.

• Received 6 March 2007

DOI:https://doi.org/10.1103/PhysRevA.75.052510