Nuclear Hydrodynamics in a Relativistic Mean Field Theory

Paper by J. D. Waleck

General study of superscaling in quasielastic (e,e′)(e,e') and (ν,μ)(\nu,\mu) reactions using the relativistic impulse approximation

The phenomenon of superscaling for quasielastic lepton induced reactions at energies of a few GeV is investigated within the framework of the relativistic impulse approximation. A global analysis of quasielastic inclusive electron and charged-current neutrino scattering reactions on nuclei is presented. Scaling and superscaling properties are shown to emerge from both types of processes. The crucial role played by final state interactions is evaluated by using different approaches. The asymmetric shape presented by the experimental scaling function, with a long tail in the region of positive values of the scaling variable, is reproduced when the interaction in the final state between the knockout nucleon and the residual nucleus is described within the relativistic mean field approach. The impact of gauge ambiguities and off-shell effects in the scaling function is also analyzed.Comment: 34 pages, 14 figures, accepted in Phys. Rev. C. Section II has been shortene

Neutral-current neutrino-nucleus cross sections based on relativistic nuclear energy density functional

Background: Inelastic neutrino-nucleus scattering through the weak neutral-current plays important role in stellar environment where transport of neutrinos determine the rate of cooling. Since there are no direct experimental data on neutral-current neutrino-nucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations. Purpose: To establish fully self-consistent framework for neutral-current neutrino-nucleus reactions based on relativistic nuclear energy density functional. Methods: Neutrino-nucleus cross sections are calculated using weak Hamiltonian and nuclear properties of initial and excited states are obtained with relativistic Hartree-Bogoliubov model and relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions. Results: Inelastic neutral-current neutrino-nucleus cross sections for 12C, 16O, 56Fe, 56Ni, and even isotopes {92-100}Mo as well as respective cross sections averaged over distribution of supernova neutrinos. Conclusions: The present study provides insight into neutrino-nucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic self-consistent large-scale calculations involving open-shell target nuclei.Comment: 25 pages, 9 figures, 2 tables, submitted to Physical Review

Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory

I study an aspect of chiral perturbation theory (\chi PT) which enables one to ``bridge'' different reactions. That is, an operator fixed in one of the reactions can then be used to predict the other. For this purpose, I calculate the partial wave amplitude for the p-wave pion production (pp\to pn\pi^+) using the pion production operator from the lowest and the next nonvanishing orders. The operator includes a contact operator whose coupling has been fixed using a matrix element of a low-energy weak process (pp\to de^+\nu_e). I find that this operator does not reproduce the partial wave amplitude extracted from experimental data, showing that the bridging over the reactions with significantly different kinematics is not necessarily successful. I study the dependence of the amplitude on the various inputs such as the NN potential, the \pi N\Delta coupling, and the cutoff. I argue the importance of a higher order calculation. In order to gain an insight into a higher order calculation, I add a higher order counter term to the operator used above, and fit the couplings to both the low-energy weak process and the pion production. The energy dependence of the partial wave amplitude for the pion production is described by the operator consistently with the data. However, I find a result which tells us to be careful about the convergence of the chiral expansion for the pp\to pn\pi^+ reaction.Comment: 30 pages, 13 figures, figures changed, compacted tex

Influence of quark boundary conditions on the pion mass in finite volume

We calculate the mass shift for the pion in a finite volume with renormalization group (RG) methods in the framework of the quark-mesons model. In particular, we investigate the importance of the quark effects on the pion mass. As in lattice gauge theory, the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes, in addition to the shift due to pion interactions. We compare our results to chiral perturbation theory calculations and find differences due to the fact that chiral perturbation theory only considers pion effects in the finite volume.Comment: 24 pages, 5 figures, RevTex4, published version, discussion of lattice results extende

Muon Capture on Deuteron and 3He: A Personal Review

The present status of theoretical and experimental studies of muon capture reactions on light nuclei is reviewed. In particular, the recent results for the two reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H are presented, and the unresolved discrepancies among different measurements and calculations, open problems, and future developments are discussed.Comment: 19 pages, submitted to International Journal of Modern Physics

Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation

Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.Comment: 28 pages, 8 figures, 2 tables, submitted to Phys. Rev.

Superscaling in electroweak excitation of nuclei

Superscaling properties of 12C, 16O and 40Ca nuclear responses, induced by electron and neutrino scattering, are studied for momentum transfer values between 300 and 700 MeV/c. We have defined two indexes to have quantitative estimates of the scaling quality. We have analyzed experimental responses to get the empirical values of the two indexes. We have then investigated the effects of finite dimensions, collective excitations, meson exchange currents, short-range correlations and final state interactions. These effects strongly modify the relativistic Fermi gas scaling functions, but they conserve the scaling properties. We used the scaling functions to predict electron and neutrino cross sections and we tested their validity by comparing them with the cross sections obtained with a full calculation. For electron scattering we also made a comparison with data. We have calculated the total charge-exchange neutrino cross sections for neutrino energies up to 300 MeV.Comment: 19 pages, 12 figures, 1 table; to be published in Physical Review

Strange-quark contribution to the ratio of neutral- to charged-current cross sections in neutrino-nucleus scattering

A formalism based on a relativistic plane wave impulse approximation is developed to investigate the strange-quark content ($g_{A}^{s}$) of the axial-vector form factor of the nucleon via neutrino-nucleus scattering. Nuclear structure effects are incorporated via an accurately calibrated relativistic mean-field model. The ratio of neutral- to charged-current cross sections is used to examine the sensitivity of this observable to $g_{A}^{s}$. For values of the incident neutrino energy in the range proposed by the FINeSSE collaboration and by adopting a value of $g_{A}^{s}=-0.19$, a 30% enhancement in the ratio is observed relative to the $g_{A}^{s}=0$ result.Comment: 20 pages, 6 figures, Revtex, Submitted to Phys. Rev.