  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.
