Useful Bases for Problems in Nuclear and Particle Physics

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly Fourier-Bessel transformed. The configuration space functions are associated Laguerre polynomials multiplied by an exponential weight, and their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in $\Lambda^2/(k^2 + \Lambda^2)$. A simple model of a meson containing a confined quark-antiquark pair shows that this basis is much better at describing the high-momentum properties of the wave function than the harmonic-oscillator basis.Comment: 12 pages LaTeX/revtex, plus 2 postscript figure

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure

Spring-block model for a single-lane highway traffic

A simple one-dimensional spring-block chain with asymmetric interactions is considered to model an idealized single-lane highway traffic. The main elements of the system are blocks (modeling cars), springs with unidirectional interactions (modeling distance keeping interactions between neighbors), static and kinetic friction (modeling inertia of drivers and cars) and spatiotemporal disorder in the values of these friction forces (modeling differences in the driving attitudes). The traveling chain of cars correspond to the dragged spring-block system. Our statistical analysis for the spring-block chain predicts a non-trivial and rich complex behavior. As a function of the disorder level in the system a dynamic phase-transition is observed. For low disorder levels uncorrelated slidings of blocks are revealed while for high disorder levels correlated avalanches dominates.Comment: 6 pages, 7 figure

Gut microbiome and brain functional connectivity in infants-a preliminary study focusing on the amygdala

Recently, there has been a surge of interest in the possibility that microbial communities inhabiting the human gut could affect cognitive development and increase risk for mental illness via the “microbiome-gut-brain axis.” Infancy likely represents a critical period for the establishment of these relationships, as it is the most dynamic stage of postnatal brain development and a key period in the maturation of the microbiome. Indeed, recent reports indicate that characteristics of the infant gut microbiome are associated with both temperament and cognitive performance. The neural circuits underlying these relationships have not yet been delineated. To address this gap, resting-state fMRI scans were acquired from 39 1-year-old human infants who had provided fecal samples for identification and relative quantification of bacterial taxa. Measures of alpha diversity were generated and tested for associations with measures of functional connectivity. Primary analyses focused on the amygdala as manipulation of the gut microbiota in animal models alters the structure and neurochemistry of this brain region. Secondary analyses explored functional connectivity of nine canonical resting-state functional networks. Alpha diversity was significantly associated with functional connectivity between the amygdala and thalamus and between the anterior cingulate cortex and anterior insula. These regions play an important role in processing/responding to threat. Alpha diversity was also associated with functional connectivity between the supplementary motor area (SMA, representing the sensorimotor network) and the inferior parietal lobule (IPL). Importantly, SMA-IPL connectivity also related to cognitive outcomes at 2 years of age, suggesting a potential pathway linking gut microbiome diversity and cognitive outcomes during infancy. These results provide exciting new insights into the gut-brain axis during early human development and should stimulate further studies into whether microbiome-associated changes in brain circuitry influence later risk for psychopathology

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

The hadron-quark phase transition in dense matter and neutron stars

We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, $1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot$. The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter.Comment: 25 pages, Revtex4, 16 figures included as postscrip

Three-Nucleon Force Effects in Nucleon Induced Deuteron Breakup: Predictions of Current Models (I)

An extensive study of three-nucleon force effects in the entire phase space of the nucleon-deuteron breakup process, for energies from above the deuteron breakup threshold up to 200 MeV, has been performed. 3N Faddeev equations have been solved rigorously using the modern high precision nucleon-nucleon potentials AV18, CD Bonn, Nijm I, II and Nijm 93, and also adding 3N forces. We compare predictions for cross sections and various polarization observables when NN forces are used alone or when the two pion-exchange Tucson-Melbourne 3NF was combined with each of them. In addition AV18 was combined with the Urbana IX 3NF and CD Bonn with the TM' 3NF, which is a modified version of the TM 3NF, more consistent with chiral symmetry. Large but generally model dependent 3NF effects have been found in certain breakup configurations, especially at the higher energies, both for cross sections and spin observables. These results demonstrate the usefulness of the kinematically complete breakup reaction in testing the proper structure of 3N forces.Comment: 42 pages, 20 ps figures, 2 gif figure

Density dependent hadron field theory for neutron stars with antikaon condensates

We investigate $K^-$ and $\bar K^0$ condensation in $\beta$-equilibrated hyperonic matter within a density dependent hadron field theoretical model. In this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by the exchange of mesons. Density dependent meson-baryon coupling constants are obtained from microscopic Dirac Brueckner calculations using Groningen and Bonn A nucleon-nucleon potential. It is found that the threshold of antikaon condensation is not only sensitive to the equation of state but also to antikaon optical potential depth. Only for large values of antikaon optical potential depth, $K^-$ condensation sets in even in the presence of negatively charged hyperons. The threshold of $\bar K^0$ condensation is always reached after $K^-$ condensation. Antikaon condensation makes the equation of state softer thus resulting in smaller maximum mass stars compared with the case without any condensate.Comment: 20 pages, 7 figures; final version to appear in Physical Review