Maria Belen Ruiz

Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be + ion

The total energies of 28 bound S, P , D, F , G, H ,a ndI 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 LS 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 was ≈1 × 10 −6 a.u. with the Hy-CI method and 1 × 10 −4 a.u. for other excited states. Analogous accuracy of the CI method is substantially lower, ≈1 × 10 −3 a.u. Rotationally excited (bound) states in the three-electron Li atom and Be + ion are evaluated here to high accuracy.

Bound state spectrum of the triplet states in the Be atom

Abstract The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet S , P , D , F , G , H and I states in the Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound Rydberg states. For the 2 3 S , 3 3 S and 4 3 S states in the Be atom we also determine a number of bound states properties.

Atomic excitations during the nuclearβ−decay in light atoms

Probabilities of various final states are determined numerically for a number of {\ss}- decaying light atoms. In our evaluations of the final state probabilities we have used the highly accurate atomic wave functions constructed for each few-electron atom/ion. We also discuss an experimental possibility to observe negatively charged ions which form during the nuclear {\ss}+ decays. High order corrections to the results obtained for {\ss}+/- decays in few-electron atoms with the use of sudden approximation are considered.

Evaluation of Hylleraas–CI atomic integrals by integration over the coordinates of one electron. IV. An improved algorithm for three-electron kinetic energy integrals

An improved algorithm to evaluate the nonrelativistic three-electron Hylleraas–Configuration Interaction (Hy–CI) kinetic energy integrals over Slater orbitals and the Hamiltonian in Hylleraas coordinates is shown. The resulting analytical expressions are general for all quantum numbers of the orbitals. From there, the restriction of employing orbitals with quantum numbers

Bound state spectra and properties of the doublet states in three-electron atomic systems

l \le 2

Hylleraas–Configuration Interaction calculations on the 11S ground state of helium atom

l≤2 of the above algorithm presented in paper I of this series has been removed. With the new algorithm it is possible, in the direct integration method described in this series, to carry out Hy–CI atomic structure calculations including f-, g-, ..., l and higher angular-momentum Slater orbitals and to determine F, G, ..., L and states of higher order symmetry.

Spin states of the light atoms

In this paper we study the level of accuracy of the electronic wave functions which is necessary to describe properly the atomic effects during nuclear β -decay. In the case of the β−-decay in the Li atom into Be+ ion, we compare the numerical values of the transition probabilities from the , , low-lying states of the initial atom and final ion calculated using both Hylleraas-configuration interaction and configuration interaction (CI) with Slater orbital wave functions. In addition, using the CI method the transition probabilities from , , and low-lying states have been calculated. The average of the absolute deviation of the transition probabilities distribution for low-lying states is <0.15%, for states it is <0.5% and larger for D and higher energy states. The numerical results demonstrate that for low-lying states the atomic effect parameters in β-decay can be calculated with sufficient accuracy using CI wave functions constructed with Slater orbitals. This result opens a new avenue for the accurate calculation of atomic effects during the β-decay in heavier atoms and molecules.

Chapter 11 – On the β−-Decay in the 8Li and 9Li Atoms

Abstract The bound state spectra of the doublet states in three-electron atomic systems are investigated. By using different variational expansions we determine various bound state properties in these systems. Such properties include the electron–nucleus and electron–electron delta-functions and cusp values. The general structure of the bound state spectra in several three-electron atomic systems (Li, Be + , C 3+ and F 6+ ) is investigated with the use of the Hylleraas-Configuration Interaction and the Configuration Interaction wave functions. The advantage of our Configuration Interaction based procedure is that it provides high numerical accuracy for all rotationally excited states, including the bound states with L ⩾ 7 .