  The electromagnetic transition between the almost degenerate 5/2+ and 3/2+
states in Th229 is deemed to be very sensitive to potential changes in the fine
structure constant alpha. State of the art Hartree-Fock and
Hartree-Fock-Bogoliubov calculations are performed to compute the difference in
Coulomb energies of the two states which determines the amplification of
variations in alpha into variations of the transition frequency. The kinetic
energies are also calculated which reflect a possible variation in the nucleon
or quark masses. A generalized Hellmann-Feynman theorem is proved including the
use of density-matrix functionals.
  As the two states differ mainly in the orbit occupied by the last unpaired
neutron the Coulomb energy difference results from a change in the nuclear
polarization of the proton distribution. This effect turns out to be rather
small and to depend on the nuclear model, the amplification varies between
about -4 x 10^4 and +4 x 10^4. Therefore much more effort must be put into the
improvement of the nuclear models before one can draw conclusions from a
measured drift in the transition frequency on a temporal drift of fundamental
constants. All calculations published so far do not reach the necessary
fidelity.
  PACS 06.20.Jr,21.60.Jz,27.90.+b
