Inelastic Form Factors Research Articles

Transverse·inelastic form factor of the first excited state in 39K

A recent measurement of the transverse electron scattering form factor for the first excited state of 39K shows a significant departure from the single-particle picture of a pure d 3 2 − → 1 s 1 2 −1 proton transition. The data are well explained by a calculation including second-order core polarization and meson-exchange current corrections to both the M1 and E2 transition densities. These results are consistent with previous work on the elastic magnetic form factor, which also shows a significant departure from the extreme single-particle model.

Comparison of the size of the [formula omitted] orbit deduced from C6 and M7 form factors

The inelastic Coulomb form factor for electroexcitation of the yrast 6 + state in 50Ti has been measured. The value for the RMS radius of the 1 f 7 2 proton orbit deduced from these data is appreciably larger than the one extracted form the M7 form factor for elastic magnetic scattering from 51V.

On the imaginary part of the form factor for inelastic excitations in heavy-ion reactions

An explicit formula is obtained for the imaginary inelastic transition form factor which accounts for second-order excitation processes. The transfer of nucleons back and forth between projectile and target is found to be the leading higher-order effect. This result and the close connection which is obtained between the imaginary form factor and the absorptive part of the optical potential explains the main features of the macroscopic prescription commonly used in data analyses.

Electron scattering form factors for fp-shell nuclei

Elastic and inelastic electron-scattering form factors for multipolarities up to L = 7 and some transition-strength distributions are calculated with shell-model wave functions for about ten target nuclei in the mass range A = 52–62. The results are compared with the available measured transition strengths and (e, e') form factors.

Structure of the21+state inC12and the inelastic form factor

We study the discrepancy between the measured ${0}_{1}^{+}$\ensuremath{\rightarrow}${2}_{1}^{+}$ form factor of $^{12}\mathrm{C}$ and the existing theoretical results, and specify a generator-coordinate state that resolves the discrepancy.

Electron scattering measurements of inelastic M3 transitions

Inelastic M3 form factors for the excitation of the 5.236 MeV 3 + state in 24Mg and for the excitation of the 10.376 MeV 3 +, T = 1 state in 28Si have been measured. These form factors are compared with full 2s1d shell-model calculations in order to investigate the experimental quenching of M3 transition strength which is expected in the light of previous work. The shell-model predictions do not agree with the experimental data. In the case of the 24Mg 5.236 MeV state the data are enhanced by a factor of ∼2 with respect to the shell-model prediction, whereas in the case of the 28Si 10.376 MeV state the data are suppressed by a factor of ∼5. In the former case it is found that a small admixture of the 3 2 + state shell-model wave function into the 3 1 + state wave function gives good agreement with the data. The effects of this admixture on other observables are investigated. No similar mechanism is found to explain the 28Si M3 transition. In view of the basic disagreement between the shell-model predictions and the experimental data, no conclusions about M3 quenching can be drawn. The validity of previous analyses using this technique is seriously questioned.

Three-body potential among alpha particles

We propose a three-body potential among alpha particles based on a single ${\ensuremath{\alpha}}^{*}$ excitation and adjust its parameters so that the experimental binding energy and charge radius of $^{12}\mathrm{C}$ in the $3\ensuremath{-}\ensuremath{\alpha}$ model is obtained. With this potential we calculate the elastic and the ${0}_{1}^{+}$\ensuremath{\rightarrow}${0}_{2}^{+}$ inelastic form factor and reduced transition probabilities. The three-body potential in conjunction with an Ali-Bodmer two-body potential yields a satisfactory fit to the ${0}_{1}^{+}$\ensuremath{\rightarrow}${0}_{2}^{+}$ inelastic form factor and a very good agreement with the measured reduced transition probability.NUCLEAR STRUCTURE $3\ensuremath{-}\ensuremath{\alpha}$ model of $^{12}\mathrm{C}$, three-body potential among alpha particles, elastic and inelastic form factors of electron scattering, reduced transition probabilities.

Strengths of transitions between0+and1+states and their relationship to inelastic electron scattering form factors: Example ofMg24

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Virtual photon spectrum in second-order Born approximation

We have evaluated expressions for E1 and M1 virtual photon spectra for relativistic electron scattering in second order Born approximation and included the effects of finite nuclear size and charge. The scattering amplitude can be evaluated analytically provided the elastic and inelastic form factors contain only poles. We have observed that the virtual photon spectrum is insensitive to details of both form factors over a wide range of electron energy and depends only on the nuclear rms radius and transition radius. The integral over the physical momentum transfer is performed numerically. We have evaluated spectra for electric dipole and magnetic dipole radiation for electron energies in the range 10--200 MeV and compared with distorted wave calculations. Except for low energy and high Z, our results compare well. A range-of-validity plot is given for each multipole, distinguishing regions of electron energy and mass number where the second order calculation is adequate and also those where the first order term alone would be sufficient and where the conventional long wavelength limit is applicable. Comparison with data on the excitation of the 16.3 MeV isobaric analog state in /sub 40//sup 90/Zr yields excellent agreement with no adjustable parameters.

