Parity mixing of the 0(+)-0(-) I=1 doublet in 14N.

We studied parity mixing of the ${0}_{2}^{+}$,${0}_{1}^{\mathrm{\ensuremath{-}}}$; I=1 doublet in $^{14}\mathrm{N}$ (${\mathit{E}}_{\mathit{x}}$\ensuremath{\sim}8.6 MeV) to probe the isoscalar component of the parity nonconserving (PNC) nucleon-nucleon interaction. The weak matrix element connecting the ${0}^{+}$ and ${0}^{\mathrm{\ensuremath{-}}}$ levels was determined by measuring the longitudinal analyzing power (${\mathit{A}}_{\mathit{L}}$) over the narrow ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${0}^{+13}$C(p\ensuremath{\rightarrow},p) resonance at ${\mathit{E}}_{\mathit{p}}$=1.16 MeV. Scattered protons were detected in two arrays of four scintillators arranged symmetrically about the beam axis at mean angles of ${\mathit{FTHET}\mathit{\ifmmode \bar{A}\else \={A}\fi{}}}_{1}$=35\ifmmode^\circ\else\textdegree\fi{} and ${\mathit{FTHET}\mathit{\ifmmode \bar{A}\else \={A}\fi{}}}_{2}$=155\ifmmode^\circ\else\textdegree\fi{}. The PNC signal was the difference in the longitudinal analyzing power observed at the two angles. Feedback loops were used to stabilize the position, angle, and spin direction of the beam on target. The observed signal was ${\mathit{A}}_{\mathit{L}}$(FTHETA${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{2}$)-${\mathit{A}}_{\mathit{L}}$(FTHETA${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{1}$) =0.9\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ which corresponds to a weak matrix element 〈${\mathit{H}}_{\mathrm{weak}}$〉=0.38\ifmmode\pm\else\textpm\fi{}0.28 eV.Our measured 〈${\mathit{H}}_{\mathrm{weak}}$〉 disagrees with theoretical expectations; recent shell-model calculations by Horoi et al. using the PNC NN amplitudes of Desplanques, Donoghue, and Holstein yield 〈${\mathit{H}}_{\mathrm{weak}}$〉's that lie in the range from -0.2 eV to -0.8 eV. We briefly discuss some theoretical uncertainities that arise because the structure of the $^{14}\mathrm{N}$ doublet differs in important ways from other known parity doublets. In ancillary studies of the $^{13}\mathrm{C}$(p,\ensuremath{\gamma}) reaction at ${\mathrm{\ensuremath{\theta}}}_{\ensuremath{\gamma}}$=90\ifmmode^\circ\else\textdegree\fi{}, we found that the excitation energies and widths of the ${0}^{+}$ and ${0}^{\mathrm{\ensuremath{-}}}$ levels were (${\mathit{E}}_{\mathit{x}}$=8624\ifmmode\pm\else\textpm\fi{}2 keV, \ensuremath{\Gamma}=4.0\ifmmode\pm\else\textpm\fi{}0.3 keV, and (${\mathit{E}}_{\mathit{x}}$=8802\ifmmode\pm\else\textpm\fi{}7 keV, \ensuremath{\Gamma}=440\ifmmode\pm\else\textpm\fi{}8 keV) respectively. We also determined the following partial widths: ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$(8624\ensuremath{\rightarrow}0)=(0.37\ifmmode\pm\else\textpm\fi{}0.05) eV , ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$(8624\ensuremath{\rightarrow}3948)=(1.26\ifmmode\pm\else\textpm\fi{}0.17) eV, ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$(8624\ensuremath{\rightarrow}5691)=(0.43\ifmmode\pm\else\textpm\fi{}0.06) eV, ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$(8624\ensuremath{\rightarrow}6204)=(2.03\ifmmode\pm\else\textpm\fi{}0.28) eV, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}}$(8802\ensuremath{\rightarrow}0)=(25.2\ifmmode\pm\else\textpm\fi{}2.0) eV. We also report new parameters for the ${\mathit{E}}_{\mathit{x}}$=8062 keV, ${\mathit{E}}_{\mathit{x}}$=9174 keV, and ${\mathit{E}}_{\mathit{x}}$=9388 keV levels.