We study the quantum field theory of a charged ϕ^4 field in lattice regularization at finite density and low temperature in 2 and 4 dimensions with the goal of analyzing the connection of condensation phenomena to scattering data in a non-perturbative way. The sign problem of the theory at non-zero chemical potential μ is overcome by using a worldline representation for the Monte Carlo simulation. At low temperature we study the particle number as a function of μ and observe the steps for 1-,

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... and 3-particle condensation. We determine the corresponding critical values μ_n^crit, n = 1,2,3 and analyze their dependence on the spatial extent L of the lattice. Linear combinations of the μ_n^crit give the interaction energies in the 2- and 3-particle sectors and their dependence on L is related to scattering data by Lüscher's formula and its generalizations to three particles. For 2-d we determine the scattering phase shift and for 4-d the scattering length. We cross-check our results with a determination of the mass and the 2- and 3-particle energies from conventional 2-, 4-, and 6-point correlators at zero chemical potential. The letter demonstrates that the physics of condensation at finite density and low temperature is closely related to scattering data of a quantum field theory.