  Electric polarizabilities of four low-J even-parity states and three low-J
odd-parity states of atomic barium in the range $35,600 $ to $36,000\
$cm$^{-1}$ are investigated. The states of interest are excited (in an atomic
beam) via an intermediate odd-parity state with a sequence of two laser pulses.
The odd-parity states can be excited due to the Stark-induced mixing with
even-parity states. The polarizabilities are measured via direct spectroscopy
on the second-stage transition. Several states have tensor and scalar
polarizabilities that exceed the values that might be expected from the known
energy levels of barium by more than two orders of magnitude. Two of the
Stark-induced transitions cannot be identified from the known energy spectrum
of barium. The observations suggest the existence of as yet unidentified
odd-parity energy states, whose energies and angular momenta are determined in
the present experiment. A tentative identification of these states as [Xe]$6s8p
^3P_{0,2}$ is suggested.
