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Momentum distribution of N$^*$ in nuclei

Due to its dominance in the low energy eta-nucleon interaction, the S11 N$^*$(1535) resonance enters as an important ingredient in the analyses of experiments aimed at finding evidence for the existence of eta-mesic nuclei. The static properties of the resonance get modified inside the nucleus and its momentum distribution is used in deciding these properties as well as the kinematics in the analyses. Here we show that given the possibility for the existence of an N$^*$-$^3$He quasibound state, the relative momentum distribution of an N$^*$ and $^3$He inside such a $^4$He is narrower than that of neutron-$^3$He in $^4$He. Results for the N$^*$-$^{24}$Mg system are also presented. The present exploratory work could be useful in motivating searches of exotic N$^*$-nucleus quasibound states as well as in performing analyses of eta meson production data.