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A rigorous gauge-invariant solution of the linearized Gor kov equations is presented, yielding the complete temperature and electron-mean-free-path dependences of the upper critical magnetic Geld H, 2 of a bulk type-IE superconductor. Comparison is made with previously known results in special cases, and it is pointed out that localized approximations such as the "dirty, " or the Ginzburg-Landau, limits represent the leading term in an asymptotic rather than convergent, expansion.

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