Spatial particle correlations in light nuclei. I two-particle systems Original Research Article

Expressions for spatial two-particle correlations in an image-coupled basis of the harmonic oscillator are used to display the probability distribution of two identical nucleons as a function of their relative distance and their distance from the center of the nucleus. It is shown that a two-nucleon state in the p shell with total orbital angular momentum image and total spin image contains a di-neutron and a cigar-like component with equal probability. This result can also be proven analytically with the use of angular correlation functions. Scattering of the nucleons from the p shell to other shells leads to the enhancement of the di-neutron configuration. A semi-quantitative application to 6He is presented which shows that the probability of the di-neutron configuration in the ground state is of the order of 60%. The long-term goal of this work is to obtain a geometric insight into the properties of nuclei with several nucleons in a valence shell.