The total energies of twenty eight bound S-, P-, D-, F-, G-, H-, and I-states in the three-electron Li atom and Be + ion, respectively, are determined with the use of the Configuration Interaction (CI) with Slater orbitals and L-S eigenfunctions, and the Hylleraas-configuration-interaction (Hy-CI) methods. We discuss the construction and selection of the configurations in the wave functions, optimization of the orbital exponents and advanced computational techniques. Finally, we have developed an effective procedure which allows one to determine the energies of the excited states in three-electron atoms and ions to high accuracy by using compact wave functions. For the ground and low lying excited states our best accuracy with the Hy-CI method was ≈ 1 · 10 −6 a.u. and 1 · 10 −4 a.u. for other excited states. Analogous accuracy of the CI method is substantially lower ≈ 1 · 10 −3 a.u. Many of the rotationally excited (bound) states in the three-electron Li atom and Be + ion have never been evaluated to such an accuracy. *
Probabilities of various final states are determined numerically for β − -decaying He, Li, and Be atoms. In our evaluations of the final-state probabilities we have used the highly accurate atomic wave functions constructed for each few-electron atom or ion. We also discuss an experimental possibility to observe negatively charged ions which form during the nuclear β + decays. Corrections on direct interaction between atomic electrons and fast β electrons or positrons are considered. It is shown that for our results obtained for β ± decays in few-electron atoms with the use of the sudden approximation such corrections are very small (≈α 4 ) and can be neglected.
A general expression for the nonrelativistic Hamiltonian for n-electronatoms with the fixed nucleus approximation is derived in a straightforward manner using the chain rule. The kinetic energy part is transformed into the mutually independent distance coordinates r i , r ij , and the polar angles i , and i . This form of the Hamiltonian is very appropriate for calculating integrals using Slater orbitals, not only of states of S symmetry, but also of states with higher angular momentum, as P states. As a first step in a study of the Hylleraas method for five-electron systems, variational calculations on the 2 P ground state of boron atom are performed without any interelectronic distance. The orbital exponents are optimized. The single-term reference wave function leads to an energy of Ϫ24.498369 atomic units (a.u.) with a virial factor of ϭ 2.0000000009, which coincides with the Hartree-Fock energy Ϫ24.498369 a.u. A 150-term wave function expansion leads to an energy of Ϫ24.541246 a.u., with a factor of ϭ 1.9999999912, which represents 28% of the correlation energy.
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