Abstract: The effectiveness of the approach for systematical reconstruction of higher order reduced density matrices with lower order ones, which was developed by Chen (Science in China B, 2006, 49: 402), was compared theoretically with that of Mazziotti's method through Harris model. In the case of omitting the cumulant terms 3△M, 4△M in the latter and the normal product terms 3△, 4△in the former, it was found that the errors from both approaches were comparable. As a better approximation, if only fourth-order terms 4△M and 4△ in both methods are neglected whereas the third-order terms 3△M and 3△are computed from their corresponding fourth-order terms 4△M and 4△ respectively through contractions, the results calculated with Chen's approach not only have the correct signs but also are very close to the exact normal products 3△ whereas some of the results calculated with Mazziotti's method do not even have the correct signs with respect to the exact cumulants 3△M.

Key words: Reduced density matrix, Contracted Schrodinger equation, Normal product, Cumulant