Transverse (e,e′) Response Functions for 4He

This poster presentation is intended to show preliminary results from calculations of the inclusive (e,e′) transverse response functions of ⁴He. Up to now we have only included the E1 and M1 multipoles and therefore no comparison with experiment is shown. That will be done once all relevant multipoles have been calculated. Details of the calculation are summarized in the text below.     

Δ Isobar Degrees of Freedom in the 3He Transverse Electron Scattering Response Function

The importance of Δ(1232) isobar degrees of freedom is investigated for the transverse (e, e′) response of ³He in the quasi-elastic peak region and beyond (considered momentum transfer range: 500 ≤ q ≤ 1,000 MeV/c). Besides Δ isobar currents (Δ-IC) meson exchange currents and relativistic corrections to the nucleonic one-body current are included. The calculation is carried out by using the Lorentz integral transform (LIT) method. Results for the transverse response function R _T are presented up to q = 700 MeV/c, whereas for higher q only some preliminary results for the LIT of R _T are discussed. In the quasi-elastic peak region Δ-IC enhance R _T by about 5% and tend to cancel three-nucleon force effects. One observes an excellent agreement with experimental R _T results. Particularly strong Δ-IC contributions are found for transitions into the final state with isospin T = 3/2, which is only reachable in three-body break-up reactions.     

3He Transverse Electron Scattering Response Function with �� Degrees of Freedom

A calculation of the ³He transverse (e, e??) inclusive response function, R _T , which includes ?? degrees of freedom is performed using the Lorentz integral transform method. The resulting coupled equations are treated in impulse approximation, where the NNN and NN?? channels are solved separately. R _T is calculated for the breakup threshold region at a momentum transfer of q?=?862 MeV/c.     

3He(e,e′pp) and 3He(e,e′pn) reactions at AmPS and MAMI

This paper reports on measurements of the ³He(e,e′pp) reaction measured at AmPS and the ³He(e,e′pn) reaction measured at MAMI. The measurements were performed in similar kinematics to allow a comparison to be made between the cross sections of the two reactions. Results are shown for both reactions together with a comparison for the ³He(e,e′pp) data with continuum Faddeev calculations.     

The quasi-free 3He(e,e′p) reaction

The proton spectral function has experimentally been determined with the ³He(e, e′p) reaction for missing energies, 0<E_m<70MeV, and recoil momenta, 0<P_B<310 MeV/c. Experimental results are obtained for both the two-body, ³He(e, e′p)²H, and three-body breakup processes. Proton momentum density distributions, obtained in a PWIA analysis, are compared with theoretical calculations: Faddeev solutions with the RSC and Paris potentials, and variational calculations with various potentials, including those with a three-nucleon interaction term. Energy-weighted sum rule results are presented and compared with theoretical predictions. The coincidence cross sections are also compared with calculations which include the effects of final state interactions and meson exchange currents. Consistency of the results with PWIA is investigated in the framework of the Chew-Low extrapolation procedure.     

Relativistic Description of 3He (e, e�� p)2H

The relativistic distorted-wave impulse approximation is used to describe the ³He(e, e?? p)²H process. We describe the ³He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the ³He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S?CV) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S?CV optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.     

Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Pion electroproduction in the 3He(e,é π+)3H reaction at intermediate energies

The differential coincident pion electroproduction cross section in the ³He(e,é π⁺)³H reaction has been measured with high resolution with the three-spectrometer set-up at the Mainz Microtron (MAMI) electron accelerator. Measurements were performed at the four incident energies E₀ = 855, 675, 600, and 555 MeV at fixed four-momentum transfer Q² = 0.045 GeV², with the pions detected in parallel kinematics. This enables a separation of the measured cross section into the transverse and longitudinal structure functions by means of the Rosenbluth method. The experimental data are compared to model calculations, in which the elementary pion production amplitude includes the standard Born-amplitudes and also delta and higher resonance terms. Three-body Fadeev wave functions are used and the final state interaction of the outgoing pion is taken into account. The calculation describes the data only after medium modifications of the delta and of the pion are included.     

He原子(e,3e)反应中末态波函数的动量相关

在前期工作的基础上,进一步考虑了He原子(e,3e)反应中末态四体的动量相关.用改进后的理论计算了高能电子入射双电离He原子的五重微分截面(FDCS).与前期理论相比,所得结果大大地改善了理论曲线与实验结果的吻合程度.     

