Non-Relativistic Electronic-Structure Computation of Neutral and Cationic Systems [Fr₂, Fr-AEM⁺ (AEM= Ca, Sr, Ba)]

The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earth-metal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr-(Ca⁺, Sr⁺, Ba⁺). We adopt a computational scheme without spin-orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr⁺, Ca²⁺, Sr²⁺, and Ba²⁺ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the ^1,3Σ_u,g⁺ and ^1,3Σ⁺ electronic states for Fr₂ and Fr-AEM⁺, respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s², 4s4p, 4s3d), Sr(5s², 5s5p, 5s4d), Ba(6s², 6s6p, 6s5d) + Fr⁺}, and {Ca⁺(4s, 3d), Sr⁺(5s, 4d), Ba⁺(6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom-ion collisions in the diverse charge or excited states. The Σ⁺-Σ⁺ transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.