Critique of the locally linearized approximation to the nuclear single particle density matrix

Approximations to the density matrix of a Fermi gas in an external potential by Baltin and by Balazs and Zipfel are shown to be closely related. Predictions for the kinetic energy density using these approximations are compared to exact solutions for two harmonic oscillator problems and for Woods-Saxon wave functions in the lead nucleus. In all three cases, the approximations yield substantial systematic discrepancies, indicating that they are inadequate for quantitative description of the nuclear density matrix