Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory

We describe a strategy for attacking the canonical nuclear structure problem ---bound-state properties of a system of point nucleons interacting via a two-body potential---which involves an expansion in the number of particles scattering at high momenta, but is otherwise exact. The required self-consistent solutions of the Bloch-Horowitz equation for effective interactions and operators are obtained by an efficient Green's function method based on the Lanczos algorithm. We carry out this program for the simplest nuclei, d and $^3$He, to contrast a rigorous effective theory with the shell model, thereby illustrating several of the uncontrolled approximations in the latter.Comment: Revtex; two columns; four pages; two figures; submitted to Phys. Rev. Let

On the correlation between the binding energies of the triton and the alpha-particle

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.Comment: 4 pages, 1 ps figure, references update

Diel turbidity cycles in a headwater stream: evidence of nocturnal bioturbation?

Purpose: A small number of recent studies have linked daily cycles in stream turbidity to nocturnal bioturbation by aquatic fauna, principally crayfish, and demonstrated this process can significantly impact upon water quality under baseflow conditions. Adding to this limited body of research, we use high-resolution water quality monitoring data to investigate evidence of diel turbidity cycles in a lowland, headwater stream with a known signal crayfish (Pacifastacus leniusculus) population and explore a range of potential causal mechanisms. Materials and methods: Automatic bankside monitoring stations measured turbidity and other water quality parameters at 30-min resolution at three locations on the River Blackwater, Norfolk, UK during 2013. Specifically, we focused on two 20-day periods of baseflow conditions during January and April 2013 which displayed turbidity trends typical of winter and spring seasons, respectively. The turbidity time-series, which were smoothed with 6.5 hour Savitzky-Golay filters to highlight diel trends, were correlated against temperature, stage, dissolved oxygen and pH to assess the importance of abiotic influences on turbidity. Turbidity was also calibrated against suspended particulate matter (SPM) over a wide range of values via linear regression. Results and discussion: Pronounced diel turbidity cycles were found at two of the three sites under baseflow conditions during April. Spring night-time turbidity values consistently peaked between 21:00 and 04:00 with values increasing by ~10 nephelometric turbidity units (NTU) compared with the lowest recorded daytime values which occurred between 10:00 and 14:00. This translated into statistically significant increases in median midnight SPM concentration of up to 76% compared with midday, with night-time (18:00 – 05:30) SPM loads also up to 30% higher than that recorded during the daytime (06:00 – 17:30). Relating turbidity to other water quality parameters exhibiting diel cycles revealed there to be neither any correlation that might indicate a causal link, nor any obvious mechanistic connections to explain the temporal turbidity trends. Diel turbidity cycles were less prominent at all sites during the winter. Conclusions: Considering the seasonality and timing of elevated turbidity, visual observations of crayfish activity, and an absence of mechanistic connections with other water quality parameters, the results presented here are consistent with the hypothesis that nocturnal bioturbation is responsible for generating diel turbidity cycles under baseflow conditions in headwater streams. However, further research in a variety of fluvial environments is required to better assess the spatial extent, importance and causal mechanisms of this phenomenon

Vortices and domain walls in a Chern-Simons theory with magnetic moment interaction

We study the structure and properties of vortices in a recently proposed Abelian Maxwell-Chern-Simons model in $2 +1$ dimensions. The model which is described by gauge field interacting with a complex scalar field, includes two parity and time violating terms: the Chern-Simons and the anomalous magnetic terms. Self-dual relativistic vortices are discussed in detail. We also find one dimensional soliton solutions of the domain wall type. The vortices are correctly described by the domain wall solutions in the large flux limit.Comment: To be published in Phys RevD 23 pages, RevTex, 5 figure

3N Scattering in a Three-Dimensional Operator Formulation

A recently developed formulation for a direct treatment of the equations for two- and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering. Starting from the spin-momentum dependence occurring as scalar products in two- and three-nucleon forces together with other scalar functions, we present the Faddeev multiple scattering series in which order by order the spin-degrees can be treated analytically leading to 3D integrations over scalar functions depending on momentum vectors only. Such formulation is especially important in view of awaiting extension of 3N Faddeev calculations to projectile energies above the pion production threshold and applications of chiral perturbation theory 3N forces, which are to be most efficiently treated directly in such three-dimensional formulation without having to expand these forces into a partial wave basis.Comment: 25 pages, 0 figure

Computational Nuclear Physics and Post Hartree-Fock Methods

We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.Comment: 82 pages, to appear in Lecture Notes in Physics (Springer), "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Shell-model calculations and realistic effective interactions

A review is presented of the development and current status of nuclear shell-model calculations in which the two-body effective interaction is derived from the free nucleon-nucleon potential. The significant progress made in this field within the last decade is emphasized, in particular as regards the so-called V-low-k approach to the renormalization of the bare nucleon-nucleon interaction. In the last part of the review we first give a survey of realistic shell-model calculations from early to present days. Then, we report recent results for neutron-rich nuclei near doubly magic 132Sn and for the whole even-mass N=82 isotonic chain. These illustrate how shell-model effective interactions derived from modern nucleon-nucleon potentials are able to provide an accurate description of nuclear structure properties.Comment: 71 pages, to be published in Progress in Particle and Nuclear Physic

The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)

We present a charge-dependent nucleon-nucleon (NN) potential that fits the world proton-proton data below 350 MeV available in the year of 2000 with a chi^2 per datum of 1.01 for 2932 data and the corresponding neutron-proton data with chi^2/datum = 1.02 for 3058 data. This reproduction of the NN data is more accurate than by any phase-shift analysis and any other NN potential. The charge-dependence of the present potential (that has been dubbed `CD-Bonn') is based upon the predictions by the Bonn Full Model for charge-symmetry and charge-independence breaking in all partial waves with J <= 4. The potential is represented in terms of the covariant Feynman amplitudes for one-boson exchange which are nonlocal. Therefore, the off-shell behavior of the CD-Bonn potential differs in a characteristic and well-founded way from commonly used local potentials and leads to larger binding energies in nuclear few- and many-body systems, where underbinding is a persistent problem.Comment: 69 pages (RevTex) including 20 tables and 9 figures (ps files

Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines

Nuclei far from stability are studied by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on two-dimensional axially symmetric lattice, in coordinate space. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. The detailed representation of the HFB equations in cylindrical coordinates is discussed. Calculations of observables for nuclei near the neutron drip line are presented to demonstrate the reliability of the method.Comment: 13 pages, 4 figures. Submitted to Physical Review C on 05/08/02. Revised on Dec/0

Excited-state transition-rate measurements in C-18

Excited states in C-18 were populated by the one-proton knockout reaction of an intermediate energy radioactive N-19 beam. The lifetime of the first 2(+) state was measured with the Koln/NSCL plunger via the recoil distance method to be tau (2(1)(+)) = 22.4 +/- 0.9(stat)(-2.2)(+3.3)(syst) ps, which corresponds to a reduced quadrupole transition strength of B(E2; 2(1)(+) -> 0(1)(+)) = 3.64(-0.14)(+ 0.15)(stat)(-0.47)(+0.40)(syst) e(2)fm(4). In addition, an upper limit on the lifetime of a higher-lying state feeding the 2(1)(+) state was measured to be tau < 4.6 ps. The results are compared to large-scale ab initio no-core shell model calculations using two accurate nucleon-nucleon interactions and the importance-truncation scheme. The comparison provides strong evidence that the inclusion of three-body forces is needed to describe the low-lying excited-state properties of this A = 18 system