Lepton Scattering off Few-Nucleon Systems at Medium and High Energies
C. Ciofi degli Atti, L. P. Kaptari, H. Morita
备注：
6 pages, 3 figures. Plenary talk given by C. Ciofi degli Atti at the XX European Conference "Few Body Problems in Physics", Pisa, Italy, September 2007. To appear in Few-Body Systems
The interpretation of recent Jlab experimental data on the exclusive process A(e,e'p)B off few-nucleon systems are analyzed in terms of realistic nuclear wave functions and Glauber multiple scattering theory, both in its original form and within a generalized eikonal approximation. The relevance of the exclusive process 4He(e,e'p)^3H for possible investigations of QCD effects is illustrated.
The possible role played by vector mesons in inclusive deep inelastic lepton-nucleon scattering is investigated. In the context of the convolution model, we calculate self-consistently the scaling contribution to the nucleon structure function using the formalism of time-ordered perturbation theory in the infinite momentum frame. Our results indicate potentially significant effects only when the vector meson---nucleon form factor is very hard. Agreement with the experimental antiquark distributions, however, requires relatively soft form factors for the $πN$, $ρN$ and $ωN$ vertices.
The two nucleon emission process off ^3He induced by medium energy electrons has been theoretically analyzed using realistic three-nucleon wave functions and taking the final state interaction into account. Various kinematical conditions have been considered in order to clarify the question whether the effects of the final state interaction could be minimized by a proper choice of the kinematics.
Within the framework of the improved quantum molecular dynamics model, the medium modifications on the free nucleon-nucleon elastic cross sections are investigated. By using various in-medium nucleon-nucleon elastic cross sections in the model, the nucleon-induced reactions on various targets are simulated, and the excitation functions of reaction cross sections in the energy range from 25 MeV to 1 GeV are calculated. By comparing the calculations with the experimental data, an isospin, density, and momentum-dependence medium correction factor on free nucleon-nucleon elastic cross sections is …
We discuss multi-hadron production in both inelastic neutrino-nucleon interactions in the current fragmentation region and neutrino-nucleus collisions in the target fragmentation region. Our analysis, carried out within the framework of the quark-gluon string model, is mainly focused on the difference between these two processes. We show that the $Q^2$ dependence of hadron multiplicity in the current and target fragmentation regions is indeed completely different. The study of inelastic $ν-A$ scattering in the target fragmentation region also provides new information on nuclear structure at sm…
The lowest-order correction of the density dependence of in-medium nucleon-nucleon cross sections is obtained from geometrical considerations of Pauli-blocking effects. As a by-product, it is shown that the medium corrections imply an 1/E energy dependence of the density-dependent term.
The article of Pastore et al, while proposing an interesting and potentially useful approach for the generalisation of Quantum Monte Carlo techniques to the treatment of the nuclear electromagnetic response, features an incorrect and misleading discussion of y-scaling. The response to interactions with transversely polarised virtual photons receives sizeable contributions from non-scaling processes, in which the momentum transfer is shared between two nucleons. It follows that, contrary to what is stated by the the authors, y-scaling in the transverse channel is accidental.
Next-to-Leading-Order (NLO) effects play a crucial role in tests of the Standard Model (SM), and require careful theoretical evaluation. Electroweak physics, which has just entered the precision age, is an excellent place to search for new physics, but also requires considerable theoretical input. We show how we applied computational packages such as FeynArts, FormCalc, Form and LoopTools for the evaluation of one-loop electroweak and hadronic radiative corrections.
The influence of medium correction from an isospin dependent nucleon nucleon cross section on the fragmentation and nucleon emission in the intermediate energy heavy ion collisions was studied by using an isospin dependent quantum molecular dynamical model (IQMD). We found that the medium correction enhances the dependence of multiplicity of intermediate mass fragment $N_{imf}$ and the number of nucleon emission $N_{n}$ on the isospin effect of the nucleon nucleon cross section,while the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the med…
Based on an isospin dependent quantum molecular dynamics model we studied the influence of a medium correction of an isospin dependent nucleon nucleon cross section on the fragmentation at the intermediate energy heavy ion collisions. We found that the medium correction from an isospin dependent nucleon nucleon cross section increases the dependence of the fragmentation on the isospin effect of in-medium nucleon nucleon cross section, at the same time, the momentum dependent interaction (MDI) produces also an important role for enhancing the influence of the medium correction on the isospin ef…
We derive in-medium nucleon-nucleon (NN) cross sections in a microscopic model. Our calculations are based upon the Bonn NN potential and the Dirac-Brueckner approach for nuclear matter. We consider energies up to 300 MeV (in the laboratory frame) and densities up to twice nuclear matter density. Our results deviate substantially from cross section parametrizations that are commonly used in the nuclear medium.
