Reconstruction of the one-particle density matrix from expectation values in position and momentum space

For the beryllium atom, it is demonstrated that coherent form factors F(k) can be insufficient for inferring the one-particle reduced density matrix (ODM). The description in terms of reciprocal form factors B(s) as the complementary momentum-space property is compared with the results for a least-squares fit to F(k) data. A virtually complete description of the true ODM may be obtained by using a combined data set, as can be shown by representing the ODM in spherically averaged form.