Quasielastic Peak Research Articles

Empirical fits to inclusive electron-carbon scattering data obtained by deep-learning methods

Employing the neural network framework, we obtain empirical fits to the electron-scattering cross sections for carbon over a broad kinematic region, extending from the quasielastic peak through resonance excitation to the onset of deep-inelastic scattering. We consider two different methods of obtaining such model-independent parametrizations and the corresponding uncertainties: based on the bootstrap approach and the Monte Carlo dropout approach. In our analysis, the χ2 defines the loss function, including point-to-point and normalization uncertainties for each independent set of measurements. Our statistical approaches lead to fits of comparable quality and similar uncertainties of the order of 7%. To test these models, we compare their predictions to test datasets excluded from the training process and theoretical predictions obtained within the spectral function approach. The predictions of both models agree with experimental measurements and theoretical calculations. We also perform a comparison to a dataset lying beyond the covered kinematic region, and find that the bootstrap approach shows better interpolation and extrapolation abilities than the one based on the dropout algorithm. Published by the American Physical Society 2024

Collective dynamics of liquid sulphur across the polymerisation transition temperature probed by inelastic x-ray scattering

Inelastic x-ray scattering (IXS) experiments on liquid sulphur were carried out below (140 ∘C) and above (180 ∘C) the polymerisation temperature T λ of about 159 ∘C to investigate changes in the collective dynamics of this unique liquid, that exhibits a liquid–liquid transition. As reported earlier, broad longitudinal acoustic excitation signals were observed at both temperatures, and only the width of the quasielastic peaks slightly decreased when the temperature crossed the transition temperature. A model analysis was performed using a generalised Langevin formalism with a memory function having one thermal and two viscoelastic decay channels with the help of simple sparse modelling, and large positive deviations from the hydrodynamic sound velocity by 51%–54% were observed. The fast viscoelastic relaxation time τ µ is close to the correlation times of intermolecular stretching and bending motions of local sulphur connections in both ring and chain structures, and is similar to those of other molecular liquids. The small contrasts in the IXS spectra across the λ transition result in large changes in only the slow viscoelastic decay time τ α of the memory function. The τ α value at 140 ∘C matches the mixed internal/external torsional modes of S8 molecules well, whereas that at 180 ∘C has no corresponding molecular motion mode. The kinematic viscosity values at the Q→0 limit are much smaller than the minimum values of macroscopic shear viscosity, indicating that large changes in relaxation dynamics are expected with Q in the GHz and MHz excitation regimes.

Emergence of a Hidden Magnetic Phase in LaFe11.8Si1.2 Investigated by Inelastic Neutron Scattering as a Function of Magnetic Field and Temperature

AbstractThe NaZn13 type itinerant magnet LaFe13−xSix has seen considerable interest due to its unique combination of large magnetocaloric effect and low hysteresis. Here, this alloy with a combination of magnetometry, bespoke microcalorimetry, and inelastic neutron scattering is investigated. Inelastic neutron scattering reveals the presence of broad quasielastic scattering that persists across the magnetic transition, which is attributed to spin fluctuations. In addition, a quasielastic peak is observed at Q = 0.52 Å−1 for x = 1.2 that exists only in the paramagnetic state in proximity to the itinerant metamagnetic transition and argue that this indicates emergence of a hidden mag the netic phase that drives the first‐order phase transition in this system.

Electron Scattering on 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}He from Coupled-Cluster Theory

We present a coupled-cluster calculation for the electron-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}He scattering in the region of the quasi-elastic peak. We show the longitudinal and transverse responses separately, and discuss results within two distinct theoretical methods: the Lorentz integral transform and spectral functions. The comparison between them allows to investigate the role of final state interactions, two-body currents and relativistic effects.

