Charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy

We study the motion of charged and spinning particles and photons in the $4D$ charged Einstein-Gauss-Bonnet (EGB) black hole vicinity. We determine the radius of the innermost stable circular orbit (ISCO) for test particles. We show that the combined effect of the Gauss-Bonnet (GB) coupling parameter and black hole charge decreases the ISCO and the radius of the photon sphere. Further, we study the gravitational deflection angle and show that the impact of GB term and black hole charge on it is quite noticeable. We also consider the effect of plasma and find the analytical form of the deflection angle in the case of a uniform and non-uniform plasma. Interestingly we find that the deflection angle becomes larger when uniform plasma is considered in comparison to the case of non-uniform plasma. We also study the center of mass energy ($E_{C.M.}$) obtained by collision process for non-spinning particles and show that the impact of GB parameter and black hole charge leads to high energy collision. In addition, we also study the $E_{C.M.}$ for the case of spinning particles and show that if the two spinning particles collide near the horizon of $4D$ charged EGB BH, the $E_{C.M.}$ becomes infinitely high which is in disparity with the non-spinning particles counterpart where $E_{C.M.}$ never grows infinitely. To achieve this, an important role is played by the spinning particle known as the \textit{near-critical} particle (i.e. a particle with fine-tuned parameters). In order to achieve the unbounded $E_{C.M}$ from the collision of two spinning particles, the energy per unit mass must be less than unity for a \textit{near-critical} particle, which means such a particle starts from some intermediate position $r>r_{h}$ and not from infinity.