METHOD FOR CALCULATING OPERATOR TRACES

A new method is presented for the calculation of operator traces in reasonably large (N≤3×104) model spaces. The method is based on the approximation of a multiparticle vector |s, which simultaneously satisfies the conditions s|Oi|s=TrOi for a given set of commuting operators {Oi}, including the Hamiltonian H. An algorithm is presented for finding such an approximation to |s, which we call |s̄. To illustrate the method we apply it to the calculation of TrHn and Tr(J→2Hn), n=0 to 8, in the model space of five nucleons in the sd shell (Ne21; T=12) using the Chung-Wildenthal matrix elements. The calculated results agree with exact diagonalization results to within a few percent. The method is economical in that it requires the storage of only the array |s̄ and the relatively small arrays for the operators {Oi}. It is also particularly appropriate for bit representation of both operators and vectors in terms of a Fock-space basis. An important characteristic of this method is the ease with which submanifolds of a particular symmetry and/or configuration may be projected out for study. This feature was used to calculate configuration traces for higher moments in the Ne21 five-nucleon problem as well as to project out the T=12 manifold. The results in this case demonstrate the inadequacy of low moment truncations in configuration level density calculations. NUCLEAR STRUCTURE Calculated level density of Ne21 using spectral distribution expansion; a new method for evaluating operator moments; results compared with values obtained from exact diagonalization. © 1979 The American Physical Society.