A note on the validity of the density matrix expansion

The density matrix expansion of Negele and Vautherin is formulated in one dimension, and compared against an analytically soluble model. In three dimensions, numerical tests are carried out using both the Brink and Boeker force and the density-dependent force G-O. These range from perturbative to Hartree-Fock calculations. It is found that the DME method overbinds spherical nuclei by 1 MeV per particle compared to exact Hartree-Fock calculations. If the direct terms are calculated exactly and DME applied only to the exchange terms, the results are much better, with slight underbinding (about 200 keV per particle) occurring for most nuclei and the radii agree to within 1%. (Auth.)