  The memory function formalism is an important tool to evaluate the frequency
dependent electronic conductivity. It is previously used within some
approximations in the case of electrons interacting with various other degrees
of freedom in metals with great success. However, one needs to go beyond those
approximations as the interaction strengths become stronger. In this work, we
propose a systematic expansion of the memory function involving its various
moments. We calculate the higher order contribution to the generalized Drude
scattering rate in case of electron-impurity interactions. Further we compare
our results with the results from previously studied lowest order calculations.
We find larger contributions from the higher moments in the low frequency
regime and also in the case of larger interaction strength.

Strongly Correlated Electrons;Statistical Mechanics