Molecular-beam optical Stark and Zeeman study of the $A$ ${}^2\Pi$--$X$ ${}^2{\Sigma }^{+}$ (0,0) band system of BaF

The $A{\hspace{0.5em}}^2\Pi -X{\hspace{0.5em}}^2{\Sigma }^{+}$ (0,0) band system of barium monofluoride (BaF) has been recorded using high-resolution laser-induced fluorescence spectroscopy both field-free and in the presence of static magnetic and electric fields. The field-free spectra for the ${}^{135}\mathrm{Ba}$F, ${}^{137}\mathrm{Ba}$F, and ${}^{138}\mathrm{Ba}$F isotopologues were modeled to generate an improved set of spectroscopic constants for the $A{\hspace{0.5em}}^2$Π($\upsilon$ $=$ 0) and $X{\hspace{0.5em}}^2$Σ${}^{+}$($\upsilon$ $=$ 0) states. The observed optical Stark shifts for the ${}^{138}\mathrm{Ba}$F isotopologue were analyzed to produce the permanent electric dipole moments of 1.50(2) and 1.31(2) D for the $A{\hspace{0.5em}}^2$Π${}_{1/2}$($\upsilon$ $=$ 0) and $A{\hspace{0.5em}}^2$Π${}_{3/2}$ ($\upsilon$ $=$ 0) states, respectively. The observed optical Zeeman shifts for the ${}^{138}\mathrm{Ba}$F isotopologue were analyzed to produce a set of magnetic $g$ factors for the $A{\hspace{0.5em}}^2$Π($\upsilon$ $=$ 0) and $X{\hspace{0.5em}}^2$Σ${}^{+}$($\upsilon$ $=$ 0) states.

Figure 1

Field-free spectrum of $A{\hspace{0.5em}}^2$Π${}_{1/2}$–$X{\hspace{0.5em}}^2$Σ${}^{+}$(0,0) subband system of BaF.

Figure 2

Field-free spectrum of $A{\hspace{0.5em}}^2$Π${}_{3/2}$–$X{\hspace{0.5em}}^2$Σ${}^{+}$(0,0) subband system of BaF.

Figure 3

Observed and predicted spectra of the $A{\hspace{0.5em}}^2$Π${}_{1/2}$–$X{\hspace{0.5em}}^2$Σ${}^{+}$(0,0) subband system of BaF in the region of the $R_1$(4) line (ν $=$ 11634.25 cm${}^{-1}$) of the ${}^{138}\mathrm{Ba}$F isotopologue. The predicted spectra were obtained using the optimized parameters of Table  and a linewidth of 20 MHz.

Figure 4

Observed and predicted spectra of the $A{\hspace{0.5em}}^2$Π${}_{3/2}$–$X{\hspace{0.5em}}^2$Σ${}^{+}$(0,0) subband system of BaF in the region of the $Q_2$(6) line (ν $=$ 12260.60 cm${}^{-1}$) and ${}^Q$$P$${}_{21}$(6) line (ν $=$ 12260.58 cm${}^{-1}$) of the ${}^{138}\mathrm{Ba}$F isotopologue. The predicted spectra were obtained using the optimized parameters of Table  and a linewidth of 20 MHz.

Figure 5

Predicted energy level pattern associated with the ${}^R$$R$${}_{12}$(4) line (ν $=$ 11634.19 cm${}^{-1}$) and the ${}^R$$R$${}_{11}$(4) line (ν $=$ 11634.35 cm${}^{-1}$) of the ${}^{137}\mathrm{Ba}$F isotopologue. The assignments of the spectral features of Fig. 3 are indicated. The energies were calculated using the optimized parameters of Table .

Figure 6

Predicted energy level pattern associated with the ${}^Q$$P$${}_{22}$(6) line (ν $=$ 12260.52 cm${}^{-1}$) and the ${}^Q$$P$${}_{21}$(6) line (ν $=$ 12260.68 cm${}^{-1}$) of the ${}^{137}\mathrm{Ba}$F isotopologue. The assignments of the spectral features of Fig. 4 are indicated. The energies were calculated using the optimized parameters of Table .

Figure 7

${}^{137}\mathrm{Ba}$F isotopologue spin-rotation and hyperfine energy level pattern for the $X{\hspace{0.5em}}^2$Σ${}^{+}$ ($v$ $=$ 0) state as a function of rotational quantum number $N$. The low rotational levels are those of a Hund's case ($b_{\beta S}$) molecule with $G$ being the appropriate intermediate quantum number, and those of the high rotational levels a Hund's case ($b_{\beta J}$) molecule where $J$ is the appropriate intermediate quantum number.

Figure 8

Observed and predicted ${}^S$$R$${}_{21}$(0) line of the ${}^{138}\mathrm{Ba}$F isotopologue recorded field-free and in the presence of a 899.4 V/cm static field with perpendicular orientation and the associated energy levels as a function of applied field. The near degeneracy of the Λ-doublets in the $J$ $=$ 3/2 level of the $A{\hspace{0.5em}}^2$Π${}_{3/2}$ state results in a linear Stark tuning of the energy levels.

Figure 9

Observed and predicted ${}^O$$P$${}_{12}$(2) line of the ${}^{138}\mathrm{Ba}$F isotopologue recorded field-free and in the presence of a 2940.9 V/cm static field with parallel orientation and the associated energy levels as a function of applied field. The large Λ doubling ( $=$ 0.257 cm${}^{-1}$) of the $J$ $=$ 1/2 levels of the $A{\hspace{0.5em}}^2$Π${}_{1/2}$ state results in a second-order Stark effect.

Figure 10

$R_1$(0) line of the ${}^{138}\mathrm{Ba}$F isotopologue recorded field free (bottom) and in the presence of a 713 G parallel (middle) and a 724 G perpendicular (top) magnetic field. The associated energy levels as a function of applied magnetic field, and the assigned transitions, are also presented.

Figure 11

${}^S$$R$${}_{21}$(0) line of the ${}^{138}\mathrm{Ba}$F isotopologue recorded field-free (bottom) and in the presence of a 192 G perpendicular (top) magnetic field. The associated energy levels as a function of applied magnetic field, and the assigned transitions, are also presented.