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Casimir force between $δ-δ^{\prime}$ mirrors transparent at high frequencies

We investigate, in the context of a real massless scalar field in $1+1$ dimensions, models of partially reflecting mirrors simulated by Dirac $δ-δ^{\prime}$ point interactions. In the literature, these models do not exhibit full transparency at high frequencies. In order to provide a more realistic feature for these models, we propose a modified $δ-δ^{\prime}$ point interaction that enables full transparency in the limit of high frequencies. Taking this modified $δ-δ^{\prime}$ model into account, we investigate the Casimir force, comparing our results with those found in the literature.