The dynamically correlated quark-diquark system $q+(qq)$ is describing the nucleon as relativistic bound state. This approach has a close analogy with nonrelativistic few-body physics. In particular, a similar ansatz, $\alpha +(2\alpha )$, was previously applied to the study of the $0_2^{+}$ three-$\alpha$ state of the ${}^{12}\mathrm{C}$ nucleus within the cluster reduction method (CRM) based on the configuration space Faddeev equation. Motivated by this analogy, we propose a nonrelativistic quark model for the nucleon based on the same method. The interaction between quarks is modeled by a Cornell-type potential, which has been extensively employed in the description of quark confinement and the spectroscopy of hadrons. We perform full CRM calculations and identify the leading term of the CRM expansion with the $q+(qq)$ configuration. Our results demonstrate that a quantitative description of the nucleon within the quark-diquark picture requires a suitable adjustment of the model parameters, effectively simulating the contribution of the second term in the CRM expansion. This correction is expected to improve the $q+(qq)$ approximation and to bring the corresponding results into good agreement with the full $qqq$ calculation.

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• Few-body systems
• Quark model
• Strong interaction