Momentum Distribution Studies of Projectile Fragments from Peripheral Collisions Below the Fermi Energy

This paper presents our recent studies of multinucleon transfer in peripheral collisions in reactions below the Fermi regime. Our current focus is the study of the mass, angular and momentum distributions of the projectile-like fragments from the reaction of an 86Kr beam at 15 MeV/nucleon with a target of 64Ni. Experimental data from our previous work with the MARS spectrometer at the Cyclotron Institute of Texas A&M University were compared with model calculations. The dynamical stage of the reaction is described with either the Deep-Inelastic Transfer Model (DIT) or with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot projectile-like fragments is performed with the GEMINI model. The momentum distributions are characterized by a quasi-elastic peak and a deep-inelastic peak. Two-body kinematics was employed to extract the total excitation energies of these regions. Through the thorough study of peripheral reactions in the Fermi energy regime we expect to gain valuable information that could lead to the understanding of how the rare isotopes in regions such as the r-process path and the neutron drip line are formed and the reaction mechanism(s) that take place.

Signatures of the Δ isobar in spin observables of 3He electrodisintegration

The electrodisintegration of He3 is considered focusing on the effects of the Δ isobar excitation which is treated dynamically on the same footing as nucleons. In the region beyond the quasi-elastic peak the predicted transverse response functions RT and RT′ are visibly affected. This leads to sizable Δ isobar effects for inclusive and exclusive electron polarization asymmetries in particular kinematic regions. A measurement performed in the proposed regime could provide judgment for models of nuclear forces and currents.

Study of Multinucleon Transfer Mechanisms in 86Kr-Induced Peripheral Reactions at 15 and 25 MeV/nucleon

This paper presents our recent studies of the multinucleon transfer in peripheral collisions in reactions near the Fermi regime. Specifically, the reactions of a 86Kr beam at 15 MeV/nucleon with targets of 124Sn ,112Sn, 64Ni and 58Ni and reactions of a 86Kr beam at 25 MeV/nucleon with targets of 124Sn and 112Sn. The experimental data were obtained from the previous work of our group with the MARS spectrometer at the Cyclotron Institute of Texas A&M University. Our current focus is the thorough study of the experimental mass and momentum distributions of the projectile-like fragments. The momentum distributions are characterised by a narrow quasi-elastic peak and a broader deep-inelastic peak. We employed two-body kinematics to characterize the excitation energies of these reactions. We also compared the data with model calculations. The dynamical stage is described with either the Deep-Inelastic Transfer Model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot projectile-like fragments is performed with the Gemini model. Studying these reactions will provide us with a better understanding as to how the energy of the beam and the different targets affect the mechanism of the multinucleon transfer reactions. With the recent work, our continued efforts in the study of peripheral reactions in the Fermi energy regime delineate new opportunities to elucidate the reaction mechanism(s) of rare isotope production and may effectively contribute to the study of unexplored regions of the nuclear chart toward the r-process and the neutron drip line.

Spectral function for He4 using the Chebyshev expansion in coupled-cluster theory

We compute spectral function for $^{4}\mathrm{He}$ by combining coupled-cluster theory with an expansion of integral transforms into Chebyshev polynomials. Our method allows us to estimate the uncertainty of spectral reconstruction. The properties of the Chebyshev polynomials make the procedure numerically stable and considerably lower in memory usage than the typically employed Lanczos algorithm. We benchmark our predictions with other calculations in the literature and with electron-scattering data in the quasi-elastic peak. The spectral function formalism allows one to extend ab initio lepton-nucleus cross sections into the relativistic regime. This makes it a promising tool for modeling this process at higher-energy transfers. The results we present open the door for studies of heavier nuclei, important for the neutrino oscillation programs.

Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals

Luttinger semimetals represent materials with strong spin–orbit coupling, harboring doubly-degenerate quadratic band touchings at the Brillouin zone center. In the presence of Coulomb interactions, such a system exhibits a non-Fermi liquid phase [dubbed as the Luttinger–Abrikosov–Beneslavskii (LAB) phase], at low temperatures and zero doping. However, a clear experimental evidence of this emergent state remains elusive to this date. Hence, we focus on extracting the Raman response as a complementary experimental signature. At frequencies much larger than the temperature, the Raman response exhibits a power-law behavior, which can be verified experimentally. On the other hand, at lower frequencies, the Raman response displays a quasi-elastic peak. We also compute the ratio of the shear viscosity and the entropy density, and the value obtained is a consequence of the hyperscaling violation that emerges in the LAB phase.

