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In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general n-dimensional deformation of the two-center problem by adding arbitrary functions supporting second-order commuting conserved quantities. The system is superintegrable for n>4 and, for certain choices of the arbitrary functions, reduces to known models previously discovered. Then, based on this extended system, we introduce an additional integrable generalization involving Calogero interactions for n=3. In all examples, including the two-center problem, we explicitly present the complete list of Liouville integrals in terms of second-order integrals of motion. Published by the American Physical Society 2024
Correa et al. (Mon,) studied this question.
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