# Rovibrational dynamics of the strontium molecule in the A1Σu+, c3Πu, and a3Σu+ manifold from state-of-the-art ab initio calculations

**ABSTRACT** State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A1Σu+, c3Πu, and a3Σu+ manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X1Σg+ to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0u+ state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knöckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]10.1140/epjd/e2011-20229-6. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A1Σu+←X1Σg+ transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the 1S0 + 3P1 dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.

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**ABSTRACT:**We predict feasibility of the photoassociative formation of Sr_2 molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the c^3\Pi_u, A^1\Sigma_u^+ and B^1\Sigma_u^+ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ^1S + ^3P_1 intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited state rovibrational levels to deeply bound rovibrational levels of the ground X^1\Sigma_g^+ potential, with v" as low as v"=6. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited state levels that have the largest bound-to-bound transition moments to deeply bound ground state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr_2 molecules in ground state levels suitable for experiments testing the electron-to-proton mass ratio.Physical Review A 03/2012; 85(4). DOI:10.1103/PhysRevA.85.043414 · 2.99 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Physical Review A 09/2012; 86(5). DOI:10.1103/PhysRevA.86.052513 · 2.99 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We report on the creation of ultracold Sr-84(2) molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain 4 X 10(4) molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow S-1(0)-P-3(1) intercombination transition, using a vibrational level of the 1(0(u)(+)) potential as an intermediate state. In preparation of our molecule association scheme, we have determined the binding energies of the last vibrational levels of the 1(0(u)(+)), 1(1(u)) excited-state and the X 1 Sigma(+)(g) ground-state potentials. Our work overcomes the previous limitation of STIRAP schemes to systems with magnetic Feshbach resonances, thereby establishing a route that is applicable to many systems beyond alkali-metal dimers.Physical Review Letters 09/2012; 109(11):115302. DOI:10.1103/PhysRevLett.109.115302 · 7.51 Impact Factor