Effects of nucleon-nucleon short-range correlations on inclusive electron scattering

The nucleon-nucleon short-range correlation (NN-SRC) is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this paper, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $(e,{e}^{\ensuremath{'}})$ cross sections are calculated within the plane-wave impulse approximation (PWIA) framework, including the quasielastic (QE) part and $\mathrm{\ensuremath{\Delta}}$ production part. Especially in the $\mathrm{\ensuremath{\Delta}}$ production region, we reconsider the electromagnetic structures of the nucleon resonance $\mathrm{\ensuremath{\Delta}}$(1232) and the scattering mechanisms, and thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $(e,{e}^{\ensuremath{'}})$ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $0.5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}<{Q}^{2}<1\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$, the QE peak and $\mathrm{\ensuremath{\Delta}}$ production peak not only reflect the mean-field structure but also are sensitive to the NN-SRC information. Finally, we provide another method to extract the strengths of NN-SRC from experimental cross sections for selected nuclei at the suitable kinematics.

Low-frequency Raman response near the Ising-nematic quantum critical point: A memory-matrix approach

Recent Raman scattering experiments have revealed a "quasi-elastic peak" in $\mathrm{FeSe_{1-x}S_x}$ near an Ising-nematic quantum critical point (QCP) \cite{zhang17}. Notably, the peak occurs at sub-temperature frequencies, and softens as $T^{\alpha}$ when temperature is decreased toward the QCP, with $\alpha>1$. In this work, we present a theoretical analysis of the low-frequency Raman response using a memory matrix approach. We show that such a quasi-elastic peak is associated with the relaxation of an Ising-nematic deformation of the Fermi surface. Specifically, we find that the peak frequency is proportional to $ \tau^{-1}\chi^{-1}$, where $\chi$ is the Ising-nematic thermodynamic susceptibility, and $\tau^{-1}$ is the decay rate of the nematic deformation due to an interplay between impurity scattering and electron-electron scattering mediated by critical Ising-nematic fluctuations. We argue that the critical fluctuations play a crucial role in determining the observed temperature dependence of the frequency of the quasi-elastic peak. At frequencies larger than the temperature, we find that the Raman response is proportional to $\omega^{1/3}$, consistently with earlier predictions \cite{klein18a}.

Nuclear Fermi momenta of 2H, 27Al and 56Fe from an analysis of CLAS data

Nuclear Fermi momentum is a basic property of a nucleus where many nucleons dwell. However, in experiments only the nuclear Fermi momenta of just a few nuclei are measured using quasielastic electron scattering on the nuclear targets so far. Particularly, we still do not know experimentally the Fermi momentum of the lightest nucleon composite – the deuteron. In this paper, we apply both gaussian distribution and Cauchy distribution to describe the quasielastic peak in the cross section of electron-nucleus scattering. The dip of the cross-section ratio at about xB=1 is explained with the nuclear Fermi momentum. By performing the least-square fits to the published CLAS data in the narrow kinematic region of quasielastic scattering, we obtain the nuclear Fermi momenta of 2H, 27Al and 56Fe, which are 116±7 MeV/c, 232±27 MeV/c, and 244±28 MeV/c respectively. The extracted nuclear Fermi momenta are compared to the simple calculations based on Fermi gas model, and the consistencies are found.