Elastic and inelastic electron scattering fromCr50,52,54

Elastic and inelastic electron scattering cross sections are given for $^{50,52,54}\mathrm{Cr}$ at momentum transfers between 0.15 and 2.6 ${\mathrm{fm}}^{\ensuremath{-}1}$. Ground state charge distributions are derived from a combined analysis of these data and muonic atom data. Deduced values of the rms charge radii are given. Comparison is made between the experimental charge distributions and density dependent Hartree-Fock-Bogolyubov calculations. Inelastic scattering form factors for ${2}^{+}$, ${4}^{+}$, and ${6}^{+}$ states up to 4 MeV excitation are given along with shell model and phenomenological model fits to those data, $B(\mathrm{EL})$ values, multipole dependence of effective charges, and other model parameters.NUCLEAR REACTIONS $^{50,52,54}\mathrm{Cr}(e, {e}^{\ensuremath{'}})$, $E=30\ensuremath{-}400$ MeV. Measured $\ensuremath{\sigma}(E, \ensuremath{\theta})$. Deduced ground state charge distributions compared to Hartree-Fock. Deduced inelastic form factors compared to shell model.

Effects of short range correlations on one- and two-body properties of nuclei

We evaluate the effects of correlations on one- and two-body densities by developing a low-order approximation (LOA) in the framework of the Jastrow formalism. The accuracy of the method is verified by comparing the predictions for the elastic form factor, the momentum distribution and the inelastic form factor with the results of an exact calculation performed in a model case. It is shown, contrary to what is often believed, that one-body quantities provide an adequate test for the presence of short-range correlations in nuclei.

The form factors in (HI, HI') direct reactions

Using a semiclassical theory, we analyze the inelastic transition form factor. We find that: (i) In the strong absorption limit, the Austern-Blair theory is a good approximation to the inelastic form factor — even in highly mismatched reactions, (ii) In weak to moderate absorption, the amplitude of the inelastic form factor oscillates due to overlapping potential resonances. Here the internal part of the form factor can be expressed in a simple form, which may easily be used to analyze heavy-ion inelastic scattering, (iii) In the presence of an isolated resonance, the inelastic form factor is enhanced greatly at the resonance due to multiple reflections inside the potential well.

Magnetic form factor of metallic iron and nickel as seen by inelastic neutron scattering from phonons

The magnetic form factors of iron and nickel have been studied by means of coherent inelastic vibrational scattering of polarized neutrons in high-symmetry directions for momentum transfers which are different from the reciprocal-lattice vectors. The vibrational scattering has been separated from other inelastic scattering processes, such as spin-wave scattering, by means of energy analysis on a triple-axis polarized-neutron spectrometer. In the case of iron we see definite departures from the interpolated elastic form factor, depending on the direction and magnitude of the scattering vector. In the case of nickel the inelastic form factor is identical, within experimental error, to the elastic form factor.

01+→02+inelastic form factor ofO16

We calculate the 0/sup +//sub 1/..-->..0/sup +//sub 2/ inelastic form factor of /sup 16/O in the alpha-particle model and study the influence of a three-body potential on it.

Elastic and inelastic form factors of light nuclei in the method of hyperspherical functions

Consideration is given to the properties of light nuclei in the method of hyperspherical functions with central realistic potentials. In general, the following set of parameters can be described satisfactorily for the nuclei: binding energy, excitation energy of monopole resonance, RMS radius, elastic and inelastic form factors. The detailed reproduction of the relevant data for each nucleus necessitates the solution of the inverse problem and requires that the corresponding nucleon-nucleon potential (which will probably vary from nucleus to nucleus) be found.

A simple method for evaluating goldstone diagrams in an angular momentum coupled representation: T. T. S. Kuo, J. Shurpin, and K. C. Tam, Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794; E. Osnes, Institute of Physics, University of Oslo, Oslo 3, Norway; and P. J. Ellis, School of Physics and Astronomy, University

Inelastic electron-scattering form factors of magnetic states in closed-shell nuclei are calculated taking into account the combined effect of the mesonic degrees of freedom and the two-particle-two-hole components of the nuclear wave functions which come from the particle-core vibration coupling. The one-body nucleon- and two-body meson-exchange current contributions to the form factor are evaluated with the same realistic mean field. Application to various high-spin magnetic states of oxygen and lead is made. The comparison with experiment shows an excellent agreement for the states 14−(6.74 MeV) and 121−(7.06 MeV) in lead, while such is not the case for the second 122−(6.43 MeV) state in lead and the 4−(18.98MeV) state in oxygen essentially due to mixing configuration effects and the non-consideration of 3p3h excitations, respectively.

Exclusive processes in perturbative quantum chromodynamics

We present a systematic analysis in perturbative quantum chromodynamics (QCD) of large-momentum-transfer exclusive processes. Predictions are given for the scaling behavior, angular dependence, helicity structure, and normalization of elastic and inelastic form factors and large-angle exclusive scattering amplitudes for hadrons and photons. We prove that these reactions are dominated by quark and gluon subprocesses at short distances, and thus that the dimensional-counting rules for the power-law falloff of these amplitudