Hyperfine Structure in the $^{87}$Rb$_{2}$ $1_{g}$ State Below $5^{2}S+5^{2}P_{1/2}$

Hyperfine structure in the Rb$_{2}$ $1_{g} P_{1/2}$ state was observed in photoassociation from cold atoms some time ago, but only partially analyzed. Our Hamiltonian includes the vibrational energy, $G(v)$, rotational energy, $B(v)$, hyperfine interaction, $A(v)\iota$, and off-diagonal elements $F_{\pm}\cdot I_{mp}$. $F$ ranges from 1 to 6, $\iota$ from $-I$ to $I$, where $I$=3. The data scans were precisely calibrated by simultaneously etalon scans. For the 22 vibrational levels (over a range of 50) for which there is precise data, $A(v)$ varies from 2.97$\times 10^{-2}$ cm$^{-1}$ to 3.15 $\times 10^{-2}$ cm$^{-1}$. The $G(v)$ and $B(v)$ values allow us to construct a potential down to 32 cm$^{-1}$ below the dissociation limit.