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We study the ground-state correlations between two atoms in a two-dimensionalisotropic harmonic trap. We consider a finite-range soft-core interaction thatcan be applied to simulate various atomic systems. We provide detailed resultson the dependence of the correlations on the parameters of the system. Ourinvestigations show that in the hardcore limit, the wave function can beapproximated as the product of the radial and angular components regardless ofthe interaction range. This implies that the radial and angular correlationsare independent of one another. However, correlations within the radial andangular components persist and are heavily influenced by the interaction range.The radial correlations are generally weaker than the angular correlations.When soft-core interactions are considered, the correlations exhibit morecomplex behavior.

Radial and Angular Correlations in a Confined System of Two Atoms in a Two-Dimensional Geometry