Fractional spin fluctuations and quantum liquid signature in Gd2ZnIrO6

Hitherto, the discrete identification of quantum spin liquid phase, holy grail of condensed matter physics, remains a challenging task experimentally. However, the precursor of quantum spin liquid state may reflect in the spin dynamics even in the paramagnetic phase over a wide temperature range as conjectured theoretically. Here we report comprehensive inelastic light (Raman) scattering measurements on the Ir based double perovskite, Gd2ZnIrO6, as a function of different incident photon energies and polarization in a broad temperature range. Our results evidenced the spin fractionalization within the paramagnetic phase reflected in the emergence of a polarization independent quasi-elastic peak at low energies with lowering temperature. Also, the fluctuating scattering amplitude measured via dynamic Raman susceptibility increases with lowering temperature and decreases mildly upon entering into long-range magnetic ordering phase, below 23 K, suggesting the magnetic origin of these fluctuations. This anomalous scattering response is thus indicative of fluctuating fractional spin evincing the quantum spin liquid phase in a three-dimensional double perovskite system.

AbInitio Computation of the Longitudinal Response Function in ^{40}Ca.

We present a consistent abinitio computation of the longitudinal response function R_{L} in ^{40}Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for R_{L} in ^{4}He and the Coulomb sum rule in ^{40}Ca against experimental data and other calculations. For R_{L} in ^{40}Ca we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards abinitio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

Destruction of long-range magnetic order in an external magnetic field and the associated spin dynamics in Cu2GaBO5 and Cu2AlBO5 ludwigites

The quantum spin systems Cu$_2$M'BO$_5$ (M' = Al, Ga) with the ludwigite crystal structure consist of a structurally ordered Cu$^{2+}$ sublattice in the form of three-leg ladders, interpenetrated by a structurally disordered sublattice with a statistically random site occupation by magnetic Cu$^{2+}$ and nonmagnetic Ga$^{3+}$ or Al$^{3+}$ ions. A microscopic analysis based on density-functional-theory calculations for Cu$_2$GaBO$_5$ reveals a frustrated quasi-two-dimensional spin model featuring five inequivalent antiferromagnetic exchanges. A broad low-temperature $^{11}$B nuclear magnetic resonance points to a considerable spin disorder in the system. In zero magnetic field, antiferromagnetic order sets in below $T_\text{N}$ $\approx$ 4.1 K and ~2.4 K for the Ga and Al compounds, respectively. From neutron diffraction, we find that the magnetic propagation vector in Cu$_2$GaBO$_5$ is commensurate and lies on the Brillouin-zone boundary in the (H0L) plane, $\mathbf{q}_\text{m}$ = (0.45 0 -0.7), corresponding to a complex noncollinear long-range ordered structure with a large magnetic unit cell. Muon spin relaxation is monotonic, consisting of a fast static component typical for complex noncollinear spin systems and a slow dynamic component originating from the relaxation on low-energy spin fluctuations. Gapless spin dynamics in the form of a diffuse quasielastic peak is also evidenced by inelastic neutron scattering. Most remarkably, application of a magnetic field above 1 T destroys the static long-range order, which is manifested in the gradual broadening of the magnetic Bragg peaks. We argue that such a crossover from a magnetically long-range ordered state to a spin-glass regime may result from orphan spins on the structurally disordered magnetic sublattice, which are polarized in magnetic field and thus act as a tuning knob for field-controlled magnetic disorder.

An event excess observed in the deeply bound region of the 12C (K−, p) missing-mass spectrum

Abstract We have measured, for the first time, the inclusive missing-mass spectrum of the $^{12}$C$(K^-, p)$ reaction at an incident kaon momentum of 1.8 GeV/$c$ at the J-PARC K1.8 beamline. We observed a prominent quasi-elastic peak ($K^-p \rightarrow K^-p$) in this spectrum. In the quasi-elastic peak region, the effect of secondary interaction is apparently observed as a peak shift, and the peak exhibits a tail in the bound region. We compared the spectrum with a theoretical calculation based on the Green’s function method by assuming different values of the parameters for the $\bar{K}$–nucleus optical potential. We found that the spectrum shape in the binding-energy region $-300 \, \text{MeV} < B_{K} < 40$ MeV is best reproduced with the potential depths $V_0 = -80$ MeV (real part) and $W_0 = -40$ MeV (imaginary part). On the other hand, we observed a significant event excess in the deeply bound region around $B_{K} \sim 100$ MeV, where the major decay channel of $K^- NN \to \pi\Sigma N$ is energetically closed, and the non-mesonic decay modes ($K^- NN \to \Lambda N$ and $\Sigma N$) should mainly contribute. The enhancement is fitted well by a Breit–Wigner function with a kaon-binding energy of 90 MeV and width 100 MeV. A possible interpretation is a deeply bound state of a $Y^{*}$-nucleus system.

