Effect of nuclear magnetization distribution within the Woods-Saxon model: Hyperfine splitting in neutral Tl

TL;DR

This study compares nuclear magnetization models to predict hyperfine structures in heavy ions and neutral thallium, extending the Woods-Saxon model to neutral systems and analyzing the model dependence of magnetic anomalies.

Contribution

It extends the Woods-Saxon nuclear magnetization model to neutral atoms and assesses the model dependence of magnetic anomalies in thallium isotopes.

Findings

Woods-Saxon model predictions agree with previous hydrogenlike ion studies.

The ratio of magnetic anomalies is nearly model-independent.

Single-particle models outperform the uniform ball model in accuracy.

Abstract

Three models of the nuclear magnetization distribution are applied to predict the hyperfine structure of the hydrogenlike heavy ions and neutral thallium atoms: the uniformly magnetized ball model and single-particle models for the valence nucleon with the uniform distribution and the distribution determined by the Woods-Saxon potential. Results for the hydrogenlike ions are in excellent agreement with previous studies. The application of the Woods-Saxon model is now extended to the neutral systems with the explicit treatment of the electron correlation effects within the relativistic coupled cluster theory using the Dirac-Coulomb Hamiltonian. We estimate the uncertainty for the ratio of magnetic anomalies and numerically confirm its near nuclear-model independence. The ratio is used as a theoretical input to predict the nuclear magnetic moments of short-lived thallium isotopes. We also show that the differential magnetic anomalies are strongly model dependent. The accuracy of the single-particle models significantly surpasses the accuracy of the simplest uniformly magnetized ball model for the prediction of this quantity. Skripnikov [Skripnikov, J. Chem. Phys. 153, 114114 (2020)] has shown that the Bohr-Weisskopf contribution to the magnetic dipole hyperfine structure constant for an atom or a molecule induced by a heavy nucleus can be factorized into the electronic part and the universal nuclear magnetization dependent part. We numerically confirm this factorization for the Woods-Saxon single-particle model with an uncertainty less than 1%.