Single-particle spatial dispersion and clusters in nuclei

Abstract

The spatial dispersion of the single-nucleon wave functions is analyzed using the self-consistent mean-field framework based on nuclear energy density functionals and with the harmonic-oscillator approximation for the nuclear potential. It is shown that the dispersion depends on the radial quantum number $n$ but displays only a very weak dependence on the orbital angular momentum. An analytic expression is derived for the localization parameter that explicitly takes into account the radial quantum number of occupied single-nucleon states. The conditions for single-nucleon localization and formation of cluster structures are fulfilled in relatively light nuclei with $A\ensuremath{\le}30$ and $n=1$ states occupied. Heavier nuclei exhibit the quantum liquid phase of nucleonic matter because occupied levels that originate from $n>1$ spherical states are largely delocalized. Nevertheless, individual $\ensuremath{\alpha}$-like clusters can be formed from valence nucleons filling single-particle levels originating from $n=1$ spherical mean-field states.