A Monte Carlo method for calculating strength functions in many-fermion systems

The calculation of moments is an essential first step in the calculation of strength functions for operators. A method for calculating approximate moments of a variety of operators in large vector spaces (dimension N_e) based on the use of sets of random multiparticle vectors (dimension N_d<N_e) is described and applied to the calculation of hamiltonian moments 〈Hⁿ〉 in two nuclear cases: ${}^{21}\text{Ne}\text{(n=1}\text{to}\text{10)}\text{and}{}^{28}\text{Si}\text{(nm=1}\text{to}\text{3)}$. The random vectors, which we call RRV's (random representative vectors), are constructed by statistically sampling a fraction f=N_d/N_e of the full space. Useful results are obtained with f?10^?6(case of ²⁸Si, N_e = 5.5 × 10⁷). For N_d=N_e case of ²¹Ne, N_e=1935) our results for the dispersions of the sets of the moments closely approximate the predictions of Porter.