Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions (A.M. Frolov, Physics Letters A {\bf 374}, 2361 (2010)) is used for variational computations of bound states in three-electron atomic systems. It appears that semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than it was originally anticipated. In particular, the 40-term Larson's wave function improved with the use of semi-exponential radial basis functions now produces the total energy \linebreak -7.47805413551 $a.u.$ for the ground $1^2S-$state in the ${}^{\infty}$Li atom (only one spin function $\chi_1 = \alpha \beta \alpha - \beta \alpha \alpha$ was used in these calculations). This variational energy is very close to the exact ground state energy of the ${}^{\infty}$Li atom and it substantially lower than the total energy obtained with the original Larson's 40-term wave function (-7.477944869 $a.u.$)

Bound state properties and photodetachment of the negatively charged hydrogen ions

Absorption of infrared and visible radiation from stellar emission spectra by the negatively charged hydrogen ions H$^{-}$ is considered. The explicit formula for the photodetachment cross-section of the negatively charged hydrogen ion(s) is derived. Photodetachemnt cross-sections of the ${}^{\infty}$H$^{-}$, ${}^{3}$H$^{-}$ (or T$^{-}$), ${}^{2}$H$^{-}$ (or D$^{-}$) and ${}^{1}$H$^{-}$ ions are determined to high accuracy and for a large number of photo-electron momenta/energies. We introduce criteria which can be used to evaluate the overall quality of highly accurate wave functions of the hydrogen ion(s). One of these criteria is based on highly accurate calculations of the lowest order QED corrections in the negatively charged hydrogen ions, including ${}^{1}$H$^{-}$ (protium), ${}^{2}$H$^{-}$ (deuterium), ${}^{3}$H$^{-}$ (tritium) and model ion with the infinitely heavy nucleus ${}^{\infty}$H$^{-}$. An effective approach has been developed to calculate three-body integrals with the Bessel functions of different orders. Some preliminary evaluations of the phototdetachment cross-sections of the negatively charged hydrogen ions are performed. Inverse bremsstrahlung in the field of the neutral hydrogen atom is briefly discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1110.343