Europhysics Letters (EPL)

Resonances in the rotational constants of $0_{g}^{-}(6s_{1/2}+6p_{1/2})$ Cs 2 levels analysed by an improved-B v -formula associated to a 2-channel model

Haikel Jelassi, Laurence Pruvost

Published Aug 1, 2016• 3 citations

Abstract

Spin-orbit coupling in 0 g − ( 6 s 1 / 2 + 6 p 1 / 2 ) long-range molecular levels of Cs 2 assigned to resonances in the rotational constant ( B v ) spectrum (L ignier L. et al. , Phys. Chem. Chem. Phys. , 13 (2011) 18910; P ichler M. et al. , J. Chem. Phys. , 121 (2004) 1796) has been analyzed with a model which associates an improved- B v -formula (established here) and a 2-channel model. The approach explains the Lorentzian shape of the observed resonances superimposing a non-horizontal background and the fit of the B v -spectrum allows us to deduce the spin-orbit coupling parameters. We compare this approach with an analysis of the binding energies using the vibrational quantum defect (VQD). The good agreement between the methods lets one conclude that the improved- B v -formula associated with a 2-channel model provides a pertinent approach for analyzing coupled molecular series.

DOI: 10.1209/0295-5075/115/43002

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Europhysics Letters (EPL)

Resonances in the rotational constants of $0_{g}^{-}(6s_{1/2}+6p_{1/2})$ Cs 2 levels analysed by an improved-B v -formula associated to a 2-channel modelResonances in the rotational constants of $0_{g}^{-}(6s_{1/2}+6p_{1/2})$ Cs 2 levels analysed by an improved-B v -formula associated to a 2-channel model

Haikel Jelassi, Laurence Pruvost

Published Aug 1, 2016• 3 citations

Publisher

Abstract

DOI: 10.1209/0295-5075/115/43002

Related papers

Theoretical treatment of channel mixing in excited Rb2 and Cs2 ultracold molecules: Perturbations in 0u+ photoassociation and fluorescence spectra

Viatcheslav Kokoouline, Olivier Dulieu, Françoise Masnou-Seeuws

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Analyzing Feshbach resonances -- A $^6$ Li - $^{133}$ Cs case studyAnalyzing Feshbach resonances -- A $^6$Li -$^{133}$Cs case study

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We provide a comprehensive comparison of a coupled channels calculation, the asymptotic bound state model (ABM), and the multichannel quantum defect theory (MQDT). Quantitative results for $^6$ Li - $^{133}$ Cs are presented and compared to previously measured $^6$ Li - $^{133}$ Cs Feshbach resonances (FRs) [M. Repp et al., Phys. Rev. A 87 010701(R) (2013)]. We demonstrate how the accuracy of the ABM can be stepwise improved by including magnetic dipole-dipole interactions and coupling to a non-dominant virtual state. We present a MQDT calculation, where magnetic dipole-dipole and second order spin-orbit interactions are included. A frame transformation formalism is introduced, which allows the assignment of measured FRs with only three parameters. All three models achieve a total rms error of < 1G on the observed FRs. We critically compare the different models in view of the accuracy for the description of FRs and the required input parameters for the calculations.We provide a comprehensive comparison of a coupled channels calculation, the asymptotic bound state model (ABM), and the multichannel quantum defect theory (MQDT). Quantitative results for $^6$Li -$^{133}$Cs are presented and compared to previously measured $^6$Li -$^{133}$Cs Feshbach resonances (FRs) [M. Repp et al., Phys. Rev. A 87 010701(R) (2013)]. We demonstrate how the accuracy of the ABM can be stepwise improved by including magnetic dipole-dipole interactions and coupling to a non-dominant virtual state. We present a MQDT calculation, where magnetic dipole-dipole and second order spin-orbit interactions are included. A frame transformation formalism is introduced, which allows the assignment of measured FRs with only three parameters. All three models achieve a total rms error of < 1G on the observed FRs. We critically compare the different models in view of the accuracy for the description of FRs and the required input parameters for the calculations.

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Resonances in the rotational constants of

0_{g}^{-}(6s_{1/2}+6p_{1/2})

Cs 2 levels analysed by an improved-B v -formula associated to a 2-channel model

{\mathrm{Cs}}_{2}{0}_{u}^{+}(6s+6p{}^{2}{P}_{1/2,3/2})

photoassociation spectrum below the lower dissociation limit. The results are shown to be very sensitive to the molecular potential curves and spin-orbit coupling. In the case of

{\mathrm{Rb}}_{2}{0}_{u}^{+}(5s+5p{}^{2}{P}_{1/2,3/2}),

a strong isotopic effect is also predicted. The results can be interpreted in the framework of generalized two-channel quantum defect theory, and generalized Lu-Fano plots are presented. This work suggests that parameters could easily be fitted to experimental spectra, eliminating the difficulties caused by limitations in the accuracy of the short-range molecular potentials.

We present an analysis of spectroscopic data concerning the long-range molecular state

(6{s}_{1∕2}+6{p}_{1∕2}){0}_{u}^{+}

^{133}\mathrm{Cs}_{2}

[M. Pichler, H. Chen, and W. C. Stwalley, J. Chem. Phys. 121, 1796 (2004)] by using the Lu-Fano method coupled to the improved LeRoy-Bernstein formula. The obtained Lu-Fano graph exhibits the coupling of molecular series to the

(6{s}_{1∕2}+6{p}_{3∕2}){0}_{u}^{+}

state. The coupling is due to the spin effects in the molecule. A two-channel model involving the improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize the perturbing levels, to evaluate the coupling in the vicinity of each perturbing level (five observed for Cs) in a two-level approach and in a more accurate multilevel description. Furthermore, we predict the energy and the width of the first predissociated level.

A reexamination of the photoassociation spectrum of the external well of the ${0}_{g}^{\ensuremath{-}}$ potential of

{\mathrm{Cs}}_{2}

converging to the

(6{s}_{1∕2}+6{p}_{3∕2})

limit is performed, in order to resolve inconsistencies arising from a previously published paper [Phys. Rev. Lett. 85, 1408 (2000)]. We use the same analytical description of the potential as in an other previous analysis [Phys. Rev. A 66, 052506 (2002)], but we make a shift of 2 in the assignment of the observed vibrational lines. The agreement between experimental and calculated energy positions is improved and the intensities calculated using the new potential account well for all available data. The fitting procedure reveals a strong interdependence of the parameters of the model, which limits the accuracy of the determination of the radiative lifetimes of the

6{p}^{2}{P}_{1∕2}

and

6{p}^{2}{P}_{3∕2}

atomic levels. Only a more precise experimental study could allow one to improve the determination of these lifetime values.

Analyzing Feshbach resonances -- A

^6

Li -

^{133}

Cs case study

We provide a comprehensive comparison of a coupled channels calculation, the asymptotic bound state model (ABM), and the multichannel quantum defect theory (MQDT). Quantitative results for

^6

Li -

^{133}

Cs are presented and compared to previously measured

^6

Li -

^{133}

Cs Feshbach resonances (FRs) [M. Repp et al., Phys. Rev. A 87 010701(R) (2013)]. We demonstrate how the accuracy of the ABM can be stepwise improved by including magnetic dipole-dipole interactions and coupling to a non-dominant virtual state. We present a MQDT calculation, where magnetic dipole-dipole and second order spin-orbit interactions are included. A frame transformation formalism is introduced, which allows the assignment of measured FRs with only three parameters. All three models achieve a total rms error of < 1G on the observed FRs. We critically compare the different models in view of the accuracy for the description of FRs and the required input parameters for the calculations.