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

S. D. Prosnyak and L. V. Skripnikov
Phys. Rev. C 103, 034314 – Published 19 March 2021

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%.

  • Figure
  • Received 8 January 2021
  • Accepted 1 March 2021

DOI:https://doi.org/10.1103/PhysRevC.103.034314

©2021 American Physical Society

Physics Subject Headings (PhySH)

Nuclear PhysicsAtomic, Molecular & Optical

Authors & Affiliations

S. D. Prosnyak* and L. V. Skripnikov

  • Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Centre “Kurchatov Institute”, Gatchina, Leningrad District 188300, Russia and Saint Petersburg State University, 7/9 Universitetskaya Naberezhnaya, St. Petersburg 199034, Russia

  • *prosnyak_sd@pnpi.nrcki.ru, prosnyak.sergey@yandex.ru
  • skripnikov_lv@pnpi.nrcki.ru, leonidos239@gmail.com

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Issue

Vol. 103, Iss. 3 — March 2021

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