Abstract
Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work, we improve the precision of such a method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2) eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.
Highlights
Laser spectroscopy in combination with atomic structure calculations can be used to directly determine nuclear moments in a nuclear-theory-independent way
We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of 229Th3þ in the framework of such a relativistic coupled-cluster single double triple method
Using the experimentally measured and theoretically calculated hyperfine structure (HFS) constants A and B, the nuclear magnetic dipole and electric quadrupole moments were determined in Ref. [9] to be μ 1⁄4 0.360ð7ÞμN and Q 1⁄4 3.11ð6Þ eb
Summary
The simplest version of this approach, the linearized coupled-cluster single double (LCCSD) method, was developed in Ref. Method of calculation.—We evaluated the energies and HFS constants A and B of the lowest-lying states using a version of the high-precision relativistic coupled-cluster method developed in Ref. In the equations for singles, doubles, and valence triples, the sums over excited states were carried out with 35 basis orbitals with the orbital quantum number l ≤ 6. The lowest-order DHF contribution to the energies (with the inclusion of the Breit interaction) is labeled “BDHF.” At the step, we carried out the calculation in the linearized coupled-cluster single double (LCCSD) approximation. Each subsequent calculation includes all terms taken into account at the previous stage and the additional terms specific for the present approximation
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