  The enhancement of the parity-violating asymmetry in the vicinity of $p$-wave
compound nuclear resonances was observed for a variety of medium-heavy nuclei.
The enhanced parity-violating asymmetry can be understood using the $s$-$p$
mixing model. The $s$-$p$ mixing model predicts several neutron
energy-dependent angular correlations between the neutron momentum $\vec k_n$,
neutron spin $\vec\sigma_n$, $\gamma$-ray momentum $\vec k_\gamma$, and
$\gamma$-ray polarization $\vec\sigma_\gamma$ in the $(n,\gamma)$ reaction. In
this paper, the improved value of the transverse asymmetry of $\gamma$-ray
emissions, corresponding to a correlation term $\vec{\sigma}_n\cdot(\vec
k_n\times\vec k_\gamma)$ in the $^{139}\mathrm{La}(\vec
n,\gamma)^{140}\mathrm{La}$ reaction, and the transverse asymmetries in the
transitions to several low excited states of $^{140}\mathrm{La}$ are reported.
