By following the Foldy-Wouthuysen (FW) transformation of the Dirac equation, we work out the exact analytic expressions up to the $1/M^4$ order for the general cases in the covariant density functional theory. These results are further compared with the corresponding ones derived from another novel non-relativistic expansion method, the similarity renormalization group (SRG). Based on that, the origin of the difference between the results obtained by the FW transformation and SRG method is explored.
Categories: nucl-th math-ph math.MP quant-ph