We present a formalism to solve the Bethe-Goldstone scattering equation without the use of partial wave expansion which is alternative to the one we developed in a previous work. The present approach is more suitable for the calculation of in-medium nucleon-nucleon cross sections, which are the focal point of this paper. The impact of removing the spherical approximation on the angle and energy dependence of, particularly, in-medium proton-proton and proton-neutron differential cross sections is discussed along with its potential implication.
The effects of the symmetry potential and the isospin dependent in-medium nucleon-nucleon (NN) cross section on the number of proton(neutron) emissions N$_p(N_n$) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N$_p(N_n$) but N$_p(N_n$) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies.We propose to make use of the N$_p(N_n$) as a probe to extract information on the isospin dependent in-medium NN cr…
The in-medium nucleon-nucleon cross section is calculated starting from the thermodynamic T-matrix at finite temperatures. The corresponding Bethe-Salpeter-equation is solved using a separable representation of the Paris nucleon-nucleon-potential. The energy-dependent in-medium N-N cross section at a given density shows a strong temperature dependence. Especially at low temperatures and low total momenta, the in-medium cross section is strongly modified by in-medium effects. In particular, with decreasing temperature an enhancement near the Fermi energy is observed. This enhancement can be dis…
We present updated predictions of effective elastic nucleon-nucleon cross sections intended for use in nucleus-nucleus reactions. A novel characteristic of the present approach combines all microscopic medium effects included in the Dirac-Brueckner-Hartree-Fock G-matrix with a Pauli blocking mechanism which is more appropriate for applications in ion-ion reaction models as compared to a previous approach. The effective in-medium cross section is found to be quite sensitive to the description of Pauli blocking in the final configurations.
We report quantum Monte Carlo calculations of single-$Λ$ hypernuclei for $A<50$ based on phenomenological two- and three-body hyperon-nucleon forces. We present results for the $Λ$ separation energy in different hyperon orbits, showing that the accuracy of theoretical predictions exceeds that of currently available experimental data, especially for medium-mass hypernuclei. We show the results of a sensitivity study that indicates the possibility to investigate the nucleon-isospin dependence of the three-body hyperon-nucleon-nucleon force in the medium-mass region of the hypernuclear chart, whe…
Semi-inclusive deep inelastic lepton scattering off few-nucleon systems is investigated assuming that virtual boson absorption occurs on a hadronic cluster which can be either a two-nucleon correlated pair or a six-quark bag. In both cases the relevance of nuclear effects on forward and backward nucleon emissions is illustrated and the differences expected in the energy distribution of the emitted nucleons are analyzed both at x>1 and x<1.
Several observables of unbound nucleons which are to some extent sensitive to the medium modifications of nucleon-nucleon elastic cross sections in neutron-rich intermediate energy heavy ion collisions are investigated. The splitting effect of neutron and proton effective masses on cross sections is discussed. It is found that the transverse flow as a function of rapidity, the $Q_{zz}$ as a function of momentum, and the ratio of halfwidths of the transverse to that of longitudinal rapidity distribution $R_{t/l}$ are very sensitive to the medium modifications of the cross sections. The transver…
Using an isospin-dependent quantum molecular dynamics, nuclear stopping in intermediate heavy ion collisions has been studied. The calculation has been done for colliding systems with different neutron-proton ratios in beam energy ranging from 15MeV/u to 150MeV/u. It is found that, in the energy region from above Fermi energy to 150MeV/u, nuclear stopping is very sensitive to the isospin dependence of in-medium nucleon-nucleon cross section, but insensitive to symmetry potential. From this investigation, we propose that nuclear stopping can be used as a new probe to extract the information on …
Elastic lepton scattering off of a nucleon has proved to be an efficient tool to study the structure of the hadron. Modern cross section and asymmetry measurements at Jefferson Lab require effects beyond the leading order Born approximation to be taken into account. Availability of unpolarized beams of both electrons and positrons in respective experiments would enable to reduce systematic uncertainties due to higher-order charge-odd contributions. In addition, information on an unpolarized electron-to-positron cross section ratio could serve as a test for theoretical models that provide predi…
The properties of nucleon-nucleon scattering inside dense nuclear matter are investigated. We use the relativistic Brueckner-Hartree-Fock model to determine on-shell and half off-shell in-medium transition amplitudes and cross sections. At finite densities the on-shell cross sections are generally suppressed. This reduction is, however, less pronounced than found in previous works. In the case that the outgoing momenta are allowed to be off energy shell the amplitudes show a strong variation with momentum. This description allows to determine in-medium cross sections beyond the quasi-particle …
We analyze the effects of an in-medium broadening of nucleon resonances on the exclusive photoproduction of mesons on nuclei as well as on the total photoabsorption cross sections in a transport calculation. We show that the resonance widths observed in semi-inclusive photoproduction on nuclei are insensitive to an in-medium broadening of nucleon resonances. This is due to a simple effect: the sizeable width of the nuclear surface and Fermi motion.
