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 Nsub(e)) based on the use of sets of random multiparticle vectors (dimension Nsub(d) < Nsub(e)) is described and applied to the calculation of hamiltonian moments in two nuclear cases: 21Ne(n = 1 to 10) and 28Si(n = 1 to 3). The random vectors, which we call RRV's (random representative vectors), are constructed by statistically sampling a fraction f = Nsub(d)/Nsub(e) of the full space. Useful results are obtained with f <= 10-6 (case of 28Si, Nsub(e) = 5.5 x 107). For Nsub(d) = Nsub(e) (case of 21Ne, Nsub(e) = 1935) our results for the dispersions of the sets of the moments closely approximate the predictions of Porter. (orig.)