Solution of Dirac equation and greybody radiation around a regular Bardeen black hole surrounded by quintessence

The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin -1/2 in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterwards, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into one-dimensional Schrödinger like wave equations with effective potentials. The effect of the quintessence on the regular Bardeen black hole is analyzed via the physical behaviors of the effective potentials. We also exhibit the potential graphs by changing the quintessence parameters, magnetic monopole charge parameter, and the frequency of the particle in the physically acceptable regions. Finally, we study the greybody factors of bosons and fermions from the BBHSQ.