Field-operator decomposition in the Lee model

The decomposition of the meson field operator into internal and external parts is shown to provide a new, relatively simple approximation scheme that gives approximate eigenvalues, eigenvectors, and scattering phase shifts in all sectors of the Lee model. The form of the internal meson mode functions involves an energy parameter $\epsilon$ that is determined in a physical way that is peculiar to systems in which the ground-state expectation value of the meson source current operator is required by the internal symmetry of the system to be zero.