Abstract
The Fourier transform spectrometer with resolution of 0.03 cm^{−1} was applied to disperse the diode laser induced B(1)^{1}Π → X ^{1}Σ^{+} fluorescence spectra of the RbCs molecule in a heat pipe. The presence of buffer gas (Ar) produced in the spectra the dense pattern of collision-induced rotation relaxation lines, thus enlarging the B(1)^{1}Π data set, allowing to determine the Λ-splitting constants and to reveal numerous local perturbations. In total, 2664 term values for ^{85}Rb^{133}Cs and ^{87}Rb^{133}Cs in the energy range from 13 770 to 15 200 cm^{−1} were obtained with accuracy about 0.01 cm^{−1}. A pointwise potential energy curve (PEC) based on inverted perturbation approach was constructed in the R-range from 3.35 to 9.00 Å for less perturbed vibrational levels v′ ∈ [0, 35] and compared with ab initio calculations. The data included in the fit were reproduced by present PEC with standard deviation (sd) 0.95 cm^{−1}. More systematic over rotational levels J ^{′} ∈ [6, 228] data set was obtained for v′ ∈ [0, 2]. These data were reproduced by the obtained PEC with sd of 0.08 cm^{−1}. The energy of PEC’s minimum T _{ e } = 13 746.65 cm^{−1}, as well as other main molecular constants were determined.
We want to thank A. V. Stolyarov and E. A. Pazyuk for numerous helpful advices. We are indebted to A. Pashov for providing his software for IPA PEC fitting and spectra analysis, and to E. Tiemann for his program for Dunham constants fit. We would like to thank A. Kruzins for his help in experiment and V. Zuters for participating in data processing. The support from ERAF Grant No. 2010/0242/2DP/2.1.1.1.0/10/APIA/VIAA/036 is gratefully acknowledged.
I. INTRODUCTION
II. EXPERIMENT
III. DATA ANALYSIS
IV. RESULTS AND DISCUSSION
A. Pointwise PEC construction
B. Description of low vibrational levels v′ ∈ [0, 2]
C. Discussion
V. CONCLUDING REMARKS
Key Topics
- Laser induced fluorescence
- 17.0
- Laser diodes
- 7.0
- Ground states
- 6.0
- Ab initio calculations
- 5.0
- Error analysis
- 4.0
Figures
Scheme of potential energy curves of the low-lying electronic states of the RbCs molecule based on Hund's case “a” calculations in Ref. ^{ 13 } (upper panel) and on Hund's case “c” calculations in Ref. ^{ 14 } (lower panel; here, the letters at notations refer to the Hund's case “a”).
Scheme of potential energy curves of the low-lying electronic states of the RbCs molecule based on Hund's case “a” calculations in Ref. ^{ 13 } (upper panel) and on Hund's case “c” calculations in Ref. ^{ 14 } (lower panel; here, the letters at notations refer to the Hund's case “a”).
Examples of RbCs B → X LIF spectra from v′ = 0, 1, and 2, which contain one strong LIF progression. Laser excitation frequency for the B-state (v′, J′)-level are: (a) 13 644.754 cm^{−1} for (0, 153); (b) 13 643.94 cm^{−1} for (1, 127); (c) 13 795.015 cm^{−1} for (2, 89). All three spectra contain also several much weaker progressions. No spin-forbidden transitions to the a ^{3}Σ^{+} state are observed.
Examples of RbCs B → X LIF spectra from v′ = 0, 1, and 2, which contain one strong LIF progression. Laser excitation frequency for the B-state (v′, J′)-level are: (a) 13 644.754 cm^{−1} for (0, 153); (b) 13 643.94 cm^{−1} for (1, 127); (c) 13 795.015 cm^{−1} for (2, 89). All three spectra contain also several much weaker progressions. No spin-forbidden transitions to the a ^{3}Σ^{+} state are observed.
A zoomed in fragment of the spectrum shown in Fig. 2(a) demonstrating rotational relaxation. The directly excited LIF lines (shown by arrows) correspond to the B(0, 153) → X(4, 152; 154) transition. Q-, P-, and R-lines from the levels populated by collisions are marked by bars below the spectrum.
A zoomed in fragment of the spectrum shown in Fig. 2(a) demonstrating rotational relaxation. The directly excited LIF lines (shown by arrows) correspond to the B(0, 153) → X(4, 152; 154) transition. Q-, P-, and R-lines from the levels populated by collisions are marked by bars below the spectrum.
J ^{′}-dependence of the experimental term values of ^{85}Rb^{133}Cs in the reduced energy scale E _{ red } = E − 0.0132J ^{′}(J ^{′} + 1) (v′-numbering is shown on the right side). Green triangles mark the levels from which LIF to the a(1)^{3}Σ^{+} state was observed. Stars above J ^{′} = 0 presents the data from Ref. ^{ 25 } , which are identified as v′-levels of the B(1)^{1}Π state (their v′ numbers are marked nearby). Lines are calculated from the present PEC. Dotted lines are extrapolation.
J ^{′}-dependence of the experimental term values of ^{85}Rb^{133}Cs in the reduced energy scale E _{ red } = E − 0.0132J ^{′}(J ^{′} + 1) (v′-numbering is shown on the right side). Green triangles mark the levels from which LIF to the a(1)^{3}Σ^{+} state was observed. Stars above J ^{′} = 0 presents the data from Ref. ^{ 25 } , which are identified as v′-levels of the B(1)^{1}Π state (their v′ numbers are marked nearby). Lines are calculated from the present PEC. Dotted lines are extrapolation.
