The formulation of Bardsley et al (Phys. Rev. A 11 1911) for evaluating the asymptotic electron exchange interaction between an alkali ion and its parent atom is extended by the use of a more accurate representation of the asymptotic wavefunction of the isolated atom and also by the inclusion of a further term in the series that accounts for the presence of the ion. The Bardsley analysis is compared with a purely numerical approach in which the Holstein–Herring integrand is constructed from a polarized wavefunction built from numerical solutions of the differential equations of Rayleigh–Schrodinger perturbation theory and the ¨ required quadrature is performed numerically. Values of the asymptotic exchange interactions are given for the molecular ions Li+ 2 , Na+ 2 , K+ 2 , Rb+ 2 and Cs+ 2 . As an example, exchange interactions for Cs+ 2 evaluated by an ab initio method are compared to those predicted by the Bardsley formula. Potentials for the lowest states of Cs+ 2 are constructed from the ab initio values matched to the asymptotic exchange and long-range polarization interactions, and these potentials are used to predict the 12+ g and 12+ u scattering lengths and low-energy charge transfer cross sections.
The formulation of Bardsley et al (Phys. Rev. A 11 1911) for evaluating the asymptotic electron exchange interaction between an alkali ion and its parent atom is extended by the use of a more accurate representation of the asymptotic wavefunction of the isolated atom and also by the inclusion of a further term in the series that accounts for the presence of the ion. The Bardsley analysis is compared with a purely numerical approach in which the Holstein–Herring integrand is constructed from a polarized wavefunction built from numerical solutions of the differential equations of Rayleigh–Schrodinger perturbation theory and the ¨ required quadrature is performed numerically. Values of the asymptotic exchange interactions are given for the molecular ions Li+ 2 , Na+ 2 , K+ 2 , Rb+ 2 and Cs+ 2 . As an example, exchange interactions for Cs+ 2 evaluated by an ab initio method are compared to those predicted by the Bardsley formula. Potentials for the lowest states of Cs+ 2 are constructed from the ab initio values matched to the asymptotic exchange and long-range polarization interactions, and these potentials are used to predict the 12+ g and 12+ u scattering lengths and low-energy charge transfer cross sections.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. The preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. On the theoretical side, highly accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. Particularly problematic is the correct description of potential features at large intermolecular distances. Franck-Condon overlap integrals for nuclear wavefunctions in barely bound vibrational states are extremely sensitive to inaccuracies of the potential at long range. In this study, we compare the predictions of common, wavefunction-based ab initio techniques for a known de-excitation mechanism in alkali-alkaline earth dimers. It is the aim to analyze the predictive power of these methods for a preliminary evaluation of potential cooling mechanisms in heteronuclear open shell systems which offer the experimentalist an electric as well as a magnetic handle for manipulation. The series of X-Sr molecules, with X = Li, Na, K and Rb, has been chosen for a direct comparison. Quantum degenerate mixtures of Rb and Sr have already been produced,\footnote{B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A, 2013, 88, 023601} making this combination very promising for the production of ultracold molecules.
Abstract We study theoretically interaction potentials and low-energy collisions between different alkali atoms and alkali ions. Specifically, we consider systems such as X + Y + , where X( Y + ) is either Li(Cs + ) or Cs(Li + ), Na(Cs + ) or Cs(Na + ) and Li(Rb + ) or Rb(Li + ). We calculate the molecular potentials of the ground and first two excited states of these three systems using a pseudopotential method and compare our results with those obtained by others. We derive ground-state scattering wave functions and analyze the cold collisional properties of these systems for a wide range of energies. We find that, in order to get convergent results for the total scattering cross sections for energies of the order 1 K, one needs to take into account at least 60 partial waves. The low-energy scattering properties calculated in this paper may serve as a precursor for experimental exploration of quantum collisions between an alkali atom and an alkali ion of a different nucleus.
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca+, Ba+, Sr+, and Ra+ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation R. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus R are given among all the considered atoms and ions.
Accurate knowledge of interaction potentials among the alkali-metal atoms and alkaline-earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali-metal atoms with the Ca+, Ba+, Sr+, and Ra+ alkaline-earth ions systematically, which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation R. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus R are given among all the alkaline ions with Rb.
Alkaline-earth dimers are now been used, as new grounds for, testing fundamental physics laws, precision measurements and quantum computation. As a starting point for such experiments, one needs a very good knowledge of the electronic structure, energetics and long-range behavior of these molecular ions. We perform accurate ab initio calculations for the ground and low-lying excited states of Be2+, Mg2+, Ca2+ and Sr2+ molecular ions. We have also calculated the spectroscopic constants, electronic transition dipole moments, polarizabilities and long-range dispersion coefficients for the various alkaline-earth ionic dimers. We have extended our calculations to study heteronuclear species of alkaline-earth molecular ions, like BeCa+, and also mixed alkali alkaline-earth species like NaCa+. We calculated photoassociation (PA) pathways for formation of cold molecular ions and also studied corrections to the Born-Oppenheimer Hamiltonian: non-adiabatic couplings and hyperfine structure due to nuclear spins and electric quadrupoles. We believe, this work would lay foundation, not only for new experiments in ultracold physics and chemistry, but would also provide valuable starting point for theoretical calculations involving low temperature scattering and resonant charge transfer.
Four different spin-dependent scattering cross sections are calculated by semiclassical and by partial-wave analyses for each of the five alkali atoms, Li, Na, K, Rb, and Cs, for 124 different relative kinetic energies. These cross sections are finally averaged thermally. The results agree very well with experiments.In the calculation, the interaction potential between two alkali atoms is calculated by individually considering the interaction due to the two valence s electrons and to the closed electronic shells of the two atoms. The two-s-electron interaction is generated ad hoc phenomenologically from the known hydrogen-hydrogen interatomic potential and the closed-shell interaction from interatomic potentials of two inert atoms corresponding to the cores. The potentials so obtained are in agreement with those constructed from band spectra.