### Particle acceleration by Black Holes in a model of $f(R)$ gravity

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Particle collisions are considered within the context of $f(R)$ gravity described by $f(R)=R+2\alpha \sqrt{R}$, where R stands for the Ricci scalar and $\alpha $ is a non-zero constant. The center of mass (CM) energy of colliding particles near the horizon grows unbounded. Addition of a cosmological constant does not change the outcome. When the collision occurs near a non- black hole, i.e. a naked singularity (for $\alpha >0)$, the particles are absorbed with zero total CM energy. Collisions of a massless outgoing Hawking photon with an infalling particle and collision of two photons following null-geodesics are also taken into account.