Ab Initio No-core Shell Model Research Articles

Continuum and three-nucleon force effects onBe9energy levels

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of p- and lower-sd-shell nuclei. As first application we concentrate on energy levels of the 9Be system for which all excited states lie above the n-8Be threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the 1/2+ resonance energy, which is of astrophysical interest, in good agreement with experiment.

Dominant Modes in Light Nuclei - Ab Initio View of Emergent Symmetries

An innovative symmetry-guided concept is discussed with a focus on emergent symmetry patterns in complex nuclei. In particular, the ab initio symmetry-adapted no-core shell model (SA-NCSM), which capitalizes on exact as well as partial symmetries that underpin the structure of nuclei, provides remarkable insight into how simple symmetry patterns emerge in the many-body nuclear dynamics from first principles. This ab initio view is complemented by a fully microscopic no-core symplectic shell-model framework (NCSpM), which, in turn, informs key features of the primary physics responsible for the emergent phenomena of large deformation and alpha-cluster substructures in studies of the challenging Hoyle state in Carbon-12 and enhanced collectivity in intermediate-mass nuclei. Furthermore, by recognizing that deformed configurations often dominate the low-energy regime, the SA-NCSM provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small subspace of the symmetry-reorganized complete model space, which opens new domains of nuclei for ab initio investigations, namely, the intermediate-mass region, including isotopes of Ne, Mg, and Si.

C12properties with evolved chiral three-nucleon interactions

We investigate selected static and transition properties of $^{12}\mathrm{C}$ using ab initio no-core shell model (NCSM) methods with chiral two- and three-nucleon interactions. We adopt the similarity renormalization group (SRG) to assist convergence including up to three-nucleon ($3N$) contributions. We examine the dependencies of the ${}^{12}$C observables on the SRG evolution scale and on the model-space parameters. We obtain nearly converged low-lying excitation spectra. We compare results of the full NCSM with the importance truncated NCSM in large model spaces for benchmarking purposes. We highlight the effects of the chiral $3N$ interaction on several spectroscopic observables. The agreement of some observables with experiment is improved significantly by the inclusion of $3N$ interactions, e.g., the $B(M1)$ from the first ${J}^{\ensuremath{\pi}}T={1}^{+}1$ state to the ground state. However, in some cases the agreement deteriorates, e.g., for the excitation energy of the first ${1}^{+}0$ state, leaving room for improved next-generation chiral Hamiltonians.

Progress on Light-Ion Fusion Reactions with Three-Nucleon Forces

The description of structural and dynamical properties of nuclei starting from the fundamental interaction between nucleons has been a long-standing goal in nuclear physics. The ab initio No-Core Shell Model combined with the Resonating-Group Method (NCSM/RGM) is capable of addressing both structural and reaction properties of light-nuclei. While promising results have already been achieved starting from a two-body Hamiltonian, a truly realistic prediction of nuclear observables requires the treatment of the three-nucleon interaction. Using similarity-renormalization-group evolved two- and three-nucleon interactions, we will present recent applications to n-4He scattering process when accounting for the chiral two- plus three-nucleon interaction versus the chiral two-nucleon interaction. We compare our results to phase shifts obtained from R-matrix analysis of data up to 16 MeV neutron energy, below the d-3H threshold.

Microscopic description of translationally invariant core+N+Noverlap functions

We derive expressions for core + N + N overlap integrals starting from microscopic wave functions obtained in the ab initio no-core shell model. These overlap integrals correspond to three-body channel form factors and can be used to investigate the clustering of many-body systems into a core plus two nucleons. We consider the case when the composite system and the core are described in Slater determinant, harmonic oscillator bases, and we show how to remove spurious center of mass components exactly in order to derive translationally-invariant overlap integrals. We study in particular the Borromean 6He nucleus using realistic chiral nuclear interactions, and we demonstrate that the observed clusterization in this system is a Pauli focusing effect. The inclusion of three-body forces has a small effect on this structure. In addition, we discuss the issue of absolute normalization for spectroscopic factors, which we show is larger than one. As part of this study we also perform extrapolations of ground-state observables and investigate the dependence of these results on the resolution scale of the interaction.

Collective Modes in Light Nuclei from First Principles

Results for ab initio no-core shell model calculations in a symmetry-adapted SU(3)-based coupling scheme demonstrate that collective modes in light nuclei emerge from first principles. The low-lying states of 6Li, 8Be, and 6He are shown to exhibit orderly patterns that favor spatial configurations with strong quadrupole deformation and complementary low intrinsic spin values, a picture that is consistent with the nuclear symplectic model. The results also suggest a pragmatic path forward to accommodate deformation-driven collective features in ab initio analyses when they dominate the nuclear landscape.

