4 The $B^2\Sigma^+{\rightarrow}X^2\Sigma^+$ transition

The ground state of LaO has been proved to be of $^2\Sigma^+$symmetry, relevant of the $b_{\rm \beta S}$ coupling case. In this situation, the Fermi contact operator, bI.S, couples the electron spin S to the nuclear spin I. The total spin momentum ${\bf G}={\bf I}+{\bf S}$ can take the values 3 and 4, since $I=\frac{7}{2}$ for ¹³⁹La and I=0 for ¹⁶O, and $S=\frac{1}{2}$ for a doublet state. All rotational levels are then split into two components corresponding to G=3 and 4, separated by four times the Fermi contact term b. For a given vibrational level v, the term values of the two sublevels have the form

$$T_{3v}(N)=T_v-\frac{9}{4}b+B_vN(N+1)-D_vN^2(N+1)^2$$ (1)

and

$$T_{4v}(N)=T_v+\frac{7}{4}b+B_vN(N+1)-D_vN^2(N+1)^2.$$ (2)

The upper state $B^2\Sigma^+$ is in the more classical $b_{\rm \beta J}$ coupling (${\bf J}={\bf N}+{\bf S}$). The F₁ and F₂ rotational sublevels correspond to $N=J-\frac{1}{2}$ and $N=J+\frac{1}{2}$, respectively. The term values can be written as

$$T_{1v}(N)=T_v+B_vN(N+1)-D_vN^2(N+1)^2+\frac{\gamma_v}{2}N$$ (3)

and

$$T_{2v}(N)=T_v+B_vN(N+1)-D_vN^2(N+1)^2-\frac{\gamma_v}{2}(N+1).$$ (4)

The spin-rotation parameter $\gamma_v$ may be replaced, if necessary, by a polynomial expansion in N(N+1), such as $\gamma_v + \gamma _{N}N(N+1)+ ...$

A large hyperfine structure appears in each rotational level of $X^2\Sigma^+$, arising from the coupling ${\bf F}={\bf N}+{\bf G}$ which gives 2G+1 hyperfine components. Likewise, for $B^2\Sigma^+$, each rotational level J is composed of 2I+1 components (${\bf F}={\bf J}+{\bf I}$). Each band of such a $^2\Sigma^+{\rightarrow}^2\Sigma^+$ transition consists of 8 branches, following the selection rule $\Delta N =\pm 1$.The lines, which correspond to the unresolved transitions ($\Delta F=\Delta N$)between the F hyperfine sublevels, may show narrow or broadened profiles, according to the branch concerned. Thus, line profiles in the R₂₃, R₁₄, P₂₃, and P₁₄ branches are narrow, whereas they are asymmetrically broadened in R₂₄, R₁₃, P₂₄, and P₁₃, their widths increasing with rotation. Typical values of the FWHM's at mid-rotation ($J\approx 50$) are about 0.040 and 0.130 cm^-1, respectively [2, (Bacis et al. 1973)].