Three-cluster dynamics within an ab initio framework

Abstract

We introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method (NCSM/RGM). Energy-independent non-local interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to an ${}^4$He+$n+n$ description of ${}^6$He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the NCSM. Differences between the two calculations provide a measure of core (${}^4$He) polarization effects.

16 pages, 9 figures

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• How many-body correlations and $\alpha$-clustering shape ${}^6$He
• ${}^4\mathrm{He}$+$n$+$n$ continuum within an ab initio framework
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• Halo nuclei 6He and 8He with the Coulomb-Sturmian basis
• Three-cluster dynamics within the ab initio no-core shell model with continuum: How many-body correlations and $\alpha$-clustering shape ${}^6$He
• Adiabatic projection method for scattering and reactions on the lattice
• Microscopic description of translationally-invariant core+N+N overlap functions
• Natural orbitals for the ab initio no-core configuration interaction approach
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• Adiabatic projection method with Euclidean time subspace projection
• Study of light $\varphi$-mesic nuclei with HAL QCD $\varphi N$ interactions
• Harmonic-oscillator excitations of precise few-body wave functions
• Ab initio NCSM/RGM for three-body cluster systems and application to ${}^4$He+n+n
• How the antisymmetrization affects a cluster-cluster interaction: two-cluster systems
• Advances in the ab initio description of nuclear three-cluster systems