Anomalous changes in the acoustic properties and central peak behaviors of PbxBa1−xNb2O6 single crystals with x = 0.5 studied by Brillouin spectroscopy

The acoustic properties of tetragonal PbxBa1−xNb2O6 (PBN-x) single crystals with x = 0.5 were studied by Brillouin spectroscopy over a wide temperature range from room temperature to 600 °C. Anomalous changes in the Brillouin frequency shift and the half width of acoustic waves were observed at ∼350 °C that corresponds to the ferroelectric–paraelectric phase transition temperature of PBN-0.50. The longitudinal sound velocity and its associated elastic constant (C33) showed substantial softening in the paraelectric phase when the phonon propagated along the polar c axis, while their degree of softening for the phonon along the a axis was small, revealing clear acoustic anisotropy. It was associated with the strong polarization dependence of the quasi-elastic central peak. The relaxation time derived from the central peak seemed to follow the critical slowing-down behavior indicating order–disorder nature of the phase transition. Among C44 and C66, the former displayed substantial softening in the ferroelectric phase resembling the order parameter behavior. The longitudinal sound velocity and the related acoustic damping showed significant anomalies in the ferroelectric phase of unpoled PBN-0.5, which disappeared completely under poled condition. The possible origin for these unexpected acoustic anomalies was suggested.

Electron- versus neutrino-nucleus scattering

We illustrate the connection between electron and neutrino scattering off nuclei and show how the former process can be used to constrain the description of the latter. After reviewing some of the nuclear models commonly used to study lepton-nucleus reactions, we describe in detail the SuSAv2 model and show how its predictions compare with the available electron- and neutrino-scattering data over the kinematical range going from the quasi-elastic peak to pion-production and highly inelastic scattering.

Double-Differential FRaGmentation (DDFRG) models for proton and light ion production in high energy nuclear collisions

A new set of Double-Differential FRaGmentation (DDFRG) models for proton and light ion production from high energy nucleus–nucleus collisions, relevant to space radiation, is introduced. The proton model employs thermal production from the projectile, central fireball and target sources, as well as quasi-elastic direct knockout production. The light ion model uses a hybrid coalescence model. The data show a prominent quasi-elastic peak at small angles which becomes highly suppressed at large angles. The models are able to describe this wide range of experimental data with only a limited set of model parameters. Closed form analytic formulas for double-differential energy and angle cross-sections as well as single-differential spectral cross-sections are developed. These analytic formulas enable highly efficient computation for radiation transport codes.

Nucleon momentum distribution extracted from the experimental scaling function

The connection between the scaling function, directly extracted from the analysis of electron scattering data, and the nuclear spectral function or nuclear momentum density is investigated at depth. The dependence of the scaling function on the two independent variables in the scattering process, the transfer momentum (q) and the scaling variable (y), is taken into account, and the analysis is extended to both, positive and negative y-values, i.e., below and above the center of the quasielastic peak, respectively. Analytical expressions for the derivatives of the scaling function, evaluated at the finite limits of integration dealing with the kinematically allowed region, are connected with the spectral function. Here, contributions corresponding to zero and finite excitation energies are included. The scaling function is described by the Gumbel density distribution, whereas short-range correlations are incorporated in the spectral function by using some simple models. Also different parameterizations for the nucleon momentum distribution, that are compatible with the general properties of the scaling function, have been considered.