Acoustic plasmon exchange in multilayered systems. I. The effective interaction potential

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Abstract
Using a plasmon exchange model, analytic expressions for the effective interaction between charge carriers in a multilayered system containing one, two, three and four conducting layers per unit cell has been calculated. The interaction is mediated by one pseudo-optical plasmon band and L-1 proper narrow acoustic plasmon bands where L is the number of layers per cell. It is found that the pseudo-optical plasmon band has a proper optical (high energy) limit, equivalent to bulk plasmon modes, as well as an acoustic (low energy) limit. In part II (ibid. vol.4, p.1814, 1992) the authors show that this interaction can lead to superconductivity in the high-Tc superconductors.