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The Journal of Chemical Physics

Radiative transition probabilities, lifetimes and dipole moments for the vibrational levels of the X 1Σ+ ground state of K8539Rb

Warren T. Zemke, William C. Stwalley

Published Dec 22, 2003• 32 citations
Publisher

Abstract

Using a potential energy curve (based primarily on the RKR potential of Amiot and Verges [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the X1Sigma+ ground state of 39K85Rb. We observe that the radiative lifetimes of vibrationally excited levels, in particular, are approximately 10(3)-10(6) seconds, far too long to be significant in most ultracold experiments involving 39K85Rb or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling (A approximately mu2nu3 approximately tau(-1)) will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.

DOI
10.1063/1.1630299

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Using a potential energy curve (based primarily on the RKR potential of Amiot and Verges [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the X1Sigma+ ground state of 39K85Rb. We observe that the radiative lifetimes of vibrationally excited levels, in particular, are approximately 10(3)-10(6) seconds, far too long to be significant in most ultracold experiments involving 39K85Rb or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling (A approximately mu2nu3 approximately tau(-1)) will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.
Calculations of the adiabatic potential energy curves and the transition dipole moments between the ground (A 1 Σ + ) and the first excited (A 1 Σ + ) states have been determined for the LiCs and NaCs molecules. The calculations are performed using an ab initio approach based on non-empirical pseudopotentials for Cs + , Li + and Na + cores, parameterized l -dependent polarization potentials and full configuration interaction calculations. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the A + Σ + state using the Franck–Condon (FC) approximation and the approximate sum rule method. The radiative lifetimes associated with the A + Σ + state are presented here for the first time. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.
The adiabatic potential energy curves and the spectroscopic constants of the ground and the first excited states of LiK+, LiRb+ and LiCs+ ionic molecules have been performed. The transition dipole moment between the ground (X2Σ+) and the first excited (22Σ+) state have been determined for each ionic molecule. We have used an ab initio approach involving non‐empirical pseudo‐potentials with core valence effects taken into account through parameterized l‐dependent polarization potentials. Our spectroscopic constants of the ground and the first excited states are in good agreement with the available theoretical works. The potential energy curves and the transition dipole moment are used to estimate the radiative lifetimes of the vibrational levels of the 22Σ+ state for the first time. In addition to the bound‐bound contribution, the bound‐free term has been evaluated exactly and using the Franck‐Condon (FC) approximation and added to the total radiative lifetime. These data can help experimentalists to optimize photoassociative formation of ultracold molecules and their longevity in a trap or in an optical lattice.
We investigate the lifetimes of vibrational states of diatomic alkali-alkaline-earth cations to determine their suitability for ultracold experiments where long decoherence time and controllability by an external electric field are desirable. The potential energy and permanent dipole moment curves for the ground electronic states of LiBe+, LiMg+, NaBe+, and NaMg+ are obtained using the coupled cluster with singles doubles and triples and multireference configuration interaction methods in combination with large all-electron cc-pCVQZ and aug-cc-pCV5Z basis sets. The energies and wave functions of all vibrational states are obtained by solving the Schrödinger equation for nuclei with the B-spline basis set method. To predict the lifetimes of vibrational states, the transition dipole moments, as well as the Einstein coefficients describing spontaneous emission, and the stimulated absorption and emission induced by black body radiation are calculated. Surprisingly, in all studied ions, the lifetimes of the highest excited vibrational states are similar to the lifetimes of the ground vibrational states indicating that highly vibrationally excited ions could be useful for the ultracold experiments requiring long decoherence time.
We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.
By using a combination of molecular beam (MB) excitation spectra and two distinct ultracold molecule excitation spectra (UM+ and UM-), we have assigned high vibrational levels of the A and 3 (1)Σ(+) states from absorption spectra of the mutually strongly perturbed A (1)Σ(+) - 3 (1)Σ(+) - 1 (1)Π - 2 (3)Σ(+) - b (3)Π states of ultracold (39)K(85)Rb molecules in the energy region between 15,116 and 16,225 cm(-1) above the minimum of the ground X (1)Σ(+) state. The ultracold molecules (UM+ and UM-) are formed by radiative decay following photoassociation (PA) to a specific level of the 3(0(+)) state (UM+) or to a specific level of the 3(0(-)) state (UM-). We observe that the A and 3 (1)Σ(+) states are observable in the UM+ spectra, but absent from the UM- spectra. This is explained by considering Hund's case (c) selection rules and transition dipole moments between the upper excited A (1)Σ(+) (2(0(+))) state and the three Ω components (0(+), 0(-), and 1) at the ground-state dissociation limit. We propose further investigations of the extended potential wells of the A and 3 (1)Σ(+) states by combining short-range MB excitation spectra in a narrow Franck-Condon (FC) window near R(e) of the X (1)Σ(+) state, and long-range UM (and PA) excitation spectra, which have much larger FC windows.
We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: 24{}^{24}24Mg7{}^{7}7Li, 40{}^{40}40Ca7{}^{7}7Li, 88{}^{88}88Sr7{}^{7}7Li, and 138{}^{138}138Ba7{}^{7}7Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $\ensuremath{\nu}$ === 0 state (24{}^{24}24Mg6{}^{6}6Li: 22 s, 40{}^{40}40Ca6{}^{6}6Li: 39 s, 88{}^{88}88Sr6{}^{6}6Li: 380 s, and 138{}^{138}138Ba6{}^{6}6Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10%.