Precision spectroscopy of the ${}^{207}\mathrm{Pb}$${}^{19}\mathrm{F}$ molecule: Implications for measurement of $P$-odd and $T$-odd effects

Here we report precision microwave spectroscopy of pure rotational transitions of the ${}^{207}\mathrm{Pb}$${}^{19}\mathrm{F}$ isotopologue. We use these data to make predictions of the sensitivity of the molecule to $P$-odd, $T$-even and $P$-odd, $T$-odd effects.

Figure 1

Left hand side: Hyperfine energy level structure of the ground electronic ($X$${}_1$) and rotational ($J=1/2$) state of the ${}^{207}\mathrm{Pb}$${}^{19}\mathrm{F}$ molecule as a function of $F$(total angular momentum) and $p_s$ (parity). Two closely spaced $F=1/2$ states of opposite parity are shown by thick lines. Right hand side: Anapole-induced avoided crossing of the $M_F=1/2$ sublevels of the closely spaced $M_F=1/2$ states. This crossing is predicted to occur at a field of $823\pm 40$ G.

Figure 2

$P$- and $T$-odd dependent splitting between $\pm M_F$ pairs of hyperfine states of the ground rotational $J=1/2$ state of ${}^{207}\mathrm{Pb}$${}^{19}\mathrm{F}$. The thick solid line corresponds to the $\left|M\right|=3/2$ lower lying $\Omega$-doublet states whereas the thin solid line corresponds to the higher lying $\left|M_F\right|=3/2$ states. The dotted lines correspond to $\left|M_F\right|=1/2$ sublevels. For the case that ${\kappa }_{P,T}=0$ and $d_e=1.6\times {10}^{-27}\hspace{0.5em}e·$cm (the current limit of Ref. [5]), the energy scale is $26$ mHz.