Session DD: Nuclear Theory I: Structure and Reactions

Faddeev approach to deuteron-induced nuclear reactions

Deuteron-induced nuclear reactions are an essential tool for probing the structure of stable and rare isotopes as well as extracting quantities of astrophysical interest such as $(n,\gamma)$ cross sections on unstable targets. While Faddeev techniques enable the exact description of the dynamics within a three-body model, their application to deuteron-induced reactions on rare isotopes is complicated by the unavailability of nucleon scattering data needed to constrain the corresponding effective nucleon-target interactions. Moreover, the use of phenomenological potentials with ambiguous off-shell properties introduces further uncertainties. In order to understand and quantify the uncertainties, we apply the Faddeev theory to light deuteron-nucleus systems that are within the reach of state-of-the-art ab initio reaction theories. We present Alt-Grassberger-Sandhas (AGS) momentum space calculations of observables for deuteron-induced reactions on $^4$He using phenomenologically constrained effective 3-body Hamiltonians. In addition, we explore the use of microscopic interactions derived from the no-core shell model (NCSM) coupled with the resonating group method (RGM).   

Quantum Monte Carlo calculations of electron scattering from light nuclei

I will present ab initio Quantum Monte Carlo calculations for quasielastic scattering of electrons from light nuclei. Using the Argonne v18 realistic two-nucleon interaction, together with a propagation in imaginary-time, we evaluate the short-time response of nuclei. This method consistently includes two-body physics, in the nucleon-nucleon interaction and the electromagnetic currents. It also allows us to study scattering channels involving nucleons in back-to-back kinematics, of experimental interest and currently tested at, e.g., JLab. I will present results for longitudinal and transverse response functions, as well as response densities.   

Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons

Low-energy scattering of the three neutron (3$n)$ and four neutron (4$n)$ systems are studied in the framework of the adiabatic hyperspherical method in the symmetries $J^{\pi \thinspace }=$ 3/2$^{\mathrm{-}}$ and $J^{\pi \thinspace }=$ 0$^{\mathrm{+}}$, respectively. The nucleon-nucleon (NN) interaction considered in this work is the phenomenological AV8' potential and the resultant hyperspherical potentials are compared to those computed with the AV18 potential and other NN potentials with and without a three-nucleon force. The lowest hyperspherical potential for each system exhibits no features that indicate the existence of a low-energy resonance. This non-resonant behavior is further substantiated through an analysis of the elastic phaseshift and density of states or Wigner-Smith time delay. However, there is an enhancement of the density of states at low energies due to a universal long-range attraction in the hyperradial potential which could help explain the enhanced 4n signal observed in the experiment by Kisamori et al. [1]. [1] K. Kisamori, et al. ``Candidate Resonant Tetraneutron State Populated by the He-4 (He-8, Be-8) Reaction'', Phys. Rev. Lett. 116, 052501 (2016).   

Shape coexistence, shape invariants, and ab initio rotation in $^{10}\mathrm{Be}$

\textit{Ab initio} theory describes nuclei from a fully microscopic formulation, with no presupposition of collective degrees of freedom, yet signatures of deformation and rotation nonetheless arise. To extract information on the nature of this emergent collectivity, we must probe the calculated wave functions through appropriate observables. The predicted spectroscopy of $^{10}\mathrm{Be}$ from no-core configuration interaction (NCCI) calculations is suggestive of coexisting rotational structures having qualitatively different intrinsic deformations: one involving triaxiality and the other with large axial deformation arising primarily from the neutrons. We use calculated $E2$ observables, and in particular quadrupole shape invariants, to obtain more direct measures of the nuclear shapes.   

Eigenvector Continuation for Two-Body Scattering

We will be describing the theoretical implementation of eigenvector continuation (EVC) for the two-body scattering problem. EVC is a technique that relies on solutions to a Hamiltonian for several sets of known parameters to formulate a basis, which can be used to accurately interpolate and extrapolate solutions for the same Hamiltonian with different parameters. Until now, this has only been applied to the bound state problem. Using the Kohn variational method, we show that EVC can be adapted to scattering in coordinate space in the form of a simple matrix inversion. In addition, we discuss how to deal with ill-conditioned matrices that naturally arise. Furthermore, we generalize to include the Coulomb and non-local potentials, as well as extending the method to momentum space and coupled channels.   

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this letter we present the first study of the convergence of eigenvector continuation. To perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between non-orthogonal vectors appearing at different orders in perturbation theory.   

Computational Applications of the Eigenvector Continuation Method to Scattering

The previous talk laid the theoretical groundwork for applying the eigenvector continuation (EVC) method to scattering problems in nuclear physics. Here, we present results for EVC as applied to various physical scattering scenarios in coordinate space---the square well (with and without a Coulomb interaction), the Minnesota potential (for the 1S0 and 3S1 states), p-alpha scattering (for the S1/2 and P3/2 states), and alpha-Pb scattering with a complex optical potential---as well as in momentum space. Computational issues that arise, including matrix ill-conditioning and careful selection of basis parameters, are also discussed.   

Ab-initio analysis of $\beta$-delayed proton emission in $^{11}$Be

The exotic $\beta$-delayed proton emission is calculated in $^{11}$Be from first principles using chiral two- and three-nucleon forces. To investigate the unexpectedly large branching ratio measured in [PRL 123, 082501 (2019)] we calculate the proposed $1/2^+$ proton resonance in $^{11}$B using the no-core shell model with continuum (NCSMC). This timely calculation helps to resolve whether this large branching ratio is caused by unknown dark decay modes or an unobserved proton resonance.   

Extrapolation of 6Li ground state properties via Artificial Neural Networks

We explore the use of feed-forward neural networks in extrapolating nuclear observables in light nuclei based on existing ab initio no-core shell model (NSCM) calculations. This work extends the approach and the applications of A. Negoita, et al., Phys. Rev. C 99, 054308 (2019). A large ensemble of neural networks is trained using NCSM results, and those networks are ranked by a criterion of performance. Those passing the criterion are then queried for a prediction at a large-model space limit; the distribution of predictions is found to be approximately Gaussian. Further, the width of the Gaussian is found to narrow either with more training data at fixed model space size or with increase of the model space size. We consider several properties of the ground state of Lithium-6, and we compare results with established extrapolation methods where available.