The $phi$-meson properties in cold nuclear matter are investigated by implementing resonant $phi N$ interactions as described in effective approaches including the unitarization of scattering amplitudes. Several $N^*$-like states are dynamically generated in these models around $2$ GeV, in the vicinity of the $phi N$ threshold. We find that both these states and the non-resonant part of the amplitude contribute sizably to the $phi$ collisional self-energy at finite nuclear density. These contributions are of a similar strength as the widely studied medium effects from the $bar K K$ cloud. Depending on model details (position of the resonances and strength of the coupling to $phi N$) we report a $phi$ broadening up to about $40$-$50$ MeV, to be added to the $phitobar K K$ in-medium decay width, and an attractive optical potential at threshold up to about $35$ MeV at normal matter density. The $phi$ spectral function develops a double peak structure as a consequence of the mixing of resonance-hole modes with the $phi$ quasi-particle peak. The former results point in the direction of making up for missing absorption as reported in $phi$ nuclear production experiments.
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