Model calculations of doubly closed shell nuclei in CBF theory III. jj coupling and isospin dependence

Abstract

two-body Euler equations provide correlation functions variationally more effective than those obtained with the same technique in infinite nuclear matter.

Translationally invariant treatment of pair correlations in nuclei: I. Spin and isospin dependent correlations

“…Bearing in mind that our results are fully variational it is clear that our TICI2(SD) calculation is better than any of the other results shown for 12 C with the B1 potential. We note also that the results based on a spherical assumption give appreciably less binding for 12 C. This is particularly so for the FHNC results [5] based on a jj coupling scheme. We show results for both the lowest-order FHNC/0 approximation of the Fantoni-Rosati scheme, in which all elementary diagrams are neglected, and for their FHNC-1 approximation in which the first-order elementary exchange diagram has been included.…”

“…[5] and references cited therein for details). One drawback of this procedure is that certain cancellations between elementary exchange diagrams are thereby ignored.…”

“…The hyperspherical harmonic method is also limited in the number of nucleons it can treat, even though the Pisa group has started an ambitious project for p-shell nuclei. Arias de Saavedra et al [5] have recently investigated the application of the Fermi hypernetted chain (FHNC) method to heavier nuclei, with some apparent success. Another promising approach is one based on a stochastic variational principle [6], but this method is also limited to relatively light nuclei.…”

Ground states of medium-heavy doubly-closed-shell nuclei in correlated-basis function theory

“…The study of Ref. [16] has shown that the main contribution to the one-body density matrix is given by ρ t 0 , which is the only term surviving in spin saturated systems having degenerate spin-orbit partners. The similarity of this term to the one appearing in the ls coupling scheme, allows us to use some simplifications in the calculations of the correlated distributions (9,10) following the procedure adopted in [25].…”

“…This part of the calculation follows step by step that presented in [16]. The two-body densities are written in terms of the scalar correlation f 1 (r), of the nodal, or chain, diagrams N xy (r 1 , r 2 ), of the non nodal (composite) diagrams X xy (r 1 , r 2 ) and of the elementary, or bridge, diagrams E xy (r 1 , r 2 ).…”