Measurement of the exclusive D(p,e+e−)3He and D(p, γ)3He reactions at 98 and 176 MeV

A high resolution magnetic pair spectrometer for medium energy photons has been used for studies of the exclusive (p, e⁺e⁻) and (p, γ) reactions on deuterium at 98 and 176 MeV. The (p, e⁺e⁻) cross sections, obtained at 40° and 80°, are compared with the corresponding data for the (p, γ) reaction measured with the same apparatus. At small virtual photon masses the (p, e⁺e⁻) cross sections show significant enhancement over what is expected from model calculations, a behaviour which has earlier been observed also for the ¹¹B(p, e⁺e⁻)¹²C reaction.     

散射粒子的相互作用对He(e,3e)五重微分截面的贡献

计算了敲出电子等能分享几何安排下,入射能量分别为5 599 eV和1 099 eV时He(e,3e)反应五重微分截面,并比较在He(e,3e)过程中散射粒子的相互作用和它们之间的干涉效应对五重微分截面的贡献.结果表明,理论计算数据在误差范围内与实验数据基本吻合,并且散射粒子的相互作用以及干涉效应对五重微分截面的影响都是不容忽视的.     

Study of the 4He(e,e′d)pn Reaction

 The cross section for the ⁴He(e,e′d)pn reaction has been measured in parallel and in (q, ω)-constant kinematics for values of the three-momentum transfer of 406, 495 and 595 MeV/c, and for a range in missing momentum. Just above threshold this reaction can be characterized as a spin/isospin flip transition of the involved pn pair. By using two electron energies (576 and 370 MeV) the longitudinal and transverse structure functions could be separated. The cross sections turn out to be purely transverse, as expected for a spin/isospin flip transition. The data are well described by new covariant and current-conserving calculations that include the major final-state interaction effects. Received August 20, 1998; modified October 12, 1998; accepted for publication January 30, 1999     

Inclusive (e,e′ N), (e,e′ NN), (e,e′ π), …v reactions in nuclei

We study the inclusive (e, e′ N), (e, e′ NN), (e, e′ π), (e, e′ πN) reactions in nuclei using a Monte Carlo simulation method to treat the multichannel problem of the final state. The input consists of reaction probabilities for the different steps evaluated using microscopical many body methods. We obtain a good agreement with experiment in some channels where there is data and make predictions for other channels which are presently under investigation in several electron laboratories. The comparison of the theoretical results with experiment for several kinematical conditions and diverse channels can serve to learn about different physical processes occurring in the reaction. The potential of this theoretical tool to make prospections for possible experiments, aiming at pinning down certain reaction probabilities, is also emphasized.     

A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media

A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.     

Production of high energy deuterons in the reaction:3He+3He→4He+2H+e ++v

Experiments on the reaction:³He+³He→⁴He+²He using a single four detector telescope have shown evidence for the production of deuteron pulses, consistent with the²He→²H+e⁺+v fusion reaction in the final state. New measurements on the same reaction using improved techniques viz.A) a windowless³He gas target andB) α- d correlation detection with 5 ns resolving time and antipileup circuitry have been performed. Calibrations were obtained from the⁷Li+³He→²H+⁴He+⁴He reaction spectra. The correlation angles were 30° and 97° for the alphas and deuterons respectively. Deuteron pulses have been observed, correlated with alpha particles. A cross section of (1.7 ±0.5)nbsr^?1MeV^?1 was obtained consistent with previous measurements using a single telescope.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.     

Doubly charged Higgs from e–γ scattering in the 3-3-1 Model

The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models.     

Modified semiclassical exchange approximation in electron–atom collision He(e, 2e) triple differential cross-section

A modified semiclassical exchange (MSCE) potential has been used in the distorted wave born approximation (DWBA) to calculate the triple differential cross-section (TDCS) for He(1s²) at 64.6 and 74.6 eV incident electron energies in non-coplanar symmetric geometry. The agreements of present results with experimental data are much better as compared with our earlier calculations based on the spin averaged static exchange potential.     

Quasi-free processes in 6Li(3He,pα)4He reaction at low energies

The ⁶Li(³He, pα)⁴He reaction was studied experimentally at 3.5, 4.4 and 5.5 MeV in the quasi-free reaction kinematical region. The effects of a resonance in the virtual ²H(³He, p)⁴He reaction on the three-body reaction cross section were investigated.