Absence of an Isotope Effect in the Pseudogap in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>as Determined by High-Resolution<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Y</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>89</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>NMR

Susceptibility and high-resolution ${}^{89}\mathrm{Y}$ NMR measurements on ${}^{16}\mathrm{O}$- and ${}^{18}\mathrm{O}$-exchanged ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ superconductors show an isotope effect in ${T}_{c}$ but not in the normal-state pseudogap. This places constraints on the microscopic origins of the pseudogap and is consistent with the pseudogap correlations being independent of the superconducting pairing correlations. We distinguish between the isotope effect ${\ensuremath{\alpha}}_{{T}_{c}}$ in ${T}_{c}$ and that, ${\ensuremath{\alpha}}_{\ensuremath{\Delta}}$, in the superconducting gap parameter ${\ensuremath{\Delta}}_{0}$. By taking account of the pseudogap, we show that ${\ensuremath{\alpha}}_{\ensuremath{\Delta}}$ remains small $(\ensuremath{\approx}0.06)$ and roughly constant, independent of hole concentration in spite of the large value of ${\ensuremath{\alpha}}_{{T}_{c}}$ in the underdoped region.

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