Proposed Experiment to Measure the Parity-Odd Asymmetry in the 0.73 eV Neutron Resonance in Polarized $^{139}$La

The 0.7 eV p-wave resonance in $^{139}$La can amplify both parity-odd (P) and time-reversal odd (T) effects from mixing of s-wave and p-wave resonances [1], and a null test of T is possible for this observable [2]. To quantify potential sources of systematic errors and to fix the spectroscopic parameter $\kappa$ which determines the P-odd/T-odd measurement sensitivity, we propose to measure the P-odd correlation term $A$ from $\mathbf{k \cdot I}$ in the forward scattering amplitude, where $\mathbf{k}$ is the neutron momentum and $\mathbf{I}$ is the nuclear polarization. We present an experiment to measure $A$ using the neutron diffraction instrument POLI at the FRM research reactor, which views a hot graphite neutron moderator. The only previous experiment [3] measured $A =0.31 \pm 0.09$, which does not suffice to determine $\kappa$. We describe our experimental design and approach which can lower the error by an order of magnitude and determine $\kappa$. [1] V. P. Gudkov, Physics Reports 212, 77 (1992). [2] J. D. Bowman and V. P. Gudkov, Phys. Rev. C 90, 065503 (2014). [3] V. P. Alfimenkov et al, Phys. Atm. Nucl. 59, 1861 (1996).