The Shell Model, the Renormalization Group and the Two-Body Interaction

The no-core shell model and the effective interaction $V_{{\rm low} k}$ can both be derived using the Lee-Suzuki projection operator formalism. The main difference between the two is the choice of basis states that define the model space. The effective interaction $V_{{\rm low} k}$ can also be derived using the renormalization group. That renormalization group derivation can be extended in a straight forward manner to also include the no-core shell model. In the nuclear matter limit the no-core shell model effective interaction in the two-body approximation reduces identically to $V_{{\rm low} k}$. The same considerations apply to the Bloch-Horowitz version of the shell model and the renormalization group treatment of two-body scattering by Birse, McGovern and Richardson

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam {\it et al.} to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N$^2$LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a cutoff-dependent coupling {\it constant} arising from zero-range contact interactions and a cutoff-independent coupling {\it function} of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A Mathematica notebook containing the novel density-dependent couplings is provided.Comment: 28 pages, 12 figures. Mathematica notebook provided with submission

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

An improved density matrix expansion for spin-unsaturated nuclei

A current objective of low-energy nuclear theory is to build non-empirical nuclear energy density functionals (EDFs) from underlying inter-nucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly non-local Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the non-local exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local-momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically-constrained starting point around which future phenomenological parameterizations can be built and refined.Comment: 24 pages, 11 figures, updated typos and plots

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

Projection Operator Formalisms and the Nuclear Shell Model

The shell model solve the nuclear many-body problem in a restricted model space and takes into account the restricted nature of the space by using effective interactions and operators. In this paper two different methods for generating the effective interactions are considered. One is based on a partial solution of the Schrodinger equation (Bloch-Horowitz or the Feshbach projection formalism) and other on linear algebra (Lee-Suzuki). The two methods are derived in a parallel manner so that the difference and similarities become apparent. The connections with the renormalization group are also pointed out.Comment: 4 pages, no figure

Contact-allergy time

The most commonly used techniques for the in vivo evaluation of the cellular immune response include intracutaneous testing with microbial recall antigens or sensitization with neoantigens. The reliability of these tests for the individual patient usually is low due to the lack of standardization and quantification. Moreover only the efferent branch of the immune response can be judged. The dinitrochlorobenzene-contact allergy time (DNCB-CAT) is a quantitative approach for the assessment of the cellular immune response. 2% DNCBointment is applied on the upper arm in a 1 cm2 area. On the following days patch-testing with 0.05% DNCB-ointment is done on the homolateral forearm in alternating localizations till an allergic contact dermatitis reaction appears. As assessed in patients with malignant melanoma (MM, n=\\5) and with lymphoproliferative disorders (LD, η = 25), the DNCB-CAT correlates with the age of the patients and can be expressed by a formula given by the age (years) χ factor (MM = 0.16; LD = 0.17) + constant figure (MM = 5.5; LD = 4.3). There was no significant difference between the two groups or subgroups investigated. By DNCB-CAT quantitative analysis of the cellular immune response in vivo is possible. It is an appropriate model for further investigations of the cellular immunity under different clinical, histological, prognostic, and therapeutic aspects

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.