Application of linear response theory to electron-phonon coupling

A numerically tractable theory of electron-phonon coupling in the frame of the local density functional approach is developed describing the self-consistent screening of an ion field to first order in its displacement. The equations are transformed such that one has to screen an effective perturbation weaker than the original dipole field and non-singular in the whole space. In this way one essentially calculates corrections to the rigid muffin tin approximation. In addition the connection to force constants is pointed out. Applying the formulation to aluminium, the Eliashberg function and force constants are evaluated. The theory is shown to account for the discrepancy between measured mass enhancement values and results based on the RMTA.