^{2}Σ

^{+}state of LiCa studied by Fourier-transform spectroscopy

^{1}, Alexander Stein

^{2}, Asen Pashov

^{1,a)}, Andrey V. Stolyarov

^{3}, Horst Knöckel

^{2}and Eberhard Tiemann

^{2}

### Abstract

The paper reports on a successful observation of high resolution Fourier transform spectra of LiCa. The fine structure of the ground state was observed and attributed to effective spin-rotation interaction. The experimental observations are described by two models using potential energy curves. One of them takes into account the fine structure splitting by means of effective constants, the other by means of a *R* dependent function γ(*R*), built in the radial Schrödinger equation. *Ab initio* calculations were performed for γ(*R*) which comes close to the experimental function.

This work was supported by the Deutsche Forschungsgemeinschaft in the frame of the cluster of excellence QUEST and by the European Commission in the frame of the Cold Molecule Research Training Network under Contract No. HPRN-CT-2002-00290. A.P. acknowledges partial support from the Bulgarian National Science Fund grant VUI 301/07. A.V.S. is grateful for the partial support from the Federal Program “Scientists and Educators for an Innovative Russia 2009-2013,” contract P 2280.

I. INTRODUCTION

II. EXPERIMENT

III. ANALYSIS

IV. MODELING THE EXPERIMENTAL DATA

V. DISCUSSION AND PERSPECTIVES

### Key Topics

- Ground states
- 21.0
- Excited states
- 10.0
- Fluorescence
- 10.0
- Spin orbit interactions
- 10.0
- Ab initio calculations
- 9.0

## Figures

The potential scheme of LiCa from *ab initio* calculations (Ref. 2). At the atomic asymptote, first the electronic state of Li and then that of Ca is given. With thin (black and red) solid lines the ^{2}Σ^{+} and ^{2}Π states are shown, the thin (black and red) dashed lines correspond to ^{4}Σ^{+} and ^{4}Π states. The thick lines indicate the two doublet states studied in this paper and the quartet state which may predissociate the upper of these two doublet states. The doublet and quartet Δ states are not shown.

The potential scheme of LiCa from *ab initio* calculations (Ref. 2). At the atomic asymptote, first the electronic state of Li and then that of Ca is given. With thin (black and red) solid lines the ^{2}Σ^{+} and ^{2}Π states are shown, the thin (black and red) dashed lines correspond to ^{4}Σ^{+} and ^{4}Π states. The thick lines indicate the two doublet states studied in this paper and the quartet state which may predissociate the upper of these two doublet states. The doublet and quartet Δ states are not shown.

Fluorescence progression in LiCa and large extension by rotational satellites.

Fluorescence progression in LiCa and large extension by rotational satellites.

The range of vibrational and rotational quantum numbers of the observed levels in the X^{2}Σ^{+} state of ^{7}Li^{40}Ca.

The range of vibrational and rotational quantum numbers of the observed levels in the X^{2}Σ^{+} state of ^{7}Li^{40}Ca.

Level scheme of the observed transitions between the 4^{2}Σ^{+} and the X^{2}Σ^{+} states. For simplicity, only two vibrational levels of the X state (with *v*″ and *v*″ + 1) are given. For the later discussion with Eqs. (3) and (4), two spacings between the *F* _{1} levels are marked on the left side giving direct access to the spin-rotation interaction of the lower state.

Level scheme of the observed transitions between the 4^{2}Σ^{+} and the X^{2}Σ^{+} states. For simplicity, only two vibrational levels of the X state (with *v*″ and *v*″ + 1) are given. For the later discussion with Eqs. (3) and (4), two spacings between the *F* _{1} levels are marked on the left side giving direct access to the spin-rotation interaction of the lower state.

Difference between the transition frequencies of the P and R lines of the vibrational progression ((*v* ^{′} = 8, *N* ^{′} = 45) → (*v*″, *N* ^{′′} = 44, 46)) for the *F* _{1} and *F* _{2} components (see Eq. (2) and the text).

Difference between the transition frequencies of the P and R lines of the vibrational progression ((*v* ^{′} = 8, *N* ^{′} = 45) → (*v*″, *N* ^{′′} = 44, 46)) for the *F* _{1} and *F* _{2} components (see Eq. (2) and the text).

(a) The averaged value of *a* ^{′′} as a function of *v*″ derived from Eq. (3). (b) Difference between the vibrational spacings Δν_{ PP1} − Δν_{ PP2} and Δν_{ RR1} − Δν_{ RR2} of progressions of *N* ^{′} = 45 according to Eq. (4). All the spacings are taken with respect to the transitions to *v*″ = 6.

(a) The averaged value of *a* ^{′′} as a function of *v*″ derived from Eq. (3). (b) Difference between the vibrational spacings Δν_{ PP1} − Δν_{ PP2} and Δν_{ RR1} − Δν_{ RR2} of progressions of *N* ^{′} = 45 according to Eq. (4). All the spacings are taken with respect to the transitions to *v*″ = 6.

The potential energy curve of the X^{2}Σ^{+} state in LiCa. In the lower panel, the uncertainties of the pointwise potential for two values of the singularity parameter ξ are given (see the text for details).

The potential energy curve of the X^{2}Σ^{+} state in LiCa. In the lower panel, the uncertainties of the pointwise potential for two values of the singularity parameter ξ are given (see the text for details).

Experimental LiCa ground state potential curve *U*(*R*) (left scale) and spin-rotation function γ(*R*) (right scale) from Table II and Eqs. (15) and (17), respectively, are shown as functions of internuclear distance as solid (black) line. The vertical dashed blue lines show the inner and outer turning points of the highest observed vibrational level; *U*(*R*) and γ(*R*) are well defined by experimental data only near the turning points and between them. The *ab initio* γ(*R*) curve is shown also as a dashed (red) line, in reasonable agreement with experiment.

Experimental LiCa ground state potential curve *U*(*R*) (left scale) and spin-rotation function γ(*R*) (right scale) from Table II and Eqs. (15) and (17), respectively, are shown as functions of internuclear distance as solid (black) line. The vertical dashed blue lines show the inner and outer turning points of the highest observed vibrational level; *U*(*R*) and γ(*R*) are well defined by experimental data only near the turning points and between them. The *ab initio* γ(*R*) curve is shown also as a dashed (red) line, in reasonable agreement with experiment.

## Tables

Pointwise representation of the potential energy curve for the X^{2}Σ^{+} state of LiCa. For interpolation, a natural cubic spline through all the listed points should be used (Ref. 18). The long-range expansion (Eq. (11)) starts at *R* _{o} = 10.2692 Å.

Pointwise representation of the potential energy curve for the X^{2}Σ^{+} state of LiCa. For interpolation, a natural cubic spline through all the listed points should be used (Ref. 18). The long-range expansion (Eq. (11)) starts at *R* _{o} = 10.2692 Å.

Parameters of the analytic representation of the X state potential. The energy reference is the dissociation asymptote. Parameters with an asterisk (*) ensure smooth continuous extrapolation of the potential at .

Parameters of the analytic representation of the X state potential. The energy reference is the dissociation asymptote. Parameters with an asterisk (*) ensure smooth continuous extrapolation of the potential at .

Selected Dunham coefficients for ^{7}Li^{40}Ca in cm^{−1}. See the supplementary material for the full list.^{25}

Selected Dunham coefficients for ^{7}Li^{40}Ca in cm^{−1}. See the supplementary material for the full list.^{25}

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