Structure of8B from elastic and inelastic7Be+pscattering

Background: Detailed experimental knowledge of the level structure of light weakly bound nuclei is necessary to guide the development of new theoretical approaches that combine nuclear structure with reaction dynamics.Purpose: The resonant structure of ${}^{8}$B is studied in this work.Method: Excitation functions for elastic and inelastic ${}^{7}$Be+$p$ scattering were measured using a ${}^{7}$Be rare isotope beam. Excitation energies ranging between 1.6 and 3.4 MeV were investigated. An $R$-matrix analysis of the excitation functions was performed.Results: New low-lying resonances at 1.9, 2.54, and 3.3 MeV in ${}^{8}$B are reported with spin-parity assignment 0${}^{+}$, 2${}^{+}$, and 1${}^{+}$, respectively. Comparison to the time-dependent continuum shell (TDCSM) model and ab initio no-core shell model/resonating-group method (NCSM/RGM) calculations is performed. This work is a more detailed analysis of the data first published as a Rapid Communication. J. P. Mitchell, G. V. Rogachev, E. D. Johnson, L. T. Baby, K. W. Kemper et al., [Phys. Rev. C 82, 011601(R) (2010)].Conclusions: Identification of the 0${}^{+}$, 2${}^{+}$, 1${}^{+}$ states that were predicted by some models at relatively low energy but never observed experimentally is an important step toward understanding the structure of ${}^{8}$B. Their identification was aided by having both elastic and inelastic scattering data. Direct comparison of the cross sections and phase shifts predicted by the TDCSM and ab initio no-core shell model coupled with the resonating group method is of particular interest and provides a good test for these theoretical approaches.

Symmetry-adapted ab initio no-core shell model calculations for 12C

Symmetry-adapted no-core shell-model calculations reveal dominant symmetry patterns in the structure of light nuclei, independent of whether the system Hamiltonian is phenomenological in nature or derived from realistic interactions. We show results of large-scale nuclear structure computations based on the ab initio symmetry-adapted no-core shell model that use only a fraction of the model space. In addition, the symmetry patterns unveiled in these results are employed to explore ultra-large model spaces for 12C. The outcome suggests a possible path forward for realizing collective theories that target correlated highly-deformed and alpha-cluster structures in terms of microscopic degrees of freedom that build forward from the nucleon-nucleon interaction itself.

Structure ofA=7–8 nuclei with two- plus three-nucleon interactions from chiral effective field theory

We solve the ab initio no-core shell model (NCSM) in the complete Nmax = 8 basis for A = 7 and A = 8 nuclei with two-nucleon and three-nucleon interactions derived within chiral effective field theory (EFT). We find that including the chiral EFT three-nucleon interaction in the Hamiltonian improves overall good agreement with experimental binding energies, excitation spectra, transitions and electromagnetic moments. We predict states that exhibit sensitivity to including the chiral EFT three-nucleon interaction but are not yet known experimentally.

The no-core shell model with general radial bases

Calculations in the ab initio no-core shell model (NCSM) have conventionally been carried out using the harmonic-oscillator many-body basis. However, the rapid falloff (Gaussian asymptotics) of the oscillator functions at large radius makes them poorly suited for the description of the asymptotic properties of the nuclear wavefunction. We establish the foundations for carrying out no-core configuration interaction (NCCI) calculations using a basis built from general radial functions and discuss some of the considerations which enter into using such a basis. In particular, we consider the Coulomb-Sturmian basis, which provides a complete set of functions with a realistic (exponential) radial fallof.

Oscillator basis, scattering and nuclear structure

We note that a Lanczos algorithm can be used to generate a harmonic oscillator basis. We use it to formulate quantum scattering theory utilizing an expansion of scattering wave functions in series of oscillator functions. The continuum spectrum solutions of the Schrödinger equation are found by means of Lanczos iterations. This formalism provides a possibility to extend a nuclear shell model, in particular, an ab initio no-core shell model, on a scattering domain.

Ab initio No-core Shell Model Calculations in a SU(3)-based Coupling Scheme

We use powerful algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based symmetry-adapted many-particle basis. We demonstrate that eigenfunctions for the low-lying states of 6Li, 8Be, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins that carry the same spatial deformation as the leading symplectic Sp(3,ℝ) irreducible representations. Our findings imply that only a small fraction of the complete model space is needed to model nuclear collective dynamics, deformation, and α-particle clustering even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This in turn points to the importance of using a symmetry-adapted framework, one based on a LS coupling scheme with the associated spatial configurations organized according to deformation.

Symmetry-Adapted Ab Initio Open Core Shell Model Theory

By using only a fraction of the model space, we gain further insight – within a symmetry-guided no-core shell model framework – into the many-body nuclear dynamics that gives rise to important single-particle configurations together with correlated highly-deformed and alpha-cluster structures. We show results of the novel ab initio symmetry-adapted no-core shell model for large-scale nuclear structure computations. In addition, we use the symmetry patterns unveiled in these results to explore ultra-large model spaces.

