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 182W which is populated in the decay of cryogenically oriented 182Ta. 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≃5×10-5 which implies an observable forward-backward asymmetry (〈J〉⋅k) in the 1189-keV gamma-ray directional distribution of OP≃2×10^-5 at 10 mK. For the PT-violating imaginary part we find ‖ɛ‖sinη≃200g̃ πNN(I=1), where g̃ πNN(I=1) is the strength of the isovector PT-violating pion-nucleon coupling. An upper limit to this constant of ≲3×10^-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〉⋅k2)(〈J〉⋅k1×k2) to an accuracy of OPT≲2×10^-8 in order to improve the limit on g̃ πNN(I=1) set by the neutron electric dipole moment
