Sensitivities and correlations of nuclear structure observables emerging from chiral interactions

Starting from a set of different two- and three-nucleon interactions from chiral effective field theory, we use the importance-truncated no-core shell model for ab initio calculations of excitation energies as well as electric quadrupole (E2) and magnetic dipole (M1) moments and transition strengths for selected p-shell nuclei. We explore the sensitivity of the excitation energies to the chiral interactions as a first step towards and systematic uncertainty propagation from chiral inputs to nuclear structure observables. The uncertainty band spanned by the different chiral interactions is typically in agreement with experimental excitation energies, but we also identify observables with notable discrepancies beyond the theoretical uncertainty that reveal insufficiencies in the chiral interactions. For electromagnetic observables we identify correlations among pairs of E2 or M1 observables based on the ab initio calculations for the different interactions. We find extremely robust correlations for E2 observables and illustrate how these correlations can be used to predict one observable based on an experimental datum for the second observable. In this way we circumvent convergence issues and arrive at far more accurate results than any direct ab initio calculation. A prime example for this approach is the quadrupole moment of the first 2^+ state in C-12, which is predicted with an drastically improved accuracy.Comment: 11 pages, 8 figure

Evolved Chiral NN+3N Hamiltonians for Ab Initio Nuclear Structure Calculations

We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p-shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p-shell. We analyze in detail the impact of various truncations of the SRG-evolved Hamiltonian, in particular the truncation of the harmonic-oscillator model space used for solving the SRG flow equations and the omission of the induced beyond-3N contributions of the evolved Hamiltonian. Both truncations lead to sizable effects in the upper p-shell and beyond and we present options to remedy these truncation effects. The analysis of the different truncations is a first step towards a systematic uncertainty quantification of all stages of the calculation.Comment: 21 pages, 16 figures, 2 table

Prime Structures in a Morita Context

In this paper, we study on the primeness and semiprimeness of a Morita context related to the rings and modules. Necessary and sufficient conditions are investigated for an ideal of a Morita context to be a prime ideal and a semiprime ideal. In particular, we determine the conditions under which a Morita context is prime and semiprime

Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Nucleon Interactions

We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for open-shell nuclei using a multi-reference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the Importance-Truncated No-Core Shell Model and the Coupled Cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.Comment: 5 pages, 4 figures, v2 corresponding to published versio

Open-Shell Nuclei and Excited States from Multi-Reference Normal-Ordered Hamiltonians

We discuss the approximate inclusion of three-nucleon interactions into ab initio nuclear structure calculations using a multi-reference formulation of normal ordering and Wick's theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens a path to open-shell nuclei and excited states. Based on different multi-determinantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that this multi-reference normal-ordered two-body approximation is able to capture the effects of the 3N interaction with sufficient accuracy, both, for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies.Comment: 6 pages, 4 figures, v2: update to published versio

Hydrographic Study of Peirce Island Wastewater Treatment Plant Effluent in the Piscataqua River of Portsmouth, New Hampshire: Report of Findings from the December 10 – 14, 2012 Study Period

In order to assist the New Hampshire Department of Environmental Services (NHDES) evaluate the impact of treated wastewater effluent from Peirce Island Wastewater Treatment Plant (WWTP) to the Lower Piscataqua River and Portsmouth Harbor a hydrographic dye study was conducted in December 2012 in Portsmouth, NH. Eight (8) shellfish cages with American oysters (Crassostrea virginica) and blue mussels (Mytilus edulis) were deployed both upstream and downstream of the Peirce Island WWTP in the Piscataqua River, Little Harbor, and the entrance of Little Bay. Eight (8) mini CTDs that monitor conductivity/salinity, temperature, and depth, and six (6) moored fluorometers, which measure dye tagged effluent from the Peirce Island WWTP were attached to the subsurface cages. A fifty (50) gallon mixture of Rhodamine WT dye and distilled water was injected into WWTP on December 11, 2012 for a half tidal cycle (approximately 12.4 hours). Additionally, boat tracking fluorometers connected with a mobile geographic information system (GIS) were used to measure dye levels on the surface in situ and in real time. Microbiological analyses of fecal coliform (FC), male-specific coliphage (MSC), Norovirus (NoV) genogroup I (GI) and genogroup II (GII), and Adenovirus (AdV) were conducted on WWTP influent and effluent composite samples collected with automated samplers to determine the WWTP efficiency in reducing indicator bacteria and viruses. Microbiological sampling and testing of oysters and mussels from the eight (8) sentinel cages was conducted to assess the impact of WWTP effluent on shellfish growing areas and growing area classifications. Prior to conducting the study, the assumption was that the FDA’s recommended minimum dilution of 1000:1was not applicable in this situation because the recommended dilution is based on a WWTP having at least secondary treatment. The microbiological findings in shellfish samples, wastewater samples from the Peirce Island WWTP, and the results of the dye study, confirm that a minimum of 1,000:1 dilution with respect to Peirce Island WWTP is currently not applicable for this WWTP. The FDA and NHDES recommend continued MSC testing of wastewater samples from the WWTP before and after the WWTP upgrade. The FDA and NHDES recommend a future field study after the WWTP upgrade in order to delineate the 1,000:1 dilution zone

Unified ab initio approaches to nuclear structure and reactions

The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, 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. After a brief overview of the field, we focus on ab initio many-body approaches - built upon the No-Core Shell Model - that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the $^6$He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of $^9$Be. Further, we discuss applications to the $^7$Be$(p,\gamma)^8$B radiative capture. Finally, we highlight our efforts to describe transfer reactions including the $^3$H$(d,n)^4$He fusion.Comment: Contribution to the Special Physica Scripta Edition - 40 year anniversary - Nobel Prize '75, 71 pages, 29 figure

Ab Initio Description of p-Shell Hypernuclei

We present the first ab initio calculations for p-shell single-Lambda hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit $\Lambda$ and $\Sigma^+$, $\Sigma^0$, $\Sigma^-$ hyperons including $\Lambda$-$\Sigma$ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two- and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-shell hypernuclei and apply it to p-shell hypernuclei, in particular to $^7_\Lambda$Li, $^9_\Lambda$Be and $^{13}_\Lambda$C. We show that the chiral hyperon-nucleon interactions provide ground-state and excitation energies that agree with experiment within the cutoff dependence. At the same time we demonstrate that hypernuclear spectroscopy provides tight constraints on the hyperon-nucleon interactions and we discuss the impact of induced hyperon-nucleon-nucleon interactions.Comment: 6 pages, 4 figure

Continuum and Three-Nucleon Force Effects on 9Be Energy 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.Comment: 6 pages, 5 figure