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

Abstract

The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earthmetal 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 + , Ca 2+ , Sr 2+ , and Ba 2+ 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 1,3 Σ u,g + and 1,3 Σ + electronic states for Fr 2 and Fr−AEM + , respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s 2 , 4s4p, 4s3d), Sr(5s 2 , 5s5p, 5s4d), Ba(6s 2 , 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.

Accurate ab initio calculations of adiabatic energy and dipole moment: Prospects for the formation of cold Alkaline-Earth-Francium molecular ions ALKE-Fr+ (ALKE = Be, Mg, Ca, and Sr)

“…We note that, for 1,3 Π and 1,3 Δ symmetries, the spectroscopic constants are investigated for the first time. As reported in table 3, the well depths and equilibrium distances for the ground and the first excited states of CaFr + , agree well with those of reference [48] as the largest differences ΔR e and ΔD e are 0.68 bohr and 132 cm −1 , respectively, for 4 1 Σ + and 5 1 Σ + excited states. In the case of SrFr + , our presented results and those of [48] are in good agreement.…”

“…As reported in table 3, the well depths and equilibrium distances for the ground and the first excited states of CaFr + , agree well with those of reference [48] as the largest differences ΔR e and ΔD e are 0.68 bohr and 132 cm −1 , respectively, for 4 1 Σ + and 5 1 Σ + excited states. In the case of SrFr + , our presented results and those of [48] are in good agreement. Where the largest ΔR e (0.24 bohr) is noted for the 2nd minimum of the second electronic excited state 3 1 Σ + , while the well depths seems to be slightly over-estimated in calculations presented in [48], as they employed different basis set.…”

“…As can be seen in tables 3 and 4, a quite good agreement is found for all spectroscopic parameters in 1,3 Σ symmetry of both CaFr + and SrFr + systems with available results [48]. We note that, for 1,3 Π and 1,3 Δ symmetries, the spectroscopic constants are investigated for the first time.…”

“…The calculated spectroscopic parameters for the investigated ground and excited electronic states of molecular-ions under consideration are gathered in Tables 1-4. The presented results for ground and excited electronic states of BeFr + and MgFr + molecular-ions are reported, here, for the first time; however, the spectroscopic results of CaFr + and SrFr + are compared with the available results of reference [48].…”

“…The calculation was based on the pseudopotential method where energies and permanent and transition dipole moments were determined and the ability to produce Fr 2 , RbFr, and CsFr cold molecules via the photoassociation process of cold atoms was also discussed. Recently, theoretical work was focused on low-laying excited states for only Σ + symmetry of Fr 2 , FrCa + , FrSr + , and FrBa + systems [48]. We note that the spectroscopic and structural information of ground and excited states of molecular-ions BeFr + and MgFr + are still missing up to date, as no theoretical or experimental data are available.…”