Temperature dependence of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi/><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi/><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:math>in pure vanadium

The ratio of the surface-nucleation field to the bulk superconducting critical field, $\frac{{H}_{c3}}{{H}_{c2}}$, has been measured over the reduced temperature range $0.2&lt;t&lt;0.92$ ($t=\frac{T}{{T}_{c}}$) in high-purity vanadium. It is found that the asymptotic value of the ratio at the low-temperature end of the range is 1.77 and as $t\ensuremath{\rightarrow}1$, $\frac{{H}_{c3}}{{H}_{c2}}$ also approaches 1 rather steeply. The experimental results are explained by considering the surface interaction potential to be slightly depressed as compared to the bulk interaction potential as suggested by Hu. This picture requires a modified boundary condition from that used in de Gennes's original calculation of a constant $\frac{{H}_{c3}}{{H}_{c2}}$ ratio. We have determined that a reduction in the interaction potential of 0.9% is needed over a distance of $1.2{\ensuremath{\xi}}_{0}$ to explain the temperature dependence of $\frac{{H}_{c3}}{{H}_{c2}}$. A few possibilities as to the cause of this phenomenon are discussed.

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