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 W-182 which is populated in the decay of cryogenically oriented Ta-182. Within the framework of the quasiparticle random-phase approximation we calculate the value of the complex "irregular" mixing ratio epsilon(E2BAR/M2) for this transition. We estimate that this mixing ratio will have a P-violating real part of \epsilon\cos-eta congruent-to 5 x 10(-5) which implies an observable forward-backward asymmetry (<J>.k) in the 1189-keV gamma-ray directional distribution of O(P) congruent-to 2 x 10(-5) at 10 mK. For the PT-violating imaginary part we find \epsilon\sin-eta congruent-to 200g approximately pi-NN(I = 1), where g approximately pi-NN(I = 1) is the strength of the isovector PT-violating pion-nucleon coupling. An upper limit to this constant of less-than-or-similar-to 3 x 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 x k2) to an accuracy of O(PT) less-than-or-similar-to 2 x 10(-8) in order to improve the limit on g approximately pi-NN(I = 1) set by the neutron electric dipole moment.
