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  • Open Access

King-Plot Analysis of Isotope Shifts in Simple Diatomic Molecules

Michail Athanasakis-Kaklamanakis*

Shane G. Wilkins

Alexander A. Breier

Gerda Neyens

  • Experimental Physics Department, CERN, CH-1211 Geneva 23, Switzerland and KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium

  • Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • Laboratory for Astrophysics, Institute of Physics, University of Kassel, 34132 Kassel, Germany

  • KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium

  • *m.athkak@cern.ch
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Phys. Rev. X 13, 011015 – Published 9 February, 2023

DOI: https://doi.org/10.1103/PhysRevX.13.011015

Abstract

We demonstrate that the isotope shift in isotopomers of diatomic molecules, where the nucleus of one of its constituent atoms is replaced by another isotope, can be expressed as the sum of a field shift and a mass shift similar to the atomic case. We show that a linear relation holds between atomic and molecular isotopes shifts, thus extending the King-plot analysis to molecular isotope shifts. Optical isotope shifts in YbF and ZrO and infrared isotope shifts in SnH are analyzed with a molecular King-plot approach utilizing Yb+ and Zr+ ionic isotope shifts and charge radii of Sn obtained with nonoptical methods. The changes in the mean-squared nuclear charge radii δ⟨r2⟩ of Yb170–174,176 and Zr90–92,94,96 extracted from the molecular transitions are found to be in excellent agreement with the values from the spectroscopy of Yb+ and Zr+, respectively. On the contrary, in the case of the vibrational-rotational transition in SnH, no sensitivity to the nuclear volume can be deduced within the experimental resolution, which makes it unsuitable for the extraction of nuclear charge radii but provides insights into the molecular electronic wave function not accessible via other methods. The new opportunities offered by the molecular King-plot analysis for research in nuclear structure and molecular physics are discussed.

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Popular Summary

Electrons in free atoms and molecules have quantized energy levels due to the strong electromagnetic interaction with the positively charged protons in the atomic nucleus. The electrons’ energy depends on the nuclear size and mass, and thus on the number of neutrons coupling to the protons. In atoms, the relationship between the nuclear radius, its mass, and the resulting electron energy shift (called the isotope shift) is well understood and known to be linear. In molecules, this specific electron-nucleus interaction is not as well understood. Here, we demonstrate that the linear relationship also holds for simple diatomic molecules, and that this knowledge can be used to learn something about the nuclear radius for elements that cannot be studied as atoms but are easily accessible in molecular form.

Starting from a semiclassical description of molecular energy levels, we construct a linearized relation between the molecular isotope shift and the difference in mass and charge radius between two isotopes of the same element. This relationship is similar in form to the simple relationship that holds for atoms, and it therefore enables using molecular data to make a King plot—a widely used graphical way to relate isotope shifts in different electronic transitions. The validity of the molecular King plot is confirmed with isotope shifts in YbF, ZrO, and SnH found in the literature.

This result can benefit research in both nuclear structure and molecular physics. While it enables measuring the charge radii of certain radioactive nuclei and of elements not accessible in atomic form, it also provides new insights into the way molecular electrons interact with nuclei.

Article Text

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Phys. Rev. X 13, 011015– Published 9 February, 2023
  • Received 8 April 2022
  • Accepted 19 December 2022
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