Full-quantum calculations of the pressure broadening \(D_{1}\) and \( D_{2}\) lines of Mg\(^{+}\) magnesium ion in a gas of ground-state He helium atoms

In this theoretical investigation, we have performed comprehensive quantum calculations to explore the pressure broadening effects on the \(D_{1}\left( 3\,s\text { }^{2}S_{1/2}-3p\text { }^{2}P_{1/2}\right) \) and \(D_{2}\left( 3\,s \text { }^{2}S_{1/2}-3p\text { }^{2}P_{3/2}\right) \) lines of the Mg\( ^{+}\) magnesium ion when surrounded by ground-state He helium atoms. Our objective is to delineate the profiles of these pressure-broadened resonance lines and scrutinize their behavior in response to binary collisions between Mg\(^{+}\) ions and He atoms. To accomplish this goal, we developed precise potential energy curves for the ground \(X\ ^{2}\Sigma _{1/2}^{+}\) and the excited \(A^{2}\Pi _{1/2},A^{2}\Pi _{3/2}\) and B \(^{2}\Sigma _{1/2}^{+}\), along with the associated transition dipole moments, using data derived from advanced ab initio methodologies such as SA-CASSCF, MRCI, and SO coupling, with Davidson and BSSE corrections. Our investigation encompasses a temperature range from 4000 to \(12000 \,\textrm{K}\) and wavelengths spanning from 200 to \(450\,\textrm{nm}\). The theoretical profiles primarily exhibit dominant free-free transitions. Notably, around the \(235\,\textrm{nm}\) wavelength region, a satellite peak appears in the blue wing, attributed to the B \(^{2}\Sigma _{1/2}^{+}\longleftarrow X\ ^{2}\Sigma _{1/2}^{+}\) transitions. We have confirmed agreement between our theoretical findings and prior research.