Rotating Bardeen black hole surrounded by perfect fluid dark matter as a particle accelerator

We study the event horizon of a rotating Bardeen black hole surrounded by perfect fluid dark matter and the black hole as a particle accelerator. The black hole is represented by four parameters: mass $M$, rotation parameter $a$, dark matter parameter $\alpha$ and magnetic charge $g$. It is interesting that when we determine the values of magnetic charge $g$ and dark matter parameters $\alpha$ we can get a critical rotation parameter $a_E$ and then we get a contour plane with $\Delta$= 0 taking three parameters as coordinates. We also derive the effective potential of the particle and the centre-of-mass (CM) energy of the two particles outside the black hole by using the motion equation of the particle in the equatorial plane of the black hole. We find that the CM energy depends not only on the rotation parameter $a$, but also on the parameters $g$ and $\alpha$. We discuss the CM energy for two particles colliding at the black hole horizon in the extreme and non-extreme cases, respectively. It is found that the CM energy can be arbitrarily high when the angular momentum of one of the two particles is the critical angular momentum under the background of extreme black holes and there is no such result for non-extreme black holes, because the particles do not reach the black hole horizon when the angular momentum of the particles is critical angular momentum. Therefore, we prove that the rotating Bardeen black hole surrounded by perfect fluid dark matter can be used as a particle accelerator.