King-Plot Analysis of Isotope Shifts in Simple Diatomic Molecules

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 <math display="inline"><mrow><msup><mrow><mi>Yb</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and <math display="inline"><mrow><msup><mrow><mi>Zr</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> ionic isotope shifts and charge radii of Sn obtained with nonoptical methods. The changes in the mean-squared nuclear charge radii <math display="inline"><mi>δ</mi><mo stretchy="false">⟨</mo><msup><mi>r</mi><mn>2</mn></msup><mo stretchy="false">⟩</mo></math> of <math display="inline"><mrow><mmultiscripts><mrow><mi>Yb</mi></mrow><mprescripts/><none/><mrow><mn>170</mn><mi>–</mi><mn>174</mn><mo>,</mo><mn>176</mn></mrow></mmultiscripts></mrow></math> and <math display="inline"><mrow><mmultiscripts><mrow><mi>Zr</mi></mrow><mprescripts/><none/><mrow><mn>90</mn><mi>–</mi><mn>92</mn><mo>,</mo><mn>94</mn><mo>,</mo><mn>96</mn></mrow></mmultiscripts></mrow></math> extracted from the molecular transitions are found to be in excellent agreement with the values from the spectroscopy of <math display="inline"><mrow><msup><mrow><mi>Yb</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and <math display="inline"><mrow><msup><mrow><mi>Zr</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>, 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.