On Th229 and time-dependent fundamental constants

TL;DR

This paper investigates the sensitivity of the Th229 nuclear transition to potential variations in fundamental constants, using advanced nuclear models to assess the feasibility of detecting such changes through transition frequency measurements.

Contribution

It provides detailed Hartree-Fock and Hartree-Fock-Bogoliubov calculations of Coulomb energy differences in Th229, highlighting the model dependence and the need for improved nuclear models for fundamental constant variation detection.

Findings

Coulomb energy difference varies between -4x10^4 and +4x10^4 depending on the nuclear model.

The effect of nuclear polarization on the energy difference is small and model-dependent.

Current nuclear models lack the fidelity needed for conclusive measurements of fundamental constant variations.

Abstract

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