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Register a new userThree-cluster dynamics within the ab initio no-core shell model with continuum: How many-body correlations and $alpha$-clustering shape $^6$He
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Sofia Quaglioni
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We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of the Hamiltonian within the harmonic-oscillator expansion of the no-core shell model are coupled with continuous microscopic three-cluster states to correctly describe the nuclear wave function both in the interior and asymptotic regions. We discuss the formalism in detail and give algebraic expressions for the case of core+$n$+$n$ systems. Using similarity-renormalization-group evolved nucleon-nucleon interactions, we analyze the role of $^4$He+$n$+$n$ clustering and many-body correlations in the ground and low-lying continuum states of the Borromean $^6$He nucleus, and study the dependence of the energy spectrum on the resolution scale of the interaction. We show that $^6$He small binding energy and extended radii compatible with experiment can be obtained simultaneously, without recurring to extrapolations. We also find that a significant portion of the ground-state energy and the narrow width of the first $2^+$ resonance stem from many-body correlations that can be interpreted as core-excitation effects.
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The Borromean $^6$He nucleus is an exotic system characterized by two `halo neutrons orbiting around a compact $^4$He (or $alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
Constructing microscopic effective interactions (`optical potentials) for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show the expectation values of the spin-orbit contribution of the struck nucleon with respect to the rest of the nucleus for $^{4}$He, $^{6}$He, $^{12}$C, and $^{16}$O and compare them with the scalar one-body density matrix.
Nuclear structure and reaction theory is undergoing a major renaissance with advances in many-body methods, strong interactions with greatly improved links to Quantum Chromodynamics (QCD), the advent of high performance computing, and improved computational algorithms. Predictive power, with well-quantified uncertainty, is emerging from non-perturbative approaches along with the potential for guiding experiments to new discoveries. We present an overview of some of our recent developments and discuss challenges that lie ahead. Our foci include: (1) strong interactions derived from chiral effective field theory; (2) advances in solving the large sparse matrix eigenvalue problem on leadership-class supercomputers; (3) selected observables in light nuclei with the JISP16 interaction; (4) effective electroweak operators consistent with the Hamiltonian; and, (5) discussion of A=48 system as an opportunity for the no-core approach with the reintroduction of the core.
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 Schrodinger 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.
[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.
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