A Proposed Search for Time Reversal Violation in Polarized Neutron Transmission Through Polarized $^{117}$Sn

We describe work towards an experimental search for a P-odd and T-odd term in the polarized neutron-polarized nucleus forward scattering amplitude [1] on the 1.33 eV p-wave resonance in $^{117}$Sn, which exhibits a $10^{5}$ amplification of P-odd amplitude. $$ \frac{\Delta \sigma _{PT}}{\Delta \sigma _{P}}= \kappa (J) \frac{W}{V} $$ This formula relates the P-odd T-odd over P-odd amplitude ratio $W/V$ to the ratio $\sigma_{PT} \over \sigma_{P}$ of the P-odd T-odd to P-odd cross sections, and a spectroscopic parameter $\kappa(J)$ involving the partial neutron resonance widths in the $J=I \pm 1/2$ channels. We present a reevaluation of ($\vec{n}$,$\gamma$) angular distribution from the resonance [2] which implies a large, nonzero value for $\kappa$ that controls the T-odd sensitivity. The $I=1/2$ $^{117}$Sn nucleus can be polarized with a technique known as SABRE which we will describe. [3] \newline References \newline [1]V. P. Gudkov, Physics Reports 212, 77 (1992).\newline [2]Vo Van Tkhuan Yu. D. Mareev L.B. Pikelner I.M. Frank A.S. Khrykin V.P. Alfimenkov, S.B. Borzakov and E.I. Sharapov. Pis’maZh. Eksp. Teor. Fiz., 39(8):346–348, 1984.\newline [3]A.M. Olaru, A. Burt, P.J. Rayner, S.J. Hart, A.C. Whitwood, G.G.R. Green, S.B. Duckett Chem. Commun. 52 14482 2016