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The meson-baryon molecular components for the $N^{\ast}$ and $\Delta ^{\ast}$resonances are investigated in terms of the compositeness, which is defined asthe norm of the two-body wave function from the meson-baryon scatteringamplitudes. The scattering amplitudes are constructed in a $\pi N$-$\etaN$-$\sigma N$-$\rho N$-$\pi \Delta$ coupled-channels problem in a mesonexchange model together with several bare $N^{\ast}$ and $\Delta ^{\ast}$states, and parameters are fitted so as to reproduce the on-shell $\pi N$partial wave amplitudes up to the center-of-mass energy 1.9 GeV with theorbital angular momentum $L \le 2$. As a result, the Roper resonance $N (1440)$is found to be dominated by the $\pi N$ and $\sigma N$ molecular componentswhile the bare-state contribution is small. The squared wave functions incoordinate space imply that both in the $\pi N$ and $\sigma N$ channels theseparation between the meson and baryon is about more than 1 fm for the $N(1440)$ resonance. On the other hand, dominant meson-baryon molecularcomponents are not observed in any other $N^{\ast}$ and $\Delta ^{\ast}$resonances in the present model, although they have some fractions of themeson-baryon clouds.

Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N ^{\ast}$ and $\Delta ^{\ast}$ resonances