High sensitivity of a future search for effects of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math> -odd/ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> -odd interactions on the 0.75 eV <mml:math xmlns:mml="http://www.w3

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