New Formulation of Nuclear Recoil and Mass Polarization in Collisional Line Broadening of Magnetized and Non-Magnetized Plasmas

Spectral line shapes are used to diagnose parameters of white dwarfs and neutron stars in particular. In magnetized plasmas, the motion of the radiating atom in the plasma needs to be considered in the collision process as the electronic structure of the atom depends on its center-of-mass translational momentum. More broadly, collision models do not explicitly or fully account for the motion of the nucleus, accounting for deflection through conservation of momentum. Traditionally, the correlation between electronic and nuclear motion has been captured through mass-polarization terms involving momenta scalar products between different electrons. We reformulate the collision problem accounting for the motion of the nucleus, taking advantage of unitary transformations. In this new formulation, Coulomb interactions between the atom and projectile/plasma particle become displaced Coulomb interactions, and exchange interactions include corrections of order 1/MA. We demonstrate the resulting impact on the elastic scattering T-matrices of the 1s state of hydrogen, where the lowest-energy electrons increase the real part by 20–30% while leaving the imaginary part practically unaltered. Lastly, we present a formulation so that the atomic motion can be explicitly included in the collision problem for magnetic-field applications.