| Summary: | The experimental critical temperature of the systems of superconducting (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>b</mi></mrow></semantics></math></inline-formula>) and normal (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>g</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>u</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>l</mi></mrow></semantics></math></inline-formula>) nanoparticles, with a random distribution and sizes less than their respective coherence lengths, is governed by the proximity effect, as shown by the experimental data. At first glance, the behavior of the variation in the critical temperature in function of the ratio of volume fractions of the superconducting and the normal metal components seems to suggest a weak coupling behavior for the superconductor. In reality, upon a more careful analysis, using Eliashberg’s theory for the proximity effect, the system instead shows a strong coupling nature. The most interesting thing is that the theory has no free parameters and perfectly explains the behavior of the experimental data just with the assumption in the case of the nanoparticles <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>g</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mi>u</mi></mrow></semantics></math></inline-formula>, that the value of the density of states at the Fermi level of silver and copper is equal to the value of lead.
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