The role of the Pauli principle in three-cluster systems composed of identical clusters

Abstract

Within the microscopic model based on the algebraic version of the resonating group method the role of the Pauli principle in the formation of continuum wave function of nuclear systems composed of three identical $s$-clusters has been investigated. Emphasis is placed upon the study of the exchange effects contained in the genuine three-cluster norm kernel. Three-fermion, three-boson, three-dineutron ($3d^{\prime }$) and $3\alpha$ systems are considered in detail. Simple analytical method of constructing the norm kernel for $3\alpha$ system is suggested. The Pauli-allowed basis functions for the $3\alpha$ and $3d^{\prime }$ systems are given in an explicit form and asymptotic behavior of these functions is established. Complete classification of the eigenfunctions and the eigenvalues of the ${}^{12}$C norm kernel by the ${}^8$Be$=\alpha +\alpha$ eigenvalues has been given for the first time. Spectrum of the ${}^{12}$C norm kernel is compared to that of the ${}^5$H system.

arXiv comment22 pages, 2 tables, submitted to Nuclear Physics A

References in corpus (5)

• Three-Cluster Equation Using Two-Cluster RGM Kernel
• Comparative variational studies of $0^{+}$ states in three-$\alpha$ models
• Peculiar properties of the cluster-cluster interaction induced by the Pauli exclusion principle
• Variational Calculations of the ${}^{12}C$ Nucleus Structure in a 3$\alpha$ Model Using a Deep Potential with Forbidden States
• How the Pauli principle governs the decay of three-cluster systems

Cited by in corpus (4)

• A Microscopic Cluster Description of 12C
• Influence of the Pauli principle on two-cluster potential energy
• How the antisymmetrization affects a cluster-cluster interaction: two-cluster systems
• On the Spectrum of the Many-Body Pauli Projector