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Register a new userEmergent properties of nuclei from ab initio coupled-cluster calculations
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Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO$_{rm sat}$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to $^{56}$Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon-nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the $J^pi = {1/2}^-,{3/2}^-,{7/2}^-,{3/2}^+$ states in $^{17,23,25}$O, and - contrary to naive shell-model expectations - the level ordering of the $J^pi = {3/2}^+,{5/2}^+,{9/2}^+$ states in $^{53,55,61}$Ca.
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We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{3max}=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain ground-state energies in $^{132}$Sn converged to within a few MeV with respect to the $E_{3max}$ truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{rm rel}>9/2$ is dominated by a basis-truncation artifact which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of $^{132}$Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.
An {em ab initio} (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable to further our understanding of the fundamental interactions among nucleons, and provide accurate predictions of crucial reaction rates for nuclear astrophysics, fusion-energy research, and other applications. In this contribution we review {em ab initio} calculations for nucleon and deuterium scattering on light nuclei starting from chiral two- and three-body Hamiltonians, obtained within the framework of the {em ab initio} no-core shell model with continuum. This is a unified approach to nuclear bound and scattering states, in which square-integrable energy eigenstates of the $A$-nucleon system are coupled to $(A-a)+a$ target-plus-projectile wave functions in the spirit of the resonating group method to obtain an efficient description of the many-body nuclear dynamics both at short and medium distances and at long ranges.
Using the ground-state energy of 16-O obtained with the realistic V_UCOM interaction as a test case, we present a comprehensive comparison of different configuration interaction (CI) and coupled-cluster (CC) methods, analyzing the intrinsic advantages and limitations of each of the approaches. In particular, we use the importance-truncated (IT) CI and no-core shell model (NCSM) schemes with up to 4-particle-4-hole (4p4h) excitations as well as the size extensive CC methods with a complete treatment of one- and two-body clusters (CCSD) and a non-iterative treatment of connected three-body clusters via the completely renormalized correction to the CCSD energy defining the CR-CC(2,3) approach. We discuss the impact of the center-of-mass contaminations, the choice of the single-particle basis, and size-extensivity on the resulting energies. When the IT-CI and IT-NCSM methods include the 4p4h excitations and when the CC calculations include the 1p1h, 2p2h, and 3p3h clusters, as in the CR-CC(2,3) approach, we observe an excellent agreement among the different methodologies. This shows that despite their individual limitations, the IT-CI, IT-NCSM, and CC methods can provide precise and consistent ab initio nuclear structure predictions. Furthermore, the IT-CI, IT-NCSM, and CC ground-state energy values obtained with 16-O are in good agreement with the experimental value, proving that the V_UCOM two-body interaction allows for a realistic description of binding energies for heavier nuclei and that all of the methods used in this study account for most of the relevant particle correlation effects.
In any finite system, the presence of a non-zero permanent electric dipole moment (EDM) would indicate CP violation beyond the small violation predicted in the Standard Model. Here, we use the ab initio no-core shell model (NCSM) framework to theoretically investigate the magnitude of the nuclear EDM. We calculate EDMs of several light nuclei using chiral two- and three-body interactions and a PT-violating Hamiltonian based on a one-meson-exchange model. We present a benchmark calculation for $^3$He, as well as results for the more complex nuclei $^{6,7}$Li, $^9$Be, $^{10,11}$B, $^{13}$C, $^{14,15}$N, and $^{19}$F. Our results suggest that different nuclei can be used to probe different terms of the PT violating interaction. These calculations allow us to suggest which nuclei may be good candidates in the search for a measurable permanent electric dipole moment.
We report converged results for the ground and excited states and matter density of 16-O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and formalism developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a 1-particle-1-hole nature, but it cannot describe the first excited 0+ state. Incorporation of triples has no effect on the latter finding.
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