Model calculations of doubly closed shell nuclei in CBF theory (I)

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

“…[14] uses single-particle wave functions generated by a Woods-Saxon potential and a scalar Jastrow correlation function obtained from a constrained Euler-Lagrange optimisation of the second order cluster expansion approximation to the energy functional. We note that the corresponding result from the lowest order FHNC calculation, in the formulation of Fantoni and Rosati, the so-called FHNC/0 method [18] in which the elementary diagrams are neglected completely, using the same single-particle wave functions and Jastrow correlation function, is 987 MeV. Secondly, the VMC result of 1103 ± 1 MeV from ref.…”

“…He estimates, using the FHNC/C approximation that the contribution from the neglected exchange diagrams is 14 MeV. We also note that by employing precisely the same nearly optimal WoodsSaxon single-particle wave functions, but with a Jastrow correlation function obtained from a constrained minimisation of the two-body cluster expansion approximation to the energy functional, a corresponding FHNC/0 calculation [18] gives a 16 O binding energy of 1152 MeV. This difference of nearly 100 MeV is presumably a measure of the uncertainty in the FHNC/0 results, in the light of the other results cited.…”

“…The difference in binding between our SI and SD calculations of over 20 MeV is clearly very appreciable. We note that the FHNC/0 and FHNC-1 results for 16 O have been done in both LS [18] and jj [5] coupling schemes. For the former case we cite results using Jastrow correlation functions both parametrised as a Gaussian form, f (r) = 1 + a exp(−r 2 /b 2 ), and from a constrained Euler-Lagrange minimisation of the second-order cluster energy.…”

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

“…In the calculations of Refs. [14,17,18], the radial part of the single particle wave function was independent on the isospin. This, joined to the fact that we studied doubly closed shell nuclei on ls coupling with the same number of protons and neutrons, allowed us to separate the spatial part from the spin and isospin dependent parts in ρ o 1 (x 1 , x ′ 1 ).…”

“…The idea was to use the Fermi Hypernetted Chain (FHNC) resummation technique, well tested in nuclear matter, to describe finite systems. We first tested the validity of our approach in model nuclei with degenerate proton and neutron states, and in ls coupling scheme [14,15]. Then, by using central interactions and scalar correlation functions, we applied the theory to describe nuclei with different single particle bases for protons and neutrons, with different number of protons and neutrons and with the more realistic jj coupling scheme [16].…”