J ^{′}-dependence of the rotational constant for v′ = 0. Inset demonstrates a relatively weak perturbation of e-component centered at J ^{′} = 130.
J ^{′}-dependence of the rotational constant for v′ = 0. Inset demonstrates a relatively weak perturbation of e-component centered at J ^{′} = 130.
J ^{′}-dependence of the differences between the measured ^{85}Rb^{133}Cs term values E _{ obs } and their counterparts E _{ calc } calculated using the data from Tables I and II . Horizontal lines indicate the experimental uncertainty ±0.01 cm^{−1}.
J ^{′}-dependence of the differences between the measured ^{85}Rb^{133}Cs term values E _{ obs } and their counterparts E _{ calc } calculated using the data from Tables I and II . Horizontal lines indicate the experimental uncertainty ±0.01 cm^{−1}.
Present empirical and ab initio PECs of the B ^{1}Π state: red points – present empirical, black solid line – ab initio calculations ^{ 14 } in Hund's “c” coupling case, solid blue line – ab initio calculations ^{ 13 } in Hund's “a” coupling case. Dotted lines represent the respective difference-based PECs: black – for Hund's “c” coupling case, ^{ 14 } blue – for Hund's “a” coupling case. ^{ 13 } Inset shows PECs close to their minima.
Present empirical and ab initio PECs of the B ^{1}Π state: red points – present empirical, black solid line – ab initio calculations ^{ 14 } in Hund's “c” coupling case, solid blue line – ab initio calculations ^{ 13 } in Hund's “a” coupling case. Dotted lines represent the respective difference-based PECs: black – for Hund's “c” coupling case, ^{ 14 } blue – for Hund's “a” coupling case. ^{ 13 } Inset shows PECs close to their minima.
J ^{′}-dependence of present experimental term values of ^{87}Rb^{133}Cs in the reduced energy scale E _{ red } = E − 0.0132J ^{′}(J ^{′} + 1). Lines are calculated from the present empirical PEC. Red lines mark vibrational levels v′ = 0, 10, 20, 30, 40. The symbols are the same as in Fig. 4 .
J ^{′}-dependence of present experimental term values of ^{87}Rb^{133}Cs in the reduced energy scale E _{ red } = E − 0.0132J ^{′}(J ^{′} + 1). Lines are calculated from the present empirical PEC. Red lines mark vibrational levels v′ = 0, 10, 20, 30, 40. The symbols are the same as in Fig. 4 .
The J ^{′}(J ^{′} + 1)-dependence of local perturbation centers at of e-component only for v _{ B } ∈ [0, 3] (triangles). Solid lines correspond to the calculations based on Ref. ^{ 20 } for . Dashed lines are calculated from the present B(1)^{1}Π state PEC. Inset shows the difference between measured E _{ obs } and calculated E _{ calc } term values.
The J ^{′}(J ^{′} + 1)-dependence of local perturbation centers at of e-component only for v _{ B } ∈ [0, 3] (triangles). Solid lines correspond to the calculations based on Ref. ^{ 20 } for . Dashed lines are calculated from the present B(1)^{1}Π state PEC. Inset shows the difference between measured E _{ obs } and calculated E _{ calc } term values.
Tables
List of the grid points U(R) of the IPA potential for the ^{85}Rb^{133}Cs B(1)^{1}Π state. Energies are given with respect to the minimum of the ground state.
List of the grid points U(R) of the IPA potential for the ^{85}Rb^{133}Cs B(1)^{1}Π state. Energies are given with respect to the minimum of the ground state.
The q _{0} and q _{1} values (in cm^{−1}) fitted for the v′ ∈ [0, 2] levels of the B(1)^{1}Π state of ^{85}Rb^{133}Cs.
The q _{0} and q _{1} values (in cm^{−1}) fitted for the v′ ∈ [0, 2] levels of the B(1)^{1}Π state of ^{85}Rb^{133}Cs.
Molecular constants for low-lying v′-levels of the B(1)^{1}Π state of ^{85}Rb^{133}Cs. The J ^{′}-range, the number of term energies (N) and the standard deviation (sd) are also presented. All constants are given in cm^{−1}.
Molecular constants for low-lying v′-levels of the B(1)^{1}Π state of ^{85}Rb^{133}Cs. The J ^{′}-range, the number of term energies (N) and the standard deviation (sd) are also presented. All constants are given in cm^{−1}.
Comparison of molecular constants of the B(1)^{1}Π state of ^{85}Rb^{133}Cs obtained in the present work with their counterparts obtained from perturbation analysis ^{ 25 } and by ab initio calculations. ^{ 12–15,17 } T _{ e } and ω_{ e } in cm^{−1}, R _{ e } in Å. a — the ω_{ e } value is roughly estimated by a fit of vibrational differences, though its meaning is ambiguous because of negative anharmonicity.
Comparison of molecular constants of the B(1)^{1}Π state of ^{85}Rb^{133}Cs obtained in the present work with their counterparts obtained from perturbation analysis ^{ 25 } and by ab initio calculations. ^{ 12–15,17 } T _{ e } and ω_{ e } in cm^{−1}, R _{ e } in Å. a — the ω_{ e } value is roughly estimated by a fit of vibrational differences, though its meaning is ambiguous because of negative anharmonicity.
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