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A relativistic coupled-cluster (RCC) theory is implemented to study electronimpact excitations of atomic species. As a test case, the electron impactexcitations of the $3s ~ ^2S_{1/2} - 3p ~ ^2P_{1/2;3/2}$ resonance transitionsare investigated in the singly charged magnesium (Mg$^+$) ion using thistheory. Accuracies of wave functions of Mg$^+$ are justified by evaluating itsattachment energies of the relevant states and compared with the experimentalvalues. The continuum wave function of the projectile electron are obtained bysolving Dirac equations assuming distortion potential as static potential ofthe ground state of Mg$^+$. Comparison of the calculated electron impactexcitation differential and total cross-sections with the availablemeasurements are found to be in very good agreements at various incidentelectron energies. Further, calculations are carried out in the plasmaenvironment in the Debye H\"uckel model framework, which could be useful in theastrophysics. Influence of plasma strength on the cross-sections as well aslinear polarization of the photon emission in the $3p ~ ^2P_{3/2} - 3s ~^2S_{1/2}$ transition is investigated for different incident electron energies.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Application of Relativistic Coupled-cluster Theory to Electron Impact Excitations of Mg$^+$ in the Plasma Environment