The Canonical Nuclear Many-Body Problem as an Effective Theory

Recently it was argued that it might be possible treat the conventional nuclear structure problem -- nonrelativistic point nucleons interacting through a static and rather singular potential -- as an effective theory in a shell-model basis. In the first half of this talk we describe how such a program can be carried out for the simplest nuclei, the deuteron and 3He, exploiting a new numerical technique for solving the self-consistent Bloch-Horowitz equation. Some of the properties of proper effective theories are thus illustrated and contrasted with the shell model. In the second half of the talk we use these examples to return to a problem that frustrated the field three decades ago, the possibility of reducing the effective interactions problem to perturbation theory. We show, by exploiting the Talmi integral expansion, that hard-core potentials can be systematically softened by the introduction of a series of contact operators familiar from effective field theory. The coefficients of these operators can be run analytically by a renormalization group method in a scheme-independent way, with the introduction of suitable counterterms. Once these coefficients are run to the shell model scale, we show that the renormalized coefficients contain all of the information needed to evaluate perturbative insertions of the remaining soft potential. The resulting perturbative expansion is shown to converge in lowest order for the simplest nucleus, the deuteron.Comment: Latex, 12 pages, 2 figures Talk presented at the International Symposium on Nuclei and Nucleons, held in honor of Achim Richter Typos corrected in this replacemen

Perturbative Effective Theory in an Oscillator Basis?

The effective interaction/operator problem in nuclear physics is believed to be highly nonperturbative, requiring extended high-momentum spaces for accurate solution. We trace this to difficulties that arise at both short and long distances when the included space is defined in terms of a basis of harmonic oscillator Slater determinants. We show, in the simplest case of the deuteron, that both difficulties can be circumvented, yielding highly perturbative results in the potential even for modest (~6hw) included spaces.Comment: 10 pages, 4 figure

Neutron Production by Muon Spallation I: Theory

We describe the physics and codes developed in the Muon Physics Package. This package is a self-contained Fortran90 module that is intended to be used with the Monte Carlo package MCNPX. We calculate simulated energy spectra, multiplicities, and angular distributions of direct neutrons and pions from muon spallation

Effective Interactions for the Three-Body Problem

The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy.Comment: 19 pages, 9 figures, submitted to PR

Effect of Stimulus Orientation on Visual Function in Children with Refractive Amblyopia.

Purpose: We investigated and characterized the patterns of meridional anisotropies in newly diagnosed refractive amblyopes using pattern onset–offset visual evoked potentials (POVEPs) and psychophysical grating acuity (GA). Methods: Twenty-five refractive amblyopes were recruited and compared with non-amblyopic controls from our previous study. Monocular POVEPs were recorded in response to sinewave 4 cycles per degree (cpd) grating stimuli oriented along each individual participants' principal astigmatic meridians, which were approximately horizontal (meridian 1) and vertical (meridian 2). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed along the same meridians using a two-alternative non-forced-choice technique. The C3 amplitudes and peak latencies of the POVEPs and GAs were compared across meridians for both groups (refractive amblyopes and controls) using linear mixed models (monocular) and ANOVA (binocular), and post hoc analysis was conducted to determine if meridional anisotropies in this cohort of amblyopes were related to low (≤1.50 diopters [D]), moderate (1.75–2.75 D) and high (≥3.00 D) astigmatism. Results: In the newly diagnosed refractive amblyopes, there were no significant meridional anisotropies across all outcome measures, but the post hoc analysis demonstrated that C3 amplitude was significantly higher in those with low (P = 0.02) and moderate (P = 0.004) astigmatism compared to those with high astigmatism. Refractive amblyopes had poorer GA and C3 amplitudes compared to controls by approximately two lines on the logMAR chart (monocular: P = 0.013; binocular: P = 0.014) and approximately 6 µV (monocular: P = 0.009; binocular: P = 0.027), respectively. Conclusions: Deleterious effects of high astigmatism was evident in newly diagnosed refractive amblyopes, but the neural deficits do not seem to be orientation-specific for the stimulus parameters investigated

Electrophysiological and Psychophysical Studies of Meridional Anisotropies in Children With and Without Astigmatism.

Purpose: We investigated the pattern of meridional anisotropies, if any, for pattern onset-offset visual evoked potential (POVEPs) responses and psychophysical grating acuity (GA) in children with normal letter visual acuity (20/20 or better). Methods: A total of 29 children (aged 3-9 years), nine of whom were astigmatic (AS), were recruited. Orientation-specific monocular POVEPs were recorded in response to sinewave grating stimuli oriented along the subjects' principal AS meridians. Horizontal and vertical gratings were designated Meridians 1 and 2, respectively, for nonastigmatic patients (Non-AS). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed monocularly and binocularly along the same meridians using the same stimuli by a 2-alternative-forced-choice staircase technique. The C3 amplitudes and peak latencies of the POVEP and GAs were compared across meridians using linear mixed models (monocular) and ANOVA (binocular). Results: There were significant meridional anisotropies in monocular C3 amplitudes regardless of astigmatism status (P = 0.001): Meridian 2 (mean ± SE Non-AS, 30.13 ± 2.07 μV; AS, 26.53 ± 2.98 μV) was significantly higher than Meridian 1 (Non-AS, 26.14 ± 1.87 μV; AS, 21.68 ± 2.73 μV; P = 0.019), but no meridional anisotropies were found for GA or C3 latency. Binocular C3 amplitude in response to horizontally oriented stimuli (180°, 29.71 ± 3.06 μV) was significantly lower than the oblique (45°, 36.62 ± 3 .05 μV; P = 0.03 and 135°, 35.95 ± 2.92 μV; P = 0.04) and vertical (90°, 37.82 ± 3.65 μV; P = 0.02) meridians, and binocular C3 latency was significantly shorter in response to vertical than oblique gratings (P ≤ 0.001). Conclusions: Meridional anisotropy was observed in children with normal vision. The findings suggest that horizontal gratings result in a small, but significantly lower POVEP amplitude than for vertical and oblique gratings

SU(2) low-energy constants from mixed-action lattice QCD

An analysis of the pion mass and pion decay constant is performed using mixed-action lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered n(f) = 2 + 1 configurations generated by the MILC Collaboration. Calculations were performed at two lattice spacings of b approximate to 0.125 fm and b approximate to 0.09 fm, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range 0.1 \u3c = m(l)/m(s) \u3c = 0.6, while pion masses are in the range 235 less than or similar to m(pi) less than or similar to 680 MeV. A two-flavor chiral perturbation theory analysis of the lattice QCD calculations constrains the Gasser-Leutwyler coefficients (l) over bar (3) and (l) over bar (4) to be (l) over bar (3) = 4.04(40)((73)(55)) and (l) over bar (4) = 4.30(51)((84)(60)). All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give f(pi)/f = 1.062(26)((42)(40)) where f is the decay constant in the chiral limit, and when combined with the experimental determination of f(pi) results in a value of f = 122.8(3.0((4.6)(4.8)) MeV. The most recent scale setting by the MILC Collaboration yields a postdiction of f(pi) = 128.2(3.6)((4.4)(6.0))((1.2)(3.3)) MeV at the physical pion mass. A detailed error analysis indicates that precise calculations at lighter pion masses is the single most important systematic to address to improve upon the present work