Nuclear Response Functions Research Articles

Neutrino quasielastic interaction and nuclear dynamics

We investigate the double differential neutrino-carbon quasielastic cross sections as measured by the MiniBooNE experiment. Our present treatment incorporates relativistic corrections in the nuclear response functions and includes the multinucleon component. We confirm our previous conclusion that it is possible to account for all the data without any modification of the axial mass. We also introduce the ${Q}^{2}$ distribution for charged and neutral current. The data point at a sizable multinucleon component beside the genuine quasielastic peak. They are also indicative of the collective character of the nuclear response, of interest for hadronic physics.

Effects of self-consistency in semiclassical pairing theory

An extended Vlasov equation, derived from the time-dependent Hartree–Fock–Bogoliubov equation of motion, is used to study the effects of pairing on the nuclear density-density linear response function in semiclassical approximation. Within the approximations adopted here, the fluctuations of the pairing field are purely imaginary and play a crucial role in eliminating a spurious mode that gives fluctuations of the number of particle and in reproducing the correct value of the energy-weighted sum rule. The semiclassical approach seems to have some difficulty in describing pairing vibrations. Further work on this problem is needed.

Nuclear effects in neutrino-nucleus interactions

An accurate description of the nuclear response functions for neutrino scattering in the Gev region is essential for the interpretation of present and future neutrino oscillation experiments. Due to the close similarity of electromagnetic and weak scattering processes, we will review the status of the scaling approach and of relativistic modeling for the inclusive electron scattering response functions in the quasielastic and Δ-resonance regions. In particular, recent studies have been focused on scaling violations and the degree to which these imply modifications of existing predictions for neutrino reactions. We will discuss sources and magnitude of such violations, emphasizing similarities and differences between electron and neutrino reactions.

Extended Skyrme interaction: I. Spin fluctuations in dense matter

Most of the Skyrme interactions are known to predict spin or isospin instabilities beyond the saturation density of nuclear matter which contradict predictions based on realistic interactions. A modification of the standard Skyrme interaction is proposed so that the ferromagnetic instability is removed. The new terms are density dependent and modify only the spin p–h interaction in the case of a spin-saturated system. Consequences for the nuclear response function and neutrino mean free path are shown. The overall effect of the RPA correlations makes dense matter more transparent for neutrino propagation by a factor of 2 to 10 depending on the density.

Nuclear response for the Skyrme effective interaction with zero-range tensor terms

The effects of a zero-range tensor component of the effective interaction on nuclear response functions are determined in the random phase approximation approach. Explicit formulas in the case of symmetric homogeneous isotropic nuclear matter are given for each spin-isospin excitation channel. It is shown for a typical interaction with tensor couplings that the effects are quantitatively important, mainly in vector channels.

Continued fraction approximation for the nuclear matter response function

A continued fraction approximation is used to calculate the Random Phase Approximation (RPA) response function of nuclear matter. The convergence of the approximation is assessed by comparing it with the numerically exact response function obtained with a typical effective finite-range interaction used in nuclear physics. It is shown that just the first order term of the expansion can give reliable results at densities up to the saturation density value.

Nuclear analyses for the ITER ECRH launcher

Computational results of the nuclear analyses for the ECRH launcher integrated into the ITER upper port are presented. The purpose of the analyses was to provide the proof for the launcher design that the nuclear requirements specified in the ITER project can be met. The aim was achieved on the basis of 3D neutronics radiation transport calculations using the Monte Carlo code MCNP. In the course of the analyses an adequate shielding configuration against neutron and gamma radiation was developed keeping the necessary empty space for mm-waves propagation in accordance with the ECRH physics guidelines. Different variants of the shielding configuration for the extended performance front steering launcher (EPL) were compared in terms of nuclear response functions in the critical positions. Neutron damage (dpa), nuclear heating, helium production rate, neutron and gamma fluxes have been calculated under the conditions of ITER operation. It has been shown that the radiation shielding criteria are satisfied and the supposed shutdown dose rates are below the ITER nuclear design limits.

