6533b82cfe1ef96bd128fdb3

RESEARCH PRODUCT

Nuclear structure of lowestTh229states and time-dependent fundamental constants

subject

description

The electromagnetic transition between the almost degenerate $5/{2}^{+}$ and $3/{2}^{+}$ states in $^{229}\mathrm{Th}$ is deemed to be very sensitive to potential changes in the fine structure constant $\ensuremath{\alpha}$. State of the art Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the difference in Coulomb energies of the two states that determines the sensitivity of the transition frequency \ensuremath{\nu} on variations in $\ensuremath{\alpha}$. The kinetic energies are also calculated that reflect a possible variation in the nucleon or quark masses. 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 sensitivity ${q}_{s}$ of the frequency shift $\ensuremath{\delta}\ensuremath{\nu}$ on $\ensuremath{\delta}\ensuremath{\alpha}/\ensuremath{\alpha}(\ensuremath{\delta}\ensuremath{\nu}={q}_{s}\ensuremath{\delta}\ensuremath{\alpha}/\ensuremath{\alpha})$ varies for the different models between about $+{10}^{20} \mathrm{Hz}$ and $\ensuremath{-}{10}^{20} \mathrm{Hz}$. 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 the size of a temporal drift of $\ensuremath{\alpha}$.