Superscaling and Neutral Current Quasielastic Neutrino-Nucleus Scattering beyond the Relativistic Fermi Gas Model

The superscaling analysis is extended to include quasielastic (QE) scattering via the weak neutral current of neutrinos and antineutrinos from nuclei. The scaling function obtained within the coherent density fluctuation model (used previously in calculations of QE inclusive electron and charge-changing (CC) neutrino scattering) is applied to neutral current neutrino and antineutrino scattering with energies of 1 GeV from $^{12}$C with a proton and neutron knockout (u-channel inclusive processes). The results are compared with those obtained using the scaling function from the relativistic Fermi gas model and the scaling function as determined from the superscaling analysis (SuSA) of QE electron scattering.Comment: 10 pages, 6 figures, published in Phys. Rev.

Superscaling in dilute Fermi gas and its relation to general properties of the nucleon momentum distribution in nuclei

The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function $f(\psi ')$ in the region $\psi ' < -1$, where the RFG result is $f(\psi ') = 0$. It is found that the behavior of $f(\psi ')$ for $\psi ' < -1$ depends on the particular form of the general power-law asymptotics of the momentum distribution $n(k)\sim 1/ k^{4+m}$ at large $k$. The best agreement with the empirical scaling function is found for $m\simeq 4.5$ in agreement with the asymptotics of $n(k)$ in the coherent density fluctuation model where $m = 4$. Thus, superscaling gives information about the asymptotics of $n(k)$ and the NN forces.Comment: 6 pages, 5 figures, accepted for publication in Physical Review

Scaling Functions and Superscaling in Medium and Heavy Nuclei

The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron scaling functions. The latter are calculated in the cases of $^{62}$Ni, $^{82}$Kr, $^{118}$Sn, and $^{197}$Au nuclei on the basis of the corresponding proton and neutron density distributions which are obtained in deformed self-consistent mean-field Skyrme HF+BCS method. The results are in a reasonable agreement with the empirical data from the inclusive electron scattering from nuclei showing superscaling for negative values of $\psi'$, including those smaller than -1. This is an improvement over the relativistic Fermi gas (RFG) model predictions where $f(\psi')$ becomes abruptly zero for $\psi'\leq -1$. It is also an improvement over the CDFM calculations made in the past for nuclei with $Z\neq N$ assuming that the neutron density is equal to the proton one and using only the phenomenological charge density.Comment: 4 pages, 1 figure, ReVTeX, accepted for publication in Phys. Rev.

Superscaling in Nuclei: A Search for Scaling Function Beyond the Relativistic Fermi Gas Model

We construct a scaling function $f(\psi^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $\psi^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental data for different transfer momenta showing superscaling for negative values of $\psi^{\prime}$, including those smaller than -1.Comment: 16 pages, 5 figures, submitted for publication to Phys. Rev.

About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage case, when the number of patterns is linearly diverging with the number of neurons. We study the infinite volume behavior of the normalized momenta of the partition function. We find a region in the parameter space where the free energy density in the infinite volume limit is self-averaging around its annealed approximation, as well as the entropy and the internal energy density. Moreover, we evaluate the corrections to their extensive counterparts with respect to their annealed expressions. The fluctuations of properly introduced overlaps, which act as order parameters, are also discussed.Comment: 15 page

Scaling Function, Spectral Function and Nucleon Momentum Distribution in Nuclei

The link between the scaling function extracted from the analysis of (e,e') cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent particle model are employed, together with the inclusion of nucleon correlations, and effects of the energy dependence arising from the width of the hole states are investigated. Although some of these approaches provide rough overall agreement with data, they are not found to be capable of reproducing one of the distinctive features of the experimental scaling function, namely its asymmetry. However, the addition of final-state interactions, incorporated in the present study using either relativistic mean field theory or via a complex optical potential, does lead to asymmetric scaling functions in accordance with data. The present analysis seems to indicate that final-state interactions constitute an essential ingredient and are required to provide a proper description of the experimental scaling function.Comment: 29 pages, 13 figures, accepted for publication in Physical Review

Charge and matter distributions and form factors of light, medium and heavy neutron-rich nuclei

Results of charge form factors calculations for several unstable neutron-rich isotopes of light, medium and heavy nuclei (He, Li, Ni, Kr, Sn) are presented and compared to those of stable isotopes in the same isotopic chain. For the lighter isotopes (He and Li) the proton and neutron densities are obtained within a microscopic large-scale shell-model, while for heavier ones Ni, Kr and Sn the densities are calculated in deformed self-consistent mean-field Skyrme HF+BCS method. We also compare proton densities to matter densities together with their rms radii and diffuseness parameter values. Whenever possible comparison of form factors, densities and rms radii with available experimental data is also performed. Calculations of form factors are carried out both in plane wave Born approximation (PWBA) and in distorted wave Born approximation (DWBA). These form factors are suggested as predictions for the future experiments on the electron-radioactive beam colliders where the effect of the neutron halo or skin on the proton distributions in exotic nuclei is planned to be studied and thereby the various theoretical models of exotic nuclei will be tested.Comment: 26 pages, 11 figures, 3 tables, accepted for publication in Phys. Rev.

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

Analysis of time-profiles with in-beam PET monitoring in charged particle therapy

Background: Treatment verification with PET imaging in charged particle therapy is conventionally done by comparing measurements of spatial distributions with Monte Carlo (MC) predictions. However, decay curves can provide additional independent information about the treatment and the irradiated tissue. Most studies performed so far focus on long time intervals. Here we investigate the reliability of MC predictions of space and time (decay rate) profiles shortly after irradiation, and we show how the decay rates can give an indication about the elements of which the phantom is made up. Methods and Materials: Various phantoms were irradiated in clinical and near-clinical conditions at the Cyclotron Centre of the Bronowice proton therapy centre. PET data were acquired with a planar 16x16 cm$^2$ PET system. MC simulations of particle interactions and photon propagation in the phantoms were performed using the FLUKA code. The analysis included a comparison between experimental data and MC simulations of space and time profiles, as well as a fitting procedure to obtain the various isotope contributions in the phantoms. Results and conclusions: There was a good agreement between data and MC predictions in 1-dimensional space and decay rate distributions. The fractions of $^{11}$C, $^{15}$O and $^{10}$C that were obtained by fitting the decay rates with multiple simple exponentials generally agreed well with the MC expectations. We found a small excess of $^{10}$C in data compared to what was predicted in MC, which was clear especially in the PE phantom.Comment: 9 pages, 5 figures, 1 table. Proceedings of the 20th International Workshop on Radiation Imaging Detectors (iWorid2018), 24-28 June 2018, Sundsvall, Swede