Longitudinal Form Factors Research Articles

Isospin mixing in the electroexcitation of the Ex = 10.84 MeV, Jπ; T = 1 −; 0 state in 12C at low momentum transfers

Electroexcitation of the isospin-forbidden transition to the broad J π ; T = 1 −; 0 state at 10.84 MeV in 12C has been studied for momentum transfers q < 0.6 fm −1. The longitudinal form factor exhibits a sensitivity to the interference of small T = 1 admixtures. The isospin breaking Coulomb matrix element is determined in a two-state model to 〈 H C〉 = 145(80) keV. A shell-model calculation using a new effective psd-shell interaction qualitatively agrees with the shape of the form factor but underpredicts its magnitude by a factor of about two.

Electron scattering by 12C in the microscopic Spperpendicular to (1,R) model

We present the formalism and numerical techniques required to perform an Sp(1,R) calculation of the longitudinal form factors. To illustrate the technique we calculate the longitudinal form factors of the states of the ground band in 12C. The form factors are calculated by the generating function method and the results of the calculation are compared with experimental data.

Li6inelastic form factors in a cluster model

Longitudinal and transverse form factors are calculated for the transition into the low-lying excited T=0 and T=1 states of $^{6}\mathrm{Li}$ in the framework of the resonating group model. All form factors are reproduced simultaneously using three cluster wavefunctions. Meson exchange currents yield only minor corrections and do not lead to any specific structures at large momentum transfers.

Electron scattering off 65Cu and 71Ga

Electron scattering on the fp-shell nuclei 65Cu and 71Ga has been investigated. Measurements have been performed up to a momentum transfer of 2.7 fm −1 at forward and at backward scattering angles in order to separate the transverse and longitudinal form factors of the low-lying excited states. This allowed the extraction of the transition densities and probabilities, which are compared to particle-core coupling calculations: particle-vibration coupling model (PVCM) and quasiparticle-cluster vibration model (QCVM). These models appear to be more applicable to 65Cu than to 71Ga. Reasons for this are discussed. In general the transition charge densities confirm the distinction between quasiparticle states and collective excitations, that one expects already on the basis of spectroscopic factors. The relative importance of quasiparticle and phonon contributions to the transitions is reflected in the specific shapes of the transition densities for each level. Transition current densities are often less well predicted than charge densities and are quite sensitive to the model used.

Nucleon polarization in three-body models of polarized 6Li.

Just as [sup 3]H[rvec e] can be approximately characterized as a polarized neutron target, polarized [sup 6]LiD has been advocated as a good [ital isoscalar] nuclear target for the extraction of the polarized gluon content of the nucleon. The original argument rests upon a presumed alpha + deuteron'' picture of [sup 6]Li, with the polarization of the nucleus carried by the polarization of the deuteron. We have calculated the polarization of the constituents of [sup 6]Li as a three-body bound state of [alpha]+[ital n]+[ital p] interacting with local potentials fitted to the scattering data. It is necessary to include partial waves up to [ital j]=17/2 (75 channels, or, when including the [ital T]=1 state, 150 channels) in the Faddeev equations before the energy eigenvalue converges. The longitudinal form factors are then described well by the wave function. Various combinations of [alpha][ital N] and [ital NN] strong and Coulomb potentials yield a straight line in the charge radius vs energy plane which, unlike those of previous calculations, passes through the experimental datum. We find for all cases a polarization of the valence neutron in excess of 90%. This may make polarized [sup 6]LiD an attractive target for many nuclear physics purposes,more » since its neutrons are effectively 45% polarized.« less

A symplectic model calculation of transverse electron scattering form factors for 24Mg

The electron scattering transverse form factors for the transitions 0 + → 2 1 + and 0 + → 2 2 + for 24Mg are calculated in the symplectic model. Results show that the predictions of the sp(3, R ) model are improved over calculations restricted to the valence shell. Unlike longitudinal form factor calculations the effects of higher shells are not accounted for by simply introducing an effective charge factor.

Electromagnetic7Li form factors including meson-exchange contributions

We have studied the transversal and longitudinal form factors of the7Li ground-state doublet within a microscopic triton + α model allowing for specific distortion effects in the internal triton cluster. Meson-exchange contributions were taken into account in form of the dominant isovector pion- and rho-meson-exchange currents. For the derivation of the respective two-body operators we have used a consistent microscopic formalism developed by Riska which guarantees that the continuity equation is satisfied. The consideration of meson-exchange contributions brings our calculation in better agreement with the data. We find that only the longitudinal inelastic form factor has a diffraction minimum belowq≈4fm−1, in agreement with the data. Although our approach reproduces the low-q form factors qualitatively well, we underestimate the data at the higher momentum transfers noticeably. Finally we find that the isoscalar part of the central force gives the dominant contribution to the exchange currents while the tensor force plays only a minor role due to cancellation effects between the pion- and rho-meson-exchange contributions.

