Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron gas

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Abstract
The dependence of the calculated Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron metal on the order of the integrations over the occupied states, and over the Fourier components of the perturbation is discussed and clarified. The correct result is derived. The range function of a magnetized layer (e.g., a magnetic layer in a multilayer material) is also calculated and compared with the range functions of point sources in the one-dimensional and in the three-dimensional cases.