Excited-state transition-rate measurements in18C

Excited states in ${}^{18}$C were populated by the one-proton knockout reaction of an intermediate energy radioactive ${}^{19}$N beam. The lifetime of the first ${2}^{+}$ state was measured with the K\"oln/NSCL plunger via the recoil distance method to be $\ensuremath{\tau}({2}_{1}^{+})=22.4\ifmmode\pm\else\textpm\fi{}0.9{(\mathrm{stat})}_{\ensuremath{-}2.2}^{+3.3}(\mathrm{syst})$ ps, which corresponds to a reduced quadrupole transition strength of $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=3.{64}_{\ensuremath{-}0.14}^{+0.15}{(\mathrm{stat})}_{\ensuremath{-}0.47}^{+0.40}(\mathrm{syst})$ e${}^{2}$fm${}^{4}$. In addition, an upper limit on the lifetime of a higher-lying state feeding the ${2}_{1}^{+}$ state was measured to be $\ensuremath{\tau}<4.6$ ps. The results are compared to large-scale ab initio no-core shell model calculations using two accurate nucleon-nucleon interactions and the importance-truncation scheme. The comparison provides strong evidence that the inclusion of three-body forces is needed to describe the low-lying excited-state properties of this $A=18$ system.

Ab InitioMany-Body Calculations of theH3(d,n)He4andHe3(d,p)He4Fusion Reactions

We apply the ab initio no-core shell model combined with the resonating-group method approach to calculate the cross sections of the $^{3}\mathrm{H}(d,n)^{4}\mathrm{He}$ and $^{3}\mathrm{He}(d,p)^{4}\mathrm{He}$ fusion reactions. These are important reactions for the big bang nucleosynthesis and the future of energy generation on Earth. Starting from a selected similarity-transformed chiral nucleon-nucleon interaction that accurately describes two-nucleon data, we performed many-body calculations that predict the $S$ factor of both reactions. Virtual three-body breakup effects are obtained by including excited pseudostates of the deuteron in the calculation. Our results are in satisfactory agreement with experimental data and pave the way for microscopic investigations of polarization and electron-screening effects, of the $^{3}\mathrm{H}(d,\ensuremath{\gamma}n)^{4}\mathrm{He}$ bremsstrahlung and other reactions relevant to fusion research.

$\boldsymbol Ab~Initio$ Calculations of Light-Ion Reactions

The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of nuclear forces, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD employing Hamiltonians constructed within chiral effective field theory. In this contribution, we present one of such promising techniques capable of describing simultaneously both bound and scattering states in light nuclei. By combining the resonating-group method (RGM) with the ab initio no-core shell model (NCSM), we complement a microscopic cluster approach with the use of realistic interactions and a microscopic and consistent description of the clusters. We discuss applications to light nuclei scattering, radiative capture and fusion reactions.

Ab Initio Theory of Light-ion Reactions

The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the many-body quantum-mechanical problem in the continuum, represent a theoretical and computational challenge for ab initio approaches. After a brief overview of the field, we present a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei. By combining the resonating-group method (RGM) with the ab initio no-core shell model (NCSM), we complement a microscopic cluster technique with the use of realistic interactions and a microscopic and consistent description of the clusters. We show results for neutron and proton scattering on light nuclei, including p-7Be and n-8He. We also highlight the first results of the d-3He and d-3H fusion calculations obtained within this approach.

Measurements of the Differential Cross Sections for the Elasticn−H3andn−H2Scattering at 14.1 MeV by Using an Inertial Confinement Fusion Facility

For the first time the differential cross section for the elastic neutron-triton (n-(3)H) and neutron-deuteron (n-(2)H) scattering at 14.1 MeV has been measured by using an inertial confinement fusion facility. In these experiments, which were carried out by simultaneously measuring elastically scattered (3)H and (2)H ions from a deuterium-tritium gas-filled inertial confinement fusion capsule implosion, the differential cross section for the elastic n-(3)H scattering was obtained with significantly higher accuracy than achieved in previous accelerator experiments. The results compare well with calculations that combine the resonating-group method with an ab initio no-core shell model, which demonstrate that recent advances in ab initio theory can provide an accurate description of light-ion reactions.

Similarity-Transformed ChiralNN+3NInteractions for theAb InitioDescription ofC12andO16

We present first ab initio no-core shell model (NCSM) calculations using similarity renormalization group (SRG) transformed chiral two-nucleon (NN) plus three-nucleon (3N) interactions for nuclei throughout the p-shell, particularly (12)C and (16)O. By introducing an adaptive importance truncation for the NCSM model space and an efficient JT-coupling scheme for the 3N matrix elements, we are able to surpass previous NCSM studies including 3N interactions. We present ground and excited states in (12)C and (16)O for model spaces up to N(max) = 12 including full 3N interactions. We analyze the contributions of induced and initial 3N interactions and probe induced 4N terms through the sensitivity of the energies on the SRG flow parameter. Unlike for light p-shell nuclei, SRG-induced 4N contributions originating from the long-range two-pion terms of the chiral 3N interaction are sizable in (12)C and (16)O.

Origin of the Anomalous Long Lifetime ofC14

We report the microscopic origins of the anomalously suppressed beta decay of ¹⁴C to ¹⁴N using the ab initio no-core shell model with the Hamiltonian from the chiral effective field theory including three-nucleon force terms. The three-nucleon force induces unexpectedly large cancellations within the p shell between contributions to beta decay, which reduce the traditionally large contributions from the nucleon-nucleon interactions by an order of magnitude, leading to the long lifetime of ¹⁴C.