Universal correlations of isotope effects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Y</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">Pr</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Ba</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Cu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mn>7</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

The oxygen-isotope $(^{16}\mathrm{O}∕^{18}\mathrm{O})$ effect on the zero-temperature superconducting energy gap ${\ensuremath{\Delta}}_{0}$ is studied for a series of ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ samples $(0.0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.45)$. In analogy to the isotope effect on the superconducting transition temperature, the isotope effect on ${\ensuremath{\Delta}}_{0}$ increases with decreasing gap magnitude. A generic correlation between both isotope effects is established, which has been predicted from a polaronic model.

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