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We find that, up to a logarithmic correction factor, $E\\propto -D^{-1}| \\sin \\theta | ^{-1}f(\\theta)$ where $f(\\theta)$ is a smooth bounded function of the angle $\\theta$ between the wires. We recover a conventional result of the form $E\\propto -D^{-4}|\\sin\\theta | ^{-1}g(\\theta)$ when we include an electronic energy gap in our calculation. 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