Method for calculating operator traces

A new method is presented for the calculation of operator traces in reasonably large (N = or = 3 x 104) model spaces. The method is based on the approximation of a multiparticle vector vertical-bars>, which simultaneously satisfies the conditions < TrO/sub i/ for a given set of commuting operators ]O/sub i/], including the Hamiltonian H. An algorithm is presented for finding such an approximation to vertical-bars>, which we call vertical-bars-bar>. To illustrate the method we apply it to the calculation of TrH/sup n/ and Tr(J2 H/sup n/), n = 0 to 8, in the model space of five nucleons in the sd shell (21Ne; T = 1/2) 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 vertical-bars-bar> and the relatively small arrays for the operators ]O/sub i/]. 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 21Ne five-nucleon problem as well as to project out the T = 1/2 manifold