Intermolecular polarizability dynamics of aqueous formamide liquid mixtures studied by molecular dynamics simulations

A molecular dynamics simulation study is presented for the relaxation of the polarizability anisotropy in liquid mixtures of formamide and water, using a dipolar induction scheme that involves the intrinsic polarizability and first hyperpolarizability tensors of the molecules, and the dipole-quadrupole polarizability of water species. The long time diffusive decay of the collective polarizability anisotropy correlations exhibits a substantial slowing down as the formamide mole fraction increases in the mixture. The diffusive times for the polarizability relaxation obtained from the authors' simulations are in good agreement with optical Kerr effect experimental data, and they are found to correlate nearly linearly with the estimated mean lifetimes of the hydrogen bonds within the mixture, suggesting that the relaxation of the hydrogen bond network is responsible to some extent for the collective relaxation of the polarizability anisotropy of the mixture. The short time behavior of the polarizability anisotropy relaxation was investigated by computing the nuclear response function, R(t), which is very rapidly dominated by the formamide contribution as it is added to water, due to the much larger polarizability anisotropy of formamide molecules compared to that of water. Several contributions to the Raman spectrum were also analyzed as a function of composition, and the dynamical origin of the different bands was determined.

Effects of spin-orbit interaction on nuclear response and neutrino mean free path

The effects of the spin-orbit component of the particle-hole interaction on nuclear response functions and neutrino mean free path are examined. A complete treatment of the full Skyrme interaction in the case of symmetric nuclear matter and pure neutron matter is given. Numerical results for neutron matter are discussed. It is shown that the effects of the spin-orbit interaction remain small, even at momentum transfer larger than the Fermi momentum. The neutrino mean free paths are marginally affected.

Effects of Molecular Association on Polarizability Relaxation in Liquid Mixtures of Benzene and Hexafluorobenzene

In this work we have studied the relaxation dynamics of the many-body polarizability anisotropy in liquid mixtures of benzene (Bz) and hexafluorobenzene (Hf) at room temperature by femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) experiments and molecular dynamics (MD) simulations. The computed polarizability response arising from intermolecular interactions was included using the first-order dipole-induced-dipole model with the molecular polarizability distributed over the carbon sites of each molecule. We found good qualitative agreement between experiments and simulations in the features exhibited by the nuclear response function R(t) for pure liquids and mixtures. The long-time diffusive decay of R(t) was observed to vary substantially with composition, slowing down noticeably with dilution of each of the species as compared with that in the corresponding pure liquids. MD simulation shows that the effect on R(t) is due to the formation of strong and localized intermolecular association between Bz and Hf species that hinder the rotational diffusive dynamics. The formation of these Bz-Hf complexes in the liquid mixtures also modifies the rotational diffusive dynamics of the component species in such a way that cannot be explained solely in terms of a viscosity effect. Even though the computed orientational diffusive relaxation times associated with Bz and Hf are larger by a factor of approximately 2 than those from experiments, we found similar trends in experiments and simulations for these characteristic times as a function of composition. Namely, the collective and single-molecule orientational correlation times associated with Bz are observed to grow monotonically with the dilution of Bz, while those corresponding to Hf species exhibit a maximum at the equimolar composition. We attribute the quantitative discrepancy between experiments and simulations to the use of the Williams potential, which seems to overestimate the intermolecular interactions and thus predicts not only a slower translational dynamics but also a slower rotational diffusion dynamics than in real fluids.

Nuclear response functions in homogeneous matter with finite range effective interactions

The question of nuclear response functions in a homogeneous medium is examined. A general method for calculating response functions in the random-phase approximation with exchange is presented. The method is applicable for finite-range nuclear interactions. Examples are shown in the case of symmetric nuclear matter described by a Gogny interaction. It is found that the convergence of the results with respect to the multipole truncation is quite fast. Various approximation schemes such as the Landau approximation, or the Landau approximation for the exchange terms only, are discussed in comparison with the exact results.

Relations among several nuclear and electronic density functional reactivity indexes

An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the “Quantum Chemical le Chatelier Principle.” Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.

The 2p–2h electromagnetic response in the quasielastic peak and beyond

The contribution to the nuclear transverse response function R T arising from two particle–two hole (2p–2h) states excited through the action of electromagnetic meson exchange currents (MEC) is computed in a fully relativistic framework. The MEC considered are those carried by the pion and by Δ degrees of freedom, the latter being viewed as a virtual nucleonic resonance. The calculation is performed in the relativistic Fermi gas model in which Lorentz covariance can be maintained. All 2p–2h many-body diagrams containing two pionic lines that contribute to R T are taken into account and the relative impact of the various components of the MEC on R T is addressed. The non-relativistic limit of the MEC contributions is also discussed and compared with the relativistic results to explore the role played by relativity in obtaining the 2p–2h nuclear response.