For detailed explanation of the experimental results of lepton production cross section in hadronic collisions such as nucleon-nucleon or nucleon-nuclei, it is of great importance to use quarks and sea quarks distribution function inside free and bound nucleons. In this paper the role of pion cloud inside the nucleus in the structure function of Cu and Pt nuclei and the EMC ratio of these nuclei were investigated by using harmonic oscillator model.
We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding …
A systematic study of the in-medium correction factor ($F$) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of $F$ on the directed, elliptic flow and nuclear stopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to $0.8A$ GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to $F$, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-m…
We investigate the kinetic freeze out scenario of a nucleon gas through a finite layer. The in-medium mass modification of nucleons and it's impact on the freeze out process is studied. A considerable modification of the thermodynamical parameters temperature, flow-velocity, energy density and particle density has been found in comparison with evaluations which use a constant vacuum nucleon mass.
Understanding quasielastic electron- and neutrino-scattering from nuclei has taken on new urgency with current and planned neutrino oscillation experiments, and with electron scattering experiments measuring specific final states, such as those involving nucleon pairs in ``back-to-back'' configurations. Accurate many-body methods are available for calculating the response of light ($A \leq 12$) nuclei to electromagnetic and weak probes, but they are computationally intensive and only applicable to the inclusive response. In the present work we introduce a novel approach, based on realistic mod…
Using a more reasonable separate density-dependent scenario instead of the total density-dependent scenario for in-medium $nn$, $pp$ and $np$ interactions, we examine effects of differences of in-medium nucleon-nucleon interactions in two density-dependent scenarios on isospin-sensitive observables in central $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon. Moreover, to more physically detect the differences between the nucleon-nucleon interactions in two density-dependent scenarios, we also map the nucleon-nucleon interaction in the separate density-dependent scenario into that in the tot…
We study the modification of the nucleon axial form factor in nuclear matter. The internal quark substructure of the nucleon is self-consistently described by the quark meson coupling model. We find that the axial form factor of the bound nucleon is quenched considerably from that of the free nucleon. The axial vector coupling constant is reduced by roughly 10% at normal nuclear matter density and the axial form factor varies within 8% for moderate momentum transfer.
The three--nucleon scattering problem in a nuclear medium is considered within the Faddeev technique. In particular the deuteron break--up cross section that governs the formation and the break--up reactions of deuterons (NNN <-> Nd) in a nuclear environment is calculated at finite temperatures and densities. A significant enhancement of the in--medium break--up cross section with increasing density has been found.
After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue th…
We study the isospin effects of the mean field and two-body collision on the nucleon emissions at the intermediate energy heavy ion collisions by using an isospin dependent transport theory. The calculated results show that the nucleon emission number $N_{n}$ depends sensitively the isospin effect of nucleon nucleon cross section and weakly on the isospin dependent mean field for neutron-poor system in higher beam energy region . In particular, the correlation between the medium correction of two-body collision and the momentum dependent interaction enhances the dependence of nucleon emission …
The momentum dependence of the medium modifications on nucleon-nucleon elastic cross sections is discussed with microscopic transport theories and numerically investigated with an updated UrQMD microscopic transport model. The semi-peripheral Au+Au reaction at beam energy $E_b=400A$ MeV is adopted as an example. It is found that the uncertainties of the momentum dependence on medium modifications of cross sections influence the yields of free nucleons and their collective flows as functions of their transverse momentum and rapidity. Among these observables, the elliptic flow is sensitively dep…
Talk given at the "International Workshop on (e,e'p) Processes", July 2-6, 2017, Bled, Slovenia. Various many-body calculations are compared and the results provided by the Normalization Conserving Linked Cluster Expansion with realistic NN interactions are reviewed and analyzed in detail, as far as ground state energies, momentum distributions and spectral functions of few-nucleon system and complex nuclei are concerned.
We study the in-medium modification of the isovector pi N amplitude using a non-linear representation of the sigma model but keeping the scalar degree of freedom. We check that our result does not depend on the representation. We discuss the connection with other approaches based on chiral perturbation theory.
We study the transverse flow throughout the mass range from $^{20}Ne+^{20}Ne$ to $^{131}Xe+^{131}Xe$ as a function of the impact parameter. We find that at smaller impact parameters the flow is negative while going through the impact parameter, transverse flow vanishes at a particular colliding geometry named GVF. We find that the mass dependence of GVF is insensitive to the equation of state and momentum dependent interactions whereas it is quite sensitive to the cross section. So it can act as a useful tool to pin down the nucleon nucleon cross section.
We compare different formalisms for the calculation of lepton pair emission in hadron-hadron collisions and discuss the consequences of the approximations inherent to each of them. Using a Lorentz-covariant and gauge-invariant formalism proposed by Lichard, we calculate lepton pair emission via bremsstrahlung in proton-proton and neutron-proton reactions at energies between 1 and 5 GeV to leading order in the virtual photon four-momentum. These new results suggest that some previous bremsstrahlung calculations based on varieties of the soft-photon approximation might have somewhat overestimate…
We analyze low-energy hyperon-nucleon scattering using an effective field theory in next-to-leading order. By fitting experimental cross sections for laboratory hyperon momenta below 200 MeV/c and using information from the hypertriton we determine twelve contact-interaction coefficients. Based on these we discuss the low-density expansion of hyperon mass shifts in the nuclear medium.
The study focuses on exploring the changes in the hyperon-baryon interaction at various nuclear densities. This approach starts by building a vacuum hyperon-nucleon interaction model based on Boson -Exchange maintaining SU(3) flavor symmetry. Bethe-Goldstone equation is then explored to investigate the medium properties over the bare interaction. A detailed investigation of the density dependence revealed clear changes in the low energy parameters with the variation of the medium density shown for different strangeness channels.
It is shown that, if inclusive lepton scattering off nuclei at high momentum transfer is analyzed in terms of proper scaling variables, useful information on Nucleon-Nucleon short range correlations in nuclei can be obtained. The traditional approach to Y-scaling is critically analyzed and a novel approach to Y-scaling, which incorporates the effects from two- and three-nucleon correlations in nuclei, is illustrated.
In-medium nucleon electromagnetic form factors are calculated in the quark meson coupling model. The form factors are typically found to be suppressed as the density increases. For example, at normal nuclear density and $Q^2 \sim 0.3 { GeV}^2$, the nucleon electric form factors are reduced by approximately 8% while the magnetic form factors are reduced by only 1 - 2%. These variations are consistent with current experimental limits but should be tested by more precise experiments in the near future.
A new version of the separable kernel of the nucleon-nucleon interaction in the Bethe-Salpeter approach is presented. The phase shifts are fitted to recent experimental data for singlet and uncoupled triplet partial waves of the neutron-proton scattering with total angular momenta J=0,1. The results are compared with other model calculations.
Lepton-nucleon elastic scattering, using the one-photon and one-scalar-boson exchange mechanisms considering all possible polarizations, is used to study searches for a new scalar boson and suggest new measurements of the nucleon form factors. A new light scalar boson, which feebly couples to leptons and nucleons, may account for the proton radius and muon $g-2$ puzzles. We show that the scalar boson produces relatively large effects in certain kinematic region when using sufficient control of lepton and nucleon spin polarization. We generalize current techniques to measure the ratio $G_E/G_M$…
We develop a new lattice Hamiltonian method for solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation. Adopting the stochastic approach to treat the collision term and using the GPU parallel computing to carry out the calculations allows for a rather high accuracy in evaluating the collision term, especially its Pauli blocking, leading thus to a new level of precision in solving the BUU equation. Applying this lattice BUU method to study the width of giant dipole resonance (GDR) in nuclei, where the accurate treatment of the collision term is crucial, we find that the obtained GDR width of $^…
Based on the requirement in the simulation of lepton-nucleus deep inelastic scattering (DIS), we construct a fortran program LDCS 1.0 calculating the differential and total cross sections for the unpolarized charged lepton-unpolarized nucleon and neutrino-unpolarized nucleon neutral current (charged current) DIS at leading order. Any set of the experimentally fitted parton distribution functions could be employed directly. The mass of incident and scattered leptons is taken into account and the boundary conditions calculating the single differential and total cross section are studied. The cal…
The problem of the near vanishing of the Gamow-Teller transition ($GT$) in the A=14 system between the lowest $J=0^+~ T=1$ and $J=1^+~ T=0$ states is revisited. The model space is extended from the valence space $(p^{-2})$ to the valence space plus all 2$\hbar ω$ excitations. The question is addressed as to what features of the effective nucleon-nucleon interaction in the medium are required to obtain the vanishing $GT$ strength in this extended space. It turns out that a combination of a realistic strength of the tensor force combined with a spin-orbit interaction which is enhanced as compare…
