By subtracting the pure-Coulomb correlation function from the Coulomb-plus-short-range one, the authors derive a divergence-free integral relation to short-range phase shifts and verify it in an exactly solvable model.
An effective field theory approach to two trapped particles
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We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.
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Toward extracting scattering phase shift from integrated correlation functions IV: Coulomb corrections
By subtracting the pure-Coulomb correlation function from the Coulomb-plus-short-range one, the authors derive a divergence-free integral relation to short-range phase shifts and verify it in an exactly solvable model.