  For many years, astronomers have promised that the study of pulsating white
dwarfs would ultimately lead to useful information about the physics of matter
under extreme conditions of temperature and pressure. In this paper we finally
make good on that promise. Using observational data from the Whole Earth
Telescope and a new analysis method employing a genetic algorithm, we
empirically determine that the central oxygen abundance in the
helium-atmosphere variable white dwarf GD 358 is 84+/-3 percent. We use this
value to place preliminary constraints on the 12C(alpha,gamma)16O nuclear
reaction cross-section. More precise constraints will be possible with
additional detailed simulations. We also show that the pulsation modes of our
best-fit model probe down to the inner few percent of the stellar mass. We
demonstrate the feasibility of reconstructing the internal chemical profiles of
white dwarfs from asteroseismological data, and find an oxygen profile for GD
358 that is qualitatively similar to recent theoretical calculations.