Based on the thermodynamic Green function approach two-nucleon correlations in nuclear matter at finite temperatures are revisited. To this end, we derive phase equivalent effective $r$-space potentials that include the effect of the Pauli blocking at a given temperature and density. These potentials enter into a Schrödinger equation that is the $r$-space representation of the Galitskii-Feynman equation for two nucleons. We explore the analytical structure of the equation in the complex $k$-plane by means of Jost functions. We find that despite the Mott effect the correlation with deuteron qua…
The in-medium neutron-proton, proton-proton(neutron-neutron) scattering cross sections($σ_{np}^{*}$, $σ_{pp(nn)}^{*}$) are studied based on QHD-II type Lagrangian within the framework of the microscopic transport theory. The results demonstrate that, for free nucleon-nucleon scattering cross sections, the isospin dependence is dominantly caused by $ρ$ meson field. The medium correction of nucleon-nucleon scattering cross sections is also isospin dependent, $σ_{np}^{*}$ depends on the baryon density weakly and $σ_{pp(nn)}^{*}$ depends on the baryon density significantly, which is due to the dif…
We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering T-matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter as well as nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential V(low-k) to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-med…
Within the $σ-ω$ model of coupled nucleon-meson systems, a generalized relativistic Lenard--Balescu--equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as fluctuation effects. It contains all possible processes due to one meson exchange and special attention is kept to the off--shell character of the particles. As a new feature of many particle effects, processes are possible which can be interpr…
We show the first results for the elastic scattering of neutrons off oxygen and calcium isotopes obtained from ab initio optical potentials. The potential is derived using self consistent Green's function theory (SCGF) with the saturating chiral interaction NNLO$_{\textrm{sat}}$. Our calculations are compared to available scattering data and show that it is possible to reproduce low energy scattering observables in medium mass nuclei from first principles.
We present the results of (anti)neutrino induced CCQE cross sections from some nuclear targets in the energy region of $E_ν\le 1 GeV$. The aim of the study is to confront electron and muon production cross sections relevant for $ν_μ\leftrightarrow ν_e$ or $\barν_μ\leftrightarrow \barν_e$ oscillation experiments. The effects due to lepton mass and its kinematic implications, second class currents and uncertainties in the axial and pseudoscalar form factors are discussed for (anti)neutrino induced reaction cross sections on free nucleon as well as the nucleons bound in a nucleus where nuclear me…
Within the $σ-ω$ model of coupled nucleon-meson systems, a generalized relativistic Lenard--Balescu--equation is presented resulting from a relativistic random phase approximation (RRPA). This provides a systematic derivation of relativistic transport equations in the frame of nonequilibrium Green's function technique including medium effects as well as flucuation effects. It contains all possible processes due to one meson exchange and special attention is kept to the off--shell character of the particles. As a new feature of many particle effects, processes are possible which can be interpre…
We investigate the asymptotic separation of the optical model potential for nucleon-nucleus scattering in momentum space, where the potential is split into a medium-independent term and another depending exclusively on the gradient of the density-dependent g matrix. This decomposition confines the medium sensitivity of the nucleon-nucleus coupling to the surface of the nucleus. We examine this feature in the context of proton-nucleus scattering at beam energies between 30 and 100 MeV and find that the pn coupling accounts for most of this sensitivity. Additionally, based on this general struct…
Based on the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, the in-medium nucleon-nucleon inelastic scattering ( which is dominated by pion production at low and intermediate energies) is explored. It is found that the in-medium modification of nucleon-nucleon inelastic scatterings appears to reduce the neutron to proton ratio n/p at higher kinetic energies. Although the in-medium modification of nucleon-nucleon inelastic scatterings, as expected, affects the value of $π^-/π^+$ ratio, considering a series of undetermined properties of delta resonance and $π$ in medium, t…
The off-shell behaviors of bound nucleons in deep inelastic lepton nucleus scattering are discussed in two scenarios with the basic constituents chosen to be baryon-mesons and quark-gluons respectively in light-cone formalism. It is found that when taking into account the effect due to internal quark structure of nucleons, the derived scaling variable for bound nucleons and the calculated nuclear structure functions are different from those in considering the baryon-mesons as the effective elementary constituents. This implies that the pure baryon-meson descriptions of nuclei give the inaccura…
