Evaluation of cluster expansions and correlated one-body properties of nuclei

Abstract

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f . The harmonic oscillator parameter b and the correlation parameter β have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position-space (Sr) and momentum-space (S k ) according to the three methods are also calculated. It is found that the larger the entropy sum S = Sr + S k (the information content of the system) the smaller the values of χ 2 . This indicates that S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called "healing" or "wound" integrals is derived with the function f considered, for any state of the relative two-nucleon motion and their values in certain cases are computed and compared.

CorrelatedN-boson systems for arbitrary scattering length

“…The second curve is the increasing λ δ (ρ) for an attractive potential (a s < 0), see eq. (18). Thus λ δ (ρ a ) = λ(ρ a ) gives…”

“…The mean-field method neglects all correlations and thus breaks down at larger densities where correlations become important. Going beyond the mean-field is often very complicated as exemplified by Jastrow theory [16][17][18], which leads to highdimensional equations. A later formulation is contained in the Faddeev-Yakubovskiȋ equations [19,20] where the wave function is expressed in terms of components describing the asymptotic behaviour of all kinds of clusters.…”