Similarity Renormalization Group for Few-Body Systems

Internucleon interactions evolved via flow equations yield soft potentials that lead to rapid variational convergence in few-body systems.Comment: 3 pages, 6 figures. To appear in the proceedings of the 20th European Conference on Few-Body Problems in Physics (EFB20), Pisa, September 10-14, 200

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

From low-momentum interactions to nuclear structure

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.Comment: 76 pages, 57 figures, two figures updated, published versio

Are low-energy nuclear observables sensitive to high-energy phase shifts?

Conventional nucleon-nucleon potentials with strong short-range repulsion require contributions from high-momentum wave function components even for low-energy observables such as the deuteron binding energy. This can lead to the misconception that reproducing high-energy phase shifts is important for such observables. Interactions derived via the similarity renormalization group decouple high-energy and low-energy physics while preserving the phase shifts from the starting potential. They are used to show that high-momentum components (and high-energy phase shifts) can be set to zero when using low-momentum interactions, without losing information relevant for low-energy observables.Comment: 13 pages, 5 figures; reference and acknowledgment adde

Operator Evolution via the Similarity Renormalization Group I: The Deuteron

Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this paper on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.Comment: 33 pages, 19 figures. Improved figures 17 and 18. Expanded comments on OPE in tex

Operator Evolution via the Similarity Renormalization Group I: The Deuteron

Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this paper on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.Comment: 33 pages, 19 figures. Improved figures 17 and 18. Expanded comments on OPE in tex

Computer Tomograph Measurements in Shear and Gravity Particle Flows

The paper reports the recent results obtained on the applicability of cross-sectional digital imaging method to study particle flow characteristics in 3D particle beds forced to move by gravity or shear. X-ray CT imaging technique is widely used in medical diagnostics and, during the last decades, its spatial and temporal resolution has been improved significantly. In this study, an attempt was made to use this technique for engineering purposes. Two experimental set-ups with different types of particle flows were investigated using Siemens Somatom Plus type CT equipment. A series of trials were carried out in a small model hopper with flat bottom and almost cylindrical side wall slightly deviating from verticality. Non steady-state flow was studied during the outflow of particulate material from this vessel, through a central hole at the bottom. Further investigation was fulfilled in a modified Cuette-type shearing device to study steady-state shear flow. This equipment consisted of an almost cylindrical vessel identical to that used for gravity flow measurements, and a smaller inner cylinder rotating within this vessel concentrically, around its vertical axis. The surface of the inner cylinder was notched vertically, i.e. perpendicularly to the direction of rotation to increase wall friction between the particles and the cylinder. Almost spherical sucrose granules, also used for gravity flow measurements, were filled into the gap between the rotating cylinder and the outer wall of the equipment. Movement of particles took place due to shear, generated within the particle bed. By using X-ray CT technique, cross-sectional digital images were obtained in every two seconds for both types of particle flows. For this, the cross-sectional variation of the local Hounsfield density values were measured in a matrix of 0.1x0.1x2.0 mm space elements. It was proved that the applied non-invasive crosssectional imaging technique was suitable to distinguish the stationary and moving particle regions, and by this, to estimate the location of the boundary zone between them