  The lowest-known excited state in nuclei is the 7.6 eV isomer of 229Th. This
energy is within the range of laser-based investigations that could allow
accurate measurements of possible temporal variation of this energy splitting.
This in turn could probe temporal variation of the fine-structure constant or
other parameters in the nuclear Hamiltonian. We investigate the sensitivity of
this transition energy to these quantities. We find that the two states are
predicted to have identical deformations and thus the same Coulomb energies
within the accuracy of the model (viz., within roughly 30 keV). We therefore
find no enhanced sensitivity to variation of the fine-structure constant. In
the case of the strong interaction the energy splitting is found to have a
complicated dependence on several parameters of the interaction, which makes an
accurate prediction of sensitivity to temporal changes of fundamental constants
problematical. Neither the strong- nor Coulomb-interaction contributions to the
energy splitting of this doublet can be constrained within an accuracy better
than a few tens of keV, so that only upper limits can be set on the possible
sensitivity to temporal variations of the fundamental constants.