A Novel Technique for the Measurement of Polarization-Specific Ultrafast Raman Responses

A simple time domain method for the observation of polarization-specific Raman responses in electronically nonresonant materials is demonstrated. When a cutoff filter is placed in the probe beam path before the detector in the conventional pump−probe configuration, the in-phase dichroic optical heterodyne-detected (OHD) response is enhanced as compared to the usual putative corresponding dichroic response observed when the probe is not dispersed. The ultrafast excited OHD responses of CS2 obtained by this method are reported for parallel, perpendicular, and magic angle relative orientations of pump and probe pulse polarizations. The observed dispersed dichroic signal can be derived from the real part alone of the third-order nuclear response function. The decay of the CS2 isotropic response is found to be dominated by a ∼500 fs decay process for times longer than ∼0.7 ps. This relaxation time scale matches the nondiffusive exponential decay seen in the birefringent and dichroic anisotropic responses of CS2. Calculated instantaneous normal mode (INM) isotropic and anisotropic nuclear response functions are found to exhibit exponential decays in this same 500−600 fs time scale, suggesting that this decay component may be predominantly determined by the distribution of Raman-weighted density of states.

Fifth-order electronically non-resonant Raman scattering: two-dimensional Fourier deconvolution

This paper presents an analytical Fourier deconvolution procedure for homodyne detected electronically non-resonant fifth-order signal that reveals the bare nuclear response function free from the influence of the electronic (hyperpolarizability) responses generated by the five potentially overlapping finite duration pulses used in the experiment. In developing the fifth-order deconvolution procedure, an analogous procedure for homodyne detected third-order responses is elaborated. The potential implementation problems with the homodyne deconvolution procedure are evaluated through comparison of the third-order homodyne deconvolution result with that of the well-known third-order heterodyne deconvolution. Then, the homodyne deconvolution is extended to fifth-order where it is used on several measured tensor elements of the direct fifth-order signal. Suggestions are given for improving implementation of the procedure in fifth order so that more information on the direct fifth-order nuclear response as well as the hyperpolarizability responses can be recovered via the deconvolution procedure.

Time-domain separation of nuclear and electronic contributions to the third-order nonlinearity in glasses

The electronic and nuclear contributions to the third-order nonlinearity of glasses are separated by use of 100-fs pulses in a time-resolved heterodyne optical Kerr effect technique. A direct estimate of the relative strengths of electronic and nuclear contributions was made by the comparison between the nuclear contribution deduced from the Raman spectra with the Kerr signal. The ratio between the electronic and nuclear response functions was ∼5/1 in a tellurium oxide glass sample. The time evolution of the nuclear contribution is in good agreement with results deduced from the Raman spectra.

The Migdal jump in the nucleon momentum distribution in nuclear matter is determined by the spin-isospin response function

The renormalization factor Z of the single-particle Green’s function in nuclear matter, equal to the jump in the nucleon momentum distribution (“Migdal jump”), is expressed in terms of the nuclear response function, using approximations that are realistic for nuclear physics. It is shown that the spin-isospin channel makes the dominant contribution to Z.

Nuclear response in electron scattering at high momentum transfer

Nuclear response functions for high energy electron scattering were calculated over a wide region of excitation energies. Three typical regions were studied: the quasi-elastic region, the Δ-excitation region, and the intermediate region where the meson-exchange currents make significant for finite-size nuclei by taking into account relativistic kinematics. Contributions from meson-exchange currents were calculated in the relativistic Fermi-gas model. The results were compared with electron scattering data from 12C and 16O at high momentum transfer.

Antisymmetrized random phase approximation for quasi-elastic scattering in nuclear matter: Non-relativistic potentials

Many-body techniques for the calculation of quasi-elastic nuclear matter response functions in the fully antisymmetrized random phase approximation on a Hartree-Fock basis are discussed in detail. The methods presented here allow for an accurate evaluation of the response functions with little numerical effort. Formulae are given for a generic non-relativistic potential parameterized in terms of meson exchanges; on the other hand, relativistic kinematical effects have been accounted for.

Inelastic nucleon contributions in(e,e′)nuclear response functions

We estimate the contribution of inelastic nucleon excitations to the $(e,e^\prime)$ inclusive cross section in the CEBAF kinematic range. Calculations are based upon parameterizations of the nucleon structure functions measured at SLAC. Nuclear binding effects are included in a vector-scalar field theory, and are assumed have a minimal effect on the nucleon excitation spectrum. We find that for $q\lsim 1$ GeV the elastic and inelastic nucleon contributions to the nuclear response functions are comparable, and can be separated, but with roughly a factor of two uncertainty in the latter from the extrapolation from data. In contrast, for $q\rsim 2$ GeV this uncertainty is greatly reduced but the elastic nucleon contribution is heavily dominated by the inelastic nucleon background.