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Physical Review A

van der Waals and resonance interaction in the quasimolecular system Eu-Sr

R. Logozar, Robert Beuc, Mladen Movre

Published Oct 1, 1988• 2 citations

Abstract

The authors outline an asymptotic calculation of adiabatic potential curves for diatomic quasimolecular systems that happens to be quite accurate in the domain of long-range forces, even for atoms with complex electronic configurations. A formula for the molecular oscillator strength expressed via the oscillator strengths of the constituent atoms and the eigenfunctions of the effective Hamiltonian is presented. Quite general theoretical results on the electrostatic interaction within these quasimolecular systems are then applied to a calculation of the dipole-dipole interaction for the quasimolecule Eu-Sr, leading to the adiabatic potentials in the region of interatomic distances larger than approximately 1.0 nm. These results are checked by comparing the quasistatic absorption coefficient for the blue quasistatic wing of the Eu resonance line broadened by the influence of Sr atoms to the experimentally derived profile [K. Niemax, Phys. Rev. Lett. 55. 56 (1985)]. Excellent agreement is obtained. A great influence of the molecular oscillator strengths on the shape of the quasistatic profile is found, so that, in general, the character of the interaction potential could not be judged from log-log plots of the absorption coefficient alone.

DOI: 10.1103/physreva.38.3969

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Physical Review A•Nov 1, 1986•64 citations

The authors outline an asymptotic calculation of adiabatic potential curves for diatomic quasimolecular systems that happens to be quite accurate in the domain of long-range forces, even for atoms with complex electronic configurations. A formula for the molecular oscillator strength expressed via the oscillator strengths of the constituent atoms and the eigenfunctions of the effective Hamiltonian is presented. Quite general theoretical results on the electrostatic interaction within these quasimolecular systems are then applied to a calculation of the dipole-dipole interaction for the quasimolecule Eu-Sr, leading to the adiabatic potentials in the region of interatomic distances larger than approximately 1.0 nm. These results are checked by comparing the quasistatic absorption coefficient for the blue quasistatic wing of the Eu resonance line broadened by the influence of Sr atoms to the experimentally derived profile [K. Niemax, Phys. Rev. Lett. 55. 56 (1985)]. Excellent agreement is obtained. A great influence of the molecular oscillator strengths on the shape of the quasistatic profile is found, so that, in general, the character of the interaction potential could not be judged from log-log plots of the absorption coefficient alone.

For the first time a transition from a second- to first-order dipole-dipole interaction (van der Waals to resonance interaction) has been observed in a study of the excited EuSr molecule which dissociates into europium 4${\mathrm{f}}^{7}$5s6p

{\mathrm{}}^{8}

{\mathrm{P}}_{9/2}

and strontium 5

{\mathrm{s}}^{2}

{\mathrm{}}^{1}

{\mathrm{P}}_{1}

atoms. The transition was verified by measurement of the wavelength dependence in the quasistatic wings of the cw-laser--excited 4595.3-A\r{} line in Eu broadened by Sr ground-state atoms.

We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state (

{n}_{A}

P) and the other is in the ground state (

{n}_{B}

S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding

{C}_{6}

constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the

{C}_{6}

constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in

{C}_{6}

constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.

The authors report strong repulsive van der Waals and dipole-quadrupole interactions in the $\ensuremath{\Sigma}$ and $\ensuremath{\Pi}$ potentials of the LiCs molecule dissociating into Li

2P

and Cs

6S

atoms. Theoretical results derived from second-order perturbation theory are verified by investigating experimentally the wavelength dependence of the quasistatic wings of the Li resonance lines broadened by Cs ground-state atoms.

With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ ( R < R F ) this dependence transforms to the formula for electric dipole interaction energy Δ E d − d = C 3 / R 3 and for R > R F it transforms to the formula for the van der Waals interaction energy Δ E VdW = − C 6 / R 6 . The van der Waals constant C 6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J . The numerical values of the irreducible components of tensor C 6 were calculated for rubidium atoms in the same Rydberg states | nlJM 〉 with large quantum numbers n . We present the calculated resonance interaction energy of two rubidium atoms in the states |43D 5/2 M 〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P 3/2 M 〉 and of the other in the state |41F 7/2 M 〉.

The close-coupled theory of collisions in a radiation field is used to calculate the absorption profile for the Sr $^{1}\ensuremath{\leftarrow}^{1}$S resonance line broadened by collisions with Ar. The calculations predict the polarization ratios of Sr

^{1}\mathrm{P}

fluorescence following line wing excitation by either linear or circular polarized light. Ab initio calculations were used to obtain the ground and excited SrAr molecular-potential curves, which were adjusted to give improved agreement with experiment. The radiative-scattering theory gives a unified description of the absorption coefficient and polarization redistribution from the small detuning impact limit region to the far spectral wings. The cross sections for elastic and inelastic depolarizing collisions of Sr

^{1}\mathrm{P}_{1}

+Ar were also calculated. The calculated absorption coefficient, impact-broadening rate, linear- and circular-polarization ratios, and depolarization rate coefficients are for the most part in good agreement with experiment.