Modelling CC neutrino cross sections in the few GeV energy region

Selected problems in modelling neutrino-nucleon and -nuclei cross sections in the neutrino energy region of the few GeV are reviewed.Comment: Presented by J.T. Sobczyk at the Cracow Epiphany Conference on Neutrinos and Dark Matter, Jan. 5-8, 2006, Cracow, Polan

Scaling within the Spectral Function approach

Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpretating neutrino- and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of $^{12}$C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. This asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole SF.Comment: 15 pages, 11 figure

Comparison of predictions for nuclear effects in the Marteau model with the NUX+FLUKA scheme

Nuclear effects in neutrino-nucleus reactions simulated by means of the NUX+FLUKA Monte Carlo generator are compared with the theoretical predictions of the Marteau model. Pion absorption in NUX+FLUKA and non-pionic Delta decays in the Marteau model differ by about 30%. The fraction of pions produced due to the re-interactions after primary quasi-elastic vertex is in the NUX+FLUKA scheme much higher then provided by the Marteau model.Comment: 6 pages, 8 figures, Presented by J.A. Nowak at the 3rd International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region, 17-21 March, Gran Sasso(Italy),to appear in the Proceeding

Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Classification of Low Dimensional Lie Super-Bialgebras

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In all the cases Poisson-Lie brackets on supergroups are found. Possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to be straightforward for all but one structures for super-E(2) group.Comment: 15 pages, LaTe

Kappa-contraction from SUq(2)SU_q(2) to Eκ(2)E_{\kappa}(2)

We present contraction prescription of the quantum groups: from $SU_q(2)$ to $E_{\kappa}(2)$. Our strategy is different then one chosen in ref. [P. Zaugg, J. Phys. A {\bf 28} (1995) 2589]. We provide explicite prescription for contraction of $a, b, c$ and $d$ generators of $SL_q(2)$ and arrive at $^*$ Hopf algebra $E_{\kappa}(2)$.Comment: 3 pages, plain TEX, harvmac, to be published in the Proceedings of the 4-th Colloqium Quantum Groups and Integrable Systems, Prague, June 1995, Czech. J. Phys. {\bf 46} 265 (1996

WroNG -- Wroclaw Neutrino Generator of events for single pion production

We constructed a new Monte Carlo generator of events for neutrino CC single pion production on free nucleon targets. The code uses dynamical models of the DIS with the PDFs modified according to the recent JLab data and of the Delta excitation. A comparison with experimental data was done in three channels for the total cross sections and for the distributions of events in invariant hadronic mass.Comment: 6 pages, 13 figures, Presented by J.T. Sobczyk at the 3rd International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region, 17-21 March, Gran Sasso(Italy),to appear in the Proceeding

NMDA receptor subunit-dependent [Ca2+] signaling in individual hippocampal dendritic spines

Ca2+ influx through synaptic NMDA receptors (NMDA-Rs) triggers a variety of adaptive cellular processes. To probe NMDA-R-mediated [Ca2+] signaling, we used two-photon glutamate uncaging to stimulate NMDA-Rs on individual dendritic spines of CA1 pyramidal neurons in rat brain slices. We measured NMDA-R currents at the soma and NMDA-R-mediated [Ca2+] transients in stimulated spines (Delta[Ca2+]). Uncaging-evoked NMDA-R current amplitudes were independent of the size of the stimulated spine, implying that smaller spines contain higher densities of functional NMDA-Rs. The ratio of Delta[Ca2+] over NMDA-R current was highly variable (factor of 10) across spines, especially for small spines. These differences were not explained by heterogeneity in spine sizes or diffusional coupling between spines and their parent dendrites. In addition, we find that small spines have NMDA-R currents that are sensitive to NMDA-R NR2B subunit-specific antagonists. With block of NR2B-containing receptors, the range of Delta[Ca2+]/NMDA-R current ratios and their average value were much reduced. Our data suggest that individual spines can regulate the subunit composition of their NMDA-Rs and the effective fractional Ca2+ current through these receptors