The influence of state dependent short range correlations on the depletion of the nuclear Fermi sea

The influence of state dependent short range correlations on the occupation numbers of the single particle shell model orbits of the doubly closed shell nuclei 16O and 40Ca is examined. The study shows that the effect of the state dependence of the short range correlations is rather small. The total depletion of the nuclear Fermi sea changes slightly compared with the one calculated by considering state independent short range correlations.

Description of the generalized momentum distribution in finite nuclei within t h e independent-particle shell model

A method for calculating the generalized momentum distribution in finite nuclear systems is presented and discussed within the context of the independent particle shell model. Application to the light closed-shell nuclei 16O and 40Ca is included.

Systematic study of the effect of short range correlations on the form factors and densities of s-p-d shell nuclei

Analytical expressions of the one- and two-body terms in the cluster expansion of the charge form factors and densities of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter 6 and the parameter β which originates from the Jastrow correlation function. These expressions are used for the systematic study of the effect of short range correlations on the form factors and densities and of the mass dependence of the parameters ò and β. These parameters have been determined by fit to the experimental charge form factors. The inclusion of the correlations reproduces the experimental charge form factors at the high momentum transfers (q > 2 fm^-1). It is found that while the parameter β is almost constant for the closed shell nuclei, 4He, 16O and 40Ca, its values are larger (less correlated systems) for the open shell nuclei, indicating a shell effect in the closed shell nuclei.

DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.