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We establish a phase diagram of a model in which scalar waves are scatteredby resonant point scatterers pinned at random positions in the freethree-dimensional (3D) space. A transition to Anderson localization takes placein a narrow frequency band near the resonance frequency provided that thenumber density of scatterers $\rho$ exceeds a critical value $\rho_c \simeq0.08 k_0^{3}$, where $k_0$ is the wave number in the free space. Thelocalization condition $\rho > \rho_c$ can be rewritten as $k_0 \ell_0 < 1$,where $\ell_0$ is the on-resonance mean free path in the independent-scatteringapproximation. At mobility edges, the decay of the average amplitude of amonochromatic plane wave is not purely exponential and the growth of its phaseis nonlinear with the propagation distance. This makes it impossible to definethe mean free path $\ell$ and the effective wave number $k$ in a usual way. Ifthe latter are defined as an effective decay length of the intensity and aneffective growth rate of the phase of the average wave field, the Ioffe-Regelparameter $(k\ell)_c$ at the mobility edges can be calculated and takes valuesfrom 0.3 to 1.2 depending on $\rho$. Thus, the Ioffe-Regel criterion oflocalization $k\ell < (k\ell)_c = \mathrm{const} \sim 1$ is valid onlyqualitatively and cannot be used as a quantitative condition of Andersonlocalization in 3D.

Ioffe-Regel criterion of Anderson localization in the model of resonant point scatterers