Extent of simultaneous parity and time violation inW182

In order to relate nuclear gamma-ray distributions to the fundamental parity-time- (PT-) and parity- (P-) violating meson-nucleon interaction, we analyze the case of the mixed (E1,M2,E3) 1189-keV gamma ray in ${}_{}{}^{182}{}_{}{}^{}\mathrm{W}$ which is populated in the decay of cryogenically oriented ${}_{}{}^{182}{}_{}{}^{}\mathrm{Ta}$. Within the framework of the quasiparticle random-phase approximation we calculate the value of the complex ‘‘irregular’’ mixing ratio ɛ(E2¯/M2) for this transition. We estimate that this mixing ratio will have a P-violating real part of ‖ɛ‖cosη≃5×${10}^{\mathrm{-}5}$ which implies an observable forward-backward asymmetry (〈J〉⋅k) in the 1189-keV gamma-ray directional distribution of ${\mathit{O}}_{\mathit{P}}$≃2×${10}^{\mathrm{-}5}$ at 10 mK. For the PT-violating imaginary part we find ‖ɛ‖sinη≃200g̃ ${}_{\mathrm{\pi }\mathit{N}\mathit{N}}{}^{(\mathit{I}=1)}{}_{}{}^{}$, where g̃ ${}_{\mathrm{\pi }\mathit{N}\mathit{N}}{}^{(\mathit{I}=1)}{}_{}{}^{}$ is the strength of the isovector PT-violating pion-nucleon coupling. An upper limit to this constant of ≲3×${10}^{\mathrm{-}10}$ may be obtained from the electric dipole moment of the neutron. Whence we conclude that at 10 mK one needs to measure the PT-violating correlation (〈J〉⋅${\mathbf{k}}_2$)(〈J〉⋅${\mathbf{k}}_1$×${\mathbf{k}}_2$) to an accuracy of ${\mathit{O}}_{\mathit{P}\mathit{T}}$≲2×${10}^{\mathrm{-}8}$ in order to improve the limit on g̃ ${}_{\mathrm{\pi }\mathit{N}\mathit{N}}{}^{(\mathit{I}=1)}{}_{}{}^{}$ set by the neutron electric dipole moment.