Recent progress in Hamiltonian light-front QCD

Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. We outline our approach and discuss the computational challenges.Comment: Invited paper at Light Cone 2008, Mulhouse, Franc

No-core shell model for 48-Ca, 48-Sc and 48-Ti

We report the first no-core shell model results for $^{48}Ca$, $^{48}Sc$ and $^{48}Ti$ with derived and modified two-body Hamiltonians. We use an oscillator basis with a limited $\hbar\Omega$ range around $45/A^{1/3}-25/A^{2/3} = 10.5 MeV$ and a limited model space up to $1\hbar\Omega$. No single-particle energies are used. We find that the charge dependence of the bulk binding energy of eight A=48 nuclei is reasonably described with an effective Hamiltonian derived from the CD-Bonn interaction while there is an overall underbinding by about 0.4 MeV/nucleon. However, the resulting spectra exhibit deficiencies that are anticipated due to: (1) basis space limitations and/or the absence of effective many-body interactions; and, (2) the absence of genuine three-nucleon interactions. We then introduce additive isospin-dependent central terms plus a tensor force to our Hamiltonian and achieve accurate binding energies and reasonable spectra for all three nuclei. The resulting no-core shell model opens a path for applications to the double-beta ($\beta\beta$) decay process.Comment: Revised content and added reference

From non-Hermitian effective operators to large-scale no-core shell model calculations for light nuclei

No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing experimental nuclear spectra. The main theoretical approach is the use of effective operators, which include correlations left out by the truncation of the model space to a numerically tractable size. We review recent applications of the effective operator approach, within a NCSM framework, to the renormalization of the nucleon-nucleon interaction, as well as scalar and tensor operators.Comment: To be submited to J. Phys. A, special issue on "The Physics of Non-Hermitian Operators

Neutrino-12C scattering in the ab initio shell model with a realistic three-body interaction

We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 hbarOmega we show that realistic nucleon-nucleon interactions, like e.g. the CD-Bonn, under predict the experimental cross sections by more than a factor of two. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time,the TM'(99) interaction improves the calculated level ordering in 12C. The comparison between the CD-Bonn and the three-body calculations provides strong confirmation for the need to include a realistic three-body interaction to account for the spin-orbit strength in p-shell nuclei.Comment: 6 pages, 2 figure

Nucleon-Nucleon Scattering in a Harmonic Potential

The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.Comment: 19 pages, 13 figure

Electron-scattering form factors for 6Li in the ab initio symmetry-guided framework

We present an ab initio symmetry-adapted no-core shell-model description for $^{6}$Li. We study the structure of the ground state of $^{6}$Li and the impact of the symmetry-guided space selection on the charge density components for this state in momentum space, including the effect of higher shells. We accomplish this by investigating the electron scattering charge form factor for momentum transfers up to $q \sim 4$ fm$^{-1}$. We demonstrate that this symmetry-adapted framework can achieve significantly reduced dimensions for equivalent large shell-model spaces while retaining the accuracy of the form factor for any momentum transfer. These new results confirm the previous outcomes for selected spectroscopy observables in light nuclei, such as binding energies, excitation energies, electromagnetic moments, E2 and M1 reduced transition probabilities, as well as point-nucleon matter rms radii.Comment: 10 pages, 7 figures; accepted to Physical Review

Benchmarks of the full configuration interaction, Monte Carlo shell model, and no-core full configuration methods

We report no-core solutions for properties of light nuclei with three different approaches in order to assess the accuracy and convergence rates of each method. Full configuration interaction (FCI), Monte Carlo shell model (MCSM) and no core full configuration (NCFC) approaches are solved separately for the ground state energy and other properties of seven light nuclei using the realistic JISP16 nucleon-nucleon interaction. The results are consistent among the different approaches. The methods differ significantly in how the required computational resources scale with increasing particle number for a given accuracy.Comment: 19 pages, 14 figures, 6 table

Underlying symmetries of realistic interactions and the nuclear many-body problem

The present study brings forward important information, within the framework of spectral distribution theory, about the types of forces that dominate three realistic interactions, CD-Bonn, CDBonn+ 3terms and GXPF1, in nuclei and their ability to account for many-particle effects such as the formation of correlated nucleon pairs and enhanced quadrupole collective modes. Like-particle and proton-neutron isovector pairing correlations are described microscopically by a model interaction with Sp(4) dynamical symmetry, which is extended to include an additional quadrupole-quadrupole interaction. The analysis of the results for the 1f7/2 level shows that both CD-Bonn+3terms and GXPF1 exhibit a well-developed pairing character compared to CD-Bonn, while the latter appears to build up more (less) rotational isovector T = 1 (isoscalar T = 0) collective features. Furthermore, the three realistic interactions are in general found to correlate strongly with the pairing+quadrupole model interaction, especially for the highest possible isospin group of states where the model interaction can be used to provide a reasonable description of the corresponding energy spectra.Comment: 12 pages, 4 figure