Nuclear structure of lowestTh229states and time-dependent fundamental constants

Abstract

The electromagnetic transition between the almost degenerate 5/2 + and 3/2 + states in 229 Th is deemed to be very sensitive to potential changes in the fine structure constant α. 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 α 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 × 10 4 and +4 × 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.

Sensitivity of ultracold-atom scattering experiments to variation of the fine-structure constant

“…For spectroscopy experiments, such an enhancement may occur due to a quasi-degeneracy of two close lying levels of different nature, found in some atoms [6,7,[14][15][16], molecules [17,18], and nuclei [19][20][21]. Chin and Flambaum pointed out that a large enhancement (on the order of 10 9 − 10 12 ) could also be achieved in ultracold atomic collision experiments near Feshbach resonances [22].…”

Variation of fundamental constants and 229Th

“…2. The next step is to include pairing correlations with the Bogoliubov ansatz (7) and do self-consistent HFB calculations based on the SkM * and SIII density-matrix functionals.…”

Nuclear clocks based on resonant excitation of γ-transitions

“…Refs. [23,59]), indicating that the sensitivity to the value of the fine structure constant depends critically on the nuclear structure. It seems likely, though, that the sensitivity will be substantially higher than in presently studied atomic clocks.…”