Density Matrix Expansion for Low-Momentum Interactions

A first step toward a universal nuclear energy density functional based on low-momentum interactions is taken using the density matrix expansion (DME) of Negele and Vautherin. The DME is adapted for non-local momentum-space potentials and generalized to include local three-body interactions. Different prescriptions for the three-body DME are compared. Exploratory results are given at the Hartree-Fock level, along with a roadmap for systematic improvements within an effective action framework for Kohn-Sham density functional theory.Comment: 50 pages, 10 figure

Do Historical Cost Financial Statements Comply with the Objectives of SFAC 1?

The Financial Accounting Standards Board has issued Statements of Financial Accounting Concepts to provide the objectives which financial reporting should comply with. As the economic environment and markets have changed, there has been some controversy over whether historical cost information complies with these objectives. This paper reviews the objectives and comes to the conclusion that historical cost is satisfactory for the present, but a change will probably be needed in the future. Several alternatives are discussed and a gradual change to a valuation basis is recommended. User and preparer opinions are discussed and the recommendations take into account their opposition to change. The main conclusion of the paper is that SFAC 1 basically says that financial reporting should provide users with the information they need and want. Historical cost information seems to be satisfactory now, but a move to supplemental information is also considered positive. Any change occurring in financial reporting will have to be implemented slowly and build on what users already understand.B.S. (Bachelor of Science

Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces

A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin-asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading order chiral three-nucleon interaction is employed with its parameters fixed in computations of nuclear few-body systems. With this input one finds for the asymmetry energy of nuclear matter the value $A(\rho_0) \simeq 26.5\,$MeV, compatible with existing semi-empirical determinations. The strength functions of the isovector surface and spin-orbit coupling terms come out much smaller than those of the analogous isoscalar coupling terms and in the relevant density range one finds agreement with phenomenological Skyrme forces. The specific isospin- and density-dependences arising from the chiral two- and three-nucleon interactions can be explored and tested in neutron-rich systems.Comment: 14 pages, 7 figures, to be published in European Physical Journal

Between Science Education and Environmental Education : How Science Motivation Relates to Environmental Values

Science education and environmental education are important gates to prepare the next generation for our society’s current and upcoming challenges. While in the informal sector, environmental education acts independently, on the formal side, science education hosts environmental issues within its interdisciplinary context. As both educational efforts traditionally bear different emphases, the question may arise of whether formal science classes can act as an appropriate host. Against the background of the declining motivation to learn science in secondary school, possible synergies between both educational efforts may have vanished. For an investigation of such linkages between science motivation and environmental perception, we monitored adolescents’ motivation to learn sciences and their environmental values. By analyzing data from 429 Irish secondary school students, we reconfirmed existing scales by using confirmatory factor analysis (CFA) and investigated potential relations via SEM. Besides gender differences, we identified a significant relationship between positive ‘green’ attitude sets and the individual motivation to learn science—positive environmental preferences predict a high science motivation, primarily intrinsic motivation. Taking advantage of this relationship, individual motivation may find support from environmental educational initiatives with the focus on green values. Especially girls, who evidentially tend to have a lower motivation in science learning, may be addressed in that way

Fully microscopic shell-model calculations with realistic effective hamiltonians

The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed interest in realistic shell-model calculations. Here we focus on calculations where a fully microscopic approach is adopted. No phenomenological input is needed in these calculations, because single-particle energies, matrix elements of the two-body interaction, and matrix elements of the electromagnetic multipole operators are derived theoretically. This has been done within the framework of the time-dependent degenerate linked-diagram perturbation theory. We present results for some nuclei in different mass regions. These evidence the ability of realistic effective hamiltonians to provide an accurate description of nuclear structure properties.Comment: 6 pages, 9 figures, talk presented at INPC2010, Vancouver, July 4 -9 2010. Accepted for publication in Journal of Physics: Conference Serie

Nuclear energy density functional from chiral two- and three-nucleon interactions

An improved density-matrix expansion is used to calculate the nuclear energy density functional from chiral two- and three-nucleon interactions. The two-body interaction comprises long-range one- and two-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition we employ the leading order chiral three-nucleon interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in calculations of nuclear few-body systems. With this input the nuclear energy density functional is derived to first order in the two- and three-nucleon interaction. We find that the strength functions $F_\nabla(\rho)$ and $F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant density range reasonably with results of phenomenological Skyrme forces. However, an improved description requires (at least) the treatment of the two-body interaction to second order. This observation is in line with the deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain in the Hartree-Fock approximation with low-momentum two- and three-nucleon interactions.Comment: 16 pages, 12 figures, submitted to Eur. Phys. J.

High-momentum tails from low-momentum effective theories

In a recent work \cite{Anderson:2010aq}, Anderson \emph{et al.} used the renormalization group (RG) evolution of the momentum distribution to show that, under appropriate conditions, operator expectation values exhibit factorization in the two-nucleon system. Factorization is useful because it provides a clean separation of long- and short-distance physics, and suggests a possible interpretation of the universal high-momentum dependence and scaling behavior found in nuclear momentum distributions. In the present work, we use simple decoupling and scale-separation arguments to extend the results of Ref. \cite{Anderson:2010aq} to arbitrary low-energy $A$-body states. Using methods that are reminiscent of the operator product expansion (OPE) in quantum field theory, we find that the high-momentum tails of momentum distributions and static structure factors factorize into the product of a universal function of momentum that is fixed by two-body physics, and a state-dependent matrix element that is the same for both and is sensitive only to low-momentum structure of the many-body state. As a check, we apply our factorization relations to two well-studied systems, the unitary Fermi gas and the electron gas, and reproduce known expressions for the high-momentum tails of each.Comment: 22 pages, 0 figure