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We consider the quasi-classical limit of Nelson-type regularized polaronmodels describing a particle interacting with a quantized bosonic field. Webreak translation-invariance by adding an attractive external potentialdecaying at infinity, acting on the particle. In the strong coupling limitwhere the field behaves classically we prove that the model's energyquasi-minimizers strongly converge to ground states of the limiting Pekar-likenon-linear model. This holds for arbitrarily small external attractivepotentials, hence this binding is fully due to the interaction with the bosonicfield. We use a new approach to the construction of quasi-classical measures torevisit energy convergence, and a localization method in aconcentration-compactness type argument to obtain convergence of states.

Convergence of states for polaron models in the classical limit