Single-particle potential in a chiral approach to nuclear matter including short range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys. Lett. B474 (2000) 7] by calculating the underlying (complex-valued) single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi-surface. Also, the imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear matter equation of state can be obtained if the short range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1pi-exchange). We also consider the equation of state of pure neutron matter $bar E_n(k_n)$ and the asymmetry energy A(k_f) in that approach. The downward bending of these quantities above nuclear matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics.Comment: 12 pages, 7 figures, submitted to Physical Review

Radiative corrections to the charged pion-pair production process {\boldmathπ−γ→π+π−π−\pi^-\gamma\to \pi^+\pi^-\pi^-} at low energies

We calculate the one-photon loop radiative corrections to the charged pion-pair production process $\pi^-\gamma\to\pi^+\pi^-\pi^-$. In the low-energy region this reaction is governed by the chiral pion-pion interaction. The pertinent set of 42 irreducible photon-loop diagrams is calculated by using the package FeynCalc. Electromagnetic counterterms with two independent low-energy constants $\widehat k_1$ and $\widehat k_2$ are included in order to remove the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved by including soft photon radiation below an energy cut-off $\lambda$. The purely electromagnetic interaction of the charged pions mediated by one-photon exchange is also taken into account. The radiative corrections to the total cross section (in the isospin limit) vary between $+10\%$ close to threshold and about $-1\%$ at a center-of-mass energy of $7m_\pi$. The largest contribution comes from the simple one-photon exchange. Radiative corrections to the $\pi^+\pi^-$ and $\pi^-\pi^-$ mass spectra are studied as well. The Coulomb singularity of the final-state interaction produces a kink in the dipion mass spectra. The virtual radiative corrections to elastic $\pi^-\pi^-$ scattering are derived additionally.Comment: 19 pages, 17 figures, accepted for publication in Eur. Phys. J.

From Caenorhabditis elegans to the Human Connectome: A Specific Modular Organisation Increases Metabolic, Functional, and Developmental Efficiency

The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values but otherwise maximally random. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of C. elegans and human connectomes are both higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in C. elegans connectome or each region of interest (ROI) in human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared to the alternative arrangements. This implies that fewer rules are needed to encode for the organisation of neural systems

Chiral 2π2\pi-exchange NN-potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3$MeV at $r=1.0$fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $\pi N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram with two second order chiral $\pi \pi NN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.Comment: 6 pages, 2 figure

Nuclear energy density functional from chiral pion-nucleon dynamics

We calculate the nuclear energy density functional relevant for N=Z even-even nuclei in the systematic framework of chiral perturbation theory. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a very good equation of state of isospin symmetric nuclear matter. We find that in the region below nuclear matter saturation density the effective nucleon mass $\widetilde M^*(\rho)$ deviates by at most 15% from its free space value $M$, with $0.89M<\widetilde M^*(\rho)<M$ for $\rho < 0.11 {\rm fm}^{-3}$ and $\widetilde M^*(\rho)>M$ for higher densities. The parameterfree strength of the $(\vec\nabla \rho)^2$-term, $F_\nabla(k_f)$, is at saturation density comparable to that of phenomenological Skyrme forces. The magnitude of $F_J(k_f)$ accompanying the squared spin-orbit density $\vec J ^2$ comes out somewhat larger. The strength of the nuclear spin-orbit interaction, $F_{so}(k_f)$, as given by iterated one-pion exchange is about half as large as the corresponding empirical value, however, with the wrong negative sign. The novel density dependencies of $\widetilde M^*(\rho)$ and $F_{\nabla,so,J}(k_f)$ as predicted by our parameterfree calculation should be examined in nuclear structure calculations (after introducing an additional short range spin-orbit contribution constant in density).Comment: 16 pages, 5 figure

Quality of life in first-admitted schizophrenia patients: a follow-up study

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