We identify a pair of near-degenerate states of opposite parity in atomic Xe, the $5p^5 10s ,, ^2[3/2]_2^o$ at $rm{E}=94759.927$ cm$^{-1}$ and $5p^5 6f ,, ^2[5/2]_2$ at $rm{E}= 94759.935$ cm$^{-1}$, for which parity- and time-odd effects are expected
to be enhanced by the small energy separation. We present theoretical calculations which indicate narrow widths for both states and we report a calculated value for the weak matrix element, arising from configuration mixing, of $|W|=2.1$ Hz for $^{132}$Xe. In addition, we measured the Stark effect of the $5p^5,6f$ $^2[5/2]_{2}$ and $5p^5 ,6f ^2[3/2]_2$ ($rm{E} =94737.121,rm{cm}^{-1}$) states. The Stark-shift of the $6f$ states is observed to be negative, revealing the presence of nearby $6g$ states at higher energies, which have not been observed before. The Stark-shift measurements imply an upper limit on the weak matrix element of $|W|!<!5$ Hz for the near-degenerate states ($10s ,, ^2[3/2]_2^o$ and $6f ,, ^2[5/2]_2$), which is in agreement with the presented calculations.
We present the theoretical basis of a cavity-enhanced polarimetric scheme for the measurement of parity-nonconserving (PNC) optical rotation. We discuss the possibility of detecting PNC optical rotation in accessible transitions in metastable Xe and
Hg, and ground state I. In particular, the physics of the PNC optical rotation is presented, and we explore the lineshape effects on the expected PNC optical rotation signals. Furthermore, we present an analysis of the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary for understanding the measurement procedure and the ability of employing robust background subtraction procedures using two novel signal reversals. Using recent atomic structure theoretical calculations, we present simulations of the PNC optical rotation signals for all proposed transitions, assuming a range of experimentally feasible parameters. Finally, the possibility of performing sensitive measurements of the nuclear-spin-dependent PNC effects is investigated, for the odd-neutron nuclei $^{129}$Xe and $^{199}$Hg, and the odd-proton nucleus $^{127}$I.
