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Neutron transmission experiments can offer a new type of highly sensitivesearch for time-reversal invariance violating (TRIV) effects in nucleon-nucleoninteractions via the same enhancement mechanism observed for large parityviolating (PV) effects in neutron-induced compound nuclear processes. In thesecompound processes, the TRIV cross-section is given as the product of the PVcross-section, a spin-factor $\kappa$, and a ratio of TRIV and PV matrixelements. We determined $\kappa$ to be $0.59\pm0.05$ for $^{139}$La+$n$ usingboth $(n, \gamma)$ spectroscopy and ($\vec{n}+^{139}\vec{\rm La}$)transmission. This result quantifies for the first time the high sensitivity ofthe $^{139}$La 0.75~eV $p$-wave resonance in a future search for P-odd/T-oddinteractions in ($\vec{n}+^{139}\vec{\rm La}$) forward transmission.

High sensitivity of a future search for P-odd/T-odd interactions on the  0.75 eV $p$-wave resonance in $\vec{n}+^{139}\vec{\rm La}$ forward  transmission determined using pulsed neutron beam