King-plot analysis of isotope shifts in simple diatomic molecules

TL;DR

This paper extends the King-plot analysis to molecular isotope shifts, demonstrating its effectiveness in extracting nuclear charge radii from molecular data and revealing insights into molecular electronic wave functions.

Contribution

It introduces a molecular King-plot approach for isotope shifts, linking atomic and molecular data, and validates this method with experimental analysis of YbF, ZrO, and SnH molecules.

Findings

Yb and Zr nuclear charge radii agree with atomic spectroscopy results

SnH vibrational-rotational transition insensitive to nuclear volume

Molecular King-plot offers new insights into nuclear and molecular structure

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 non-optical methods. The changes in the mean-squared nuclear charge radii $\delta \langle r^2 \rangle$ of $^{170-174,176}$Yb and $^{90-92,94,96}$Zr 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 could 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.