Electroexcitation of negative-parity states in 18O.

Form-factor measurements in the momentum-transfer range 0.6\ensuremath{\le}q\ensuremath{\le}2.7 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ are presented for the ${1}^{\mathrm{\ensuremath{-}}}$ levels in $^{18}\mathrm{O}$ at 4.46, 6.20, 7.62, and 8.04 MeV, the ${3}^{\mathrm{\ensuremath{-}}}$ levels at 5.10, 6.40, and 8.29 MeV, and the ${5}^{\mathrm{\ensuremath{-}}}$ levels at 7.86 and 8.13 MeV. These are the first measurements of the ${5}^{\mathrm{\ensuremath{-}}}$ states by inelastic scattering and the first electron-scattering measurements of the higher ${1}^{\mathrm{\ensuremath{-}}}$ and ${3}^{\mathrm{\ensuremath{-}}}$ states. A Rosenbluth separation of the longitudinal and transverse form factors was performed by fitting the data with a phenomenological polynomial-times-Gaussian parametrization motivated by the form of theoretical form factors when harmonic-oscillator wave functions are used. Comparisons are made with structure models. The Coulomb form factors of several levels indicate the significance of small admixtures of 3\ensuremath{\Elzxh}\ensuremath{\omega} components in the negative-parity wave functions.

7Li form factors in a microscopic cluster calculation

Longitudinal and transverse electromagnetic form factors are calculated for the transitions into the three lowest 7Li states for momentum transfers q up to 5 fm −1 in the framework of the resonating group model. Most of the data are described well if the wave functions contain not only an α−t structure but also additional configurations. Mesonic effects yield only smaller corrections and lead to rather unspecific structures in the form factors at large momentum transfers.

On the γNΔ quadrupole coupling constant(s)

The extraction of the gamma N Delta transverse and longitudinal quadrupole transition form factors gE and gC from the interference measured in (ep, e'p' pi 0) at resonance is discussed. It is shown that the background mechanisms in the non-resonant channels are substantially depressed thus allowing the direct determination of gC and gE. The two quantities, which have to be equal at pseudo-threshold, vary for 0>k2>-0.6 (GeV/c)2 between 0 and -0.1 gM. The necessity of an explicit evaluation of dispersive effects coming from pionic contributions to confirm their four-momentum transfer dependence and their connection with the pseudo-threshold value is stressed.

Large basis space effects in electron scattering form factors of light nuclei.

Large basis space projected Hartree-Fock wave functions have been used to calculate the longitudinal and transverse (electric) form factors from the excitations of 2{sub 1}{sup +} and 4{sub 1}{sup +} states in {sup 12}C, {sup 20}Ne, and {sup 24}Mg. The results obtained by use of such large basis space models of structure are compared with limited basis space (shell-model) predictions to show that momentum-transfer-dependent corrections can be quite diverse.

Exchange and correlation effects in the electromagnetic structure of light nuclei

A microscopic version of the multicluster dynamic model with the Pauli projection (MDMP) for light nuclei is constructed as applied to 6 Li allowing for nucleon exchange between the clusters due to antisymmetrization. The effects of correlations and exchanges on the electromagnetic structure of light nuclei are examined. A proper simultaneous description of the elastic longitudinal and transversal form factors of 6 Li has been attained.

Coherent π0 electroproduction on the deuteron at threshold

Abstract We studied the effect of the exchange current on the longitudinal form factor of neutral pion electroproduction. As a result, we obtained a large effect of the exchange current on pion production at threshold with a momentum transfer of 2–3 fm −1 . This reaction may serve as a clear test of the exchange current, which is related to the exchange axial-change.

Finite nucleus Dirac mean field theory and random phase approximation using finite B splines.

We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic \ensuremath{\sigma}-\ensuremath{\omega} model for the closed-shell nuclei $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar ${1}^{\mathrm{\ensuremath{-}}}$ and ${3}^{\mathrm{\ensuremath{-}}}$ longitudinal form factors of $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results.

High momentum transfer longitudinal and transverse form factors of the 7Li ground-state doublet

Longitudinal and transverse electromagnetic form factors of the 7Li ground-state doublet (the J π= 3 2 − ground state and the E x=478 keV, J π= 1 2 − first excited state) were measured by electron scattering up to momentum transfers of 4.2 and 4.5 fm −1, respectively. The transverse form factors show no diffraction structures in the high momentum transfer region which could be unambiguously identified as signatures of meson-exchange currents; however, they lie above existing calculations which do not include such contributions. The longitudinal elastic form factor has a second maximum as does the C2 form factor of the first excited state.

Transverse isoscalar excitations in 24Mg by 180 degrees electron scattering.

Transverse electron scattering form factors have been measured for isoscalar transitions to T=0 levels in $^{24}\mathrm{Mg}$ at 1.37 MeV (${J}^{\ensuremath{\pi}}$${=2}^{+}$), 5.24 MeV (${3}^{+}$), 6.01 MeV (${4}^{+}$), and for the unresolved T=0 doublet at 4.12 MeV (${4}^{+}$) and 4.24 MeV (${2}^{+}$). Because of the large longitudinal form factors for these transitions, sometimes exceeding the transverse form factor by more than a factor of ${10}^{4}$, it was necessary to observe electrons scattered at 180\ifmmode^\circ\else\textdegree\fi{} so that longitudinal scattering was minimized. Several incident energies from 80.1 to 200.5 MeV were used to span effective momentum transfers from 0.84 to 2.07 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Results are compared with predictions calculated using Dirac wave functions for the nuclear bound states in a Woods-Saxon potential well.

Core polarization and quenching in stretched spin states: Case study of the 9- Ex=3.522 MeV state in 116Sn.

The role of core polarization and of the quenching of the leading shell model configuration in stretched spin states is investigated in a case study of the ${9}^{\mathrm{\ensuremath{-}}}$ state at 3.522 MeV in $^{116}\mathrm{Sn}$. With data on five independent observables available, this is the best documented example of a natural parity stretched (yrast) state. The observables are the electron scattering longitudinal and transverse form factors, the proton-scattering cross section and asymmetry, and the proton-stripping cross section on $^{115}\mathrm{In}$. By introducing a fully microscopic description of the core polarization, it is possible to account quantitatively for all five observables using an effective nucleon-nucleon interaction based on the free t matrix for the proton scattering and the free values for the coupling constants for electron scattering. A short discussion on the ${5}^{\mathrm{\ensuremath{-}}}$ ${E}_{x}$=9.70 MeV state in $^{28}\mathrm{Si}$ and the ${12}^{+}$ ${E}_{x}$=6.026 MeV state in $^{208}\mathrm{Pb}$ is given. Quenching factors for the leading shell model components are found to be similar in magnitude as for unnatural parity states.

An application of boson second quantization techniques to the calculation of electron scattering form factors

It is suggested that boson second quantization, in terms of harmonic oscillator bosons, may be much more useful than its fermion counterpart for shell-model calculations in an LS coupled basis. The bosons carry the fundamental representation of SU(3). The combined set of boson creation and annihilation operators also carry the fundamental representation of Sp(3, R). Boson second quantization therefore provides a mechanism for expressing operators in terms of SU(3) and Sp(3, R) irreducible tensors. This is of major importance for shell-model calculations in an SU(3) basis and for the development of the symplectic shell model. Applications are made to the calculation of electron scattering form factors and it is shown how major simplifications arise when the space is restricted to a single major shell. For example, longitudinal form factors for 0 → 2 transitions in the sd-shell are shown to depend on just three parameters while the corresponding transverse form factors are uniquely determined up to an overall multiplicative constant. Further simplifications result on restriction to a single SU(3) irreducible representation.

Electromagnetic form factors in the Skyrme model.

The electric and magnetic form factors for the nucleon and the $N\ensuremath{-}\ensuremath{\Delta}$ transition are computed in the semiclassical approximation to the Skyrme model and compared with phenomenological dipole parametrizations. A model-independent relation between the magnetic form factors is obtained. The transverse electric transition form factor is identically zero in this approximation, while the longitudinal form factor is nonzero.

Shell-model analysis of high-resolution data for elastic and inelastic electron scattering on 19F.

A comprehensive theoretical and experimental investigation of electron scattering on /sup 19/F is presented. Theoretical procedures for calculating the various components of electron scattering form factors from multiparticle shell-model wave functions are summarized. These procedures are used to compare shell-model predictions with data from electron scattering on /sup 19/F. For the positive-parity states of /sup 19/F we use 1s0d shell-model wave functions obtained with a new ''universal'' Hamiltonian and for the negative-parity states we use 0p-1s0d shell-model wave functions based on the cross-shell Hamiltonian of Millener and Kurath. The comparisons are made with measured longitudinal and transverse form factors for momentum transfers up to 2.4 fm/sup -1/ which are extracted from experimental data obtained with electron energies from 78 to 340 MeV, and angles of 45/sup 0/, 90/sup 0/, and 160/sup 0/. The energy resolution was 25--50 keV and most of the known levels below 8 MeV in excitation were resolved and compared with theory.