Abstract

A simple 1D relativistic model for a diatomic molecule with a double-point interaction potential is solved exactly in a constant electric field. The Weyl–Titchmarsh–Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeau’s generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasi-bound states, which move in the complex energy plane as the model parameters are varied. It is observed that for a monotonically increasing interatomic distance, the ground-state resonance can either go deeper into the negative continuum or can give rise to a sequence of avoided crossings, depending on the strength of the potential wells. For the sufficiently low electric field strength or small interatomic distance, the behavior of resonances is qualitatively similar to non-relativistic results.

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