Some Effects of Parity Nonconservation in Nuclear Electromagnetic Decays

The matrix elements for decay of a nucleus by $\gamma$ emission or electron conversion are considered with relaxation of the usual parity selection rules. Four types of pseudoscalar observables are calculated assuming, in particular, mixed $\mathrm{ML}$ and $\mathrm{EL}$ multipole matrix elements with arbitrary relative amplitude. These are (1) $\gamma$-ray nuclear polarization with unpolarized initial and final nuclei, (2) $\gamma$-ray angular distribution (terms odd in $cos\theta$) with polarized initial nucleus, (3) helicity of conversion electrons with unpolarized initial and final nuclei, and (4) circular polarization of the succeeding $\gamma$ ray relative to the direction of the first, mixedparity $\gamma$ ray in the two-photon cascade of an unpolarized nucleus. A proof is presented that the helicity of the conversion electron (3) approaches the circular polarization (1) in the mathematical limit of infinite transition energy. Numerical results are presented for ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}_{}^m{}_{}{}^{}$ based on a recent conjecture of parity mixing in one of its transitions.