Extent of simultaneous parity and time violation in 182W.

Abstract

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 \ensuremath{\varepsilon}(E2\ifmmode\bar\else\textasciimacron\fi{}/M2) for this transition. We estimate that this mixing ratio will have a P-violating real part of \ensuremath{\Vert}\ensuremath{\varepsilon}\ensuremath{\Vert}cos\ensuremath{\eta}\ensuremath{\simeq}5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ which implies an observable forward-backward asymmetry (〈J〉\ensuremath{\cdot}k) in the 1189-keV gamma-ray directional distribution of ${\mathit{O}}_{\mathit{P}}$\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ at 10 mK. For the PT-violating imaginary part we find \ensuremath{\Vert}\ensuremath{\varepsilon}\ensuremath{\Vert}sin\ensuremath{\eta}\ensuremath{\simeq}200g\ifmmode \tilde{}\else \~{}\fi{} $_{\mathrm{\ensuremath{\pi}}\mathit{N}\mathit{N}}^{(\mathit{I}=1)}$, where g\ifmmode \tilde{}\else \~{}\fi{} $_{\mathrm{\ensuremath{\pi}}\mathit{N}\mathit{N}}^{(\mathit{I}=1)}$ is the strength of the isovector PT-violating pion-nucleon coupling. An upper limit to this constant of \ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ 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〉\ensuremath{\cdot}${\mathbf{k}}_{2}$)(〈J〉\ensuremath{\cdot}${\mathbf{k}}_{1}$\ifmmode\times\else\texttimes\fi{}${\mathbf{k}}_{2}$) to an accuracy of ${\mathit{O}}_{\mathit{P}\mathit{T}}$\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ in order to improve the limit on g\ifmmode \tilde{}\else \~{}\fi{} $_{\mathrm{\ensuremath{\pi}}\mathit{N}\mathit{N}}^{(\mathit{I}=1)}$ set by the neutron electric dipole moment.