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 $A\le 30$ 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 $\alpha$-like clusters can be formed from valence nucleons filling single-particle levels originating from $n=1$ spherical mean-field states.

arXiv comment5 pages, 4 figures

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Cited by in corpus (7)

• Cluster structures in ${}^{12}$C from global energy density functionals
• Alpha-particle condensation: a nuclear quantum phase transition
• Microscopic description of the self-conjugate ${}^{108}$Xe and ${}^{104}$Te $\alpha$-decay chain
• Low-energy cluster vibrations in N = Z nuclei
• Low-energy monopole strength in spherical and deformed nuclei : cluster and soft modes
• Localisation and alpha radioactivity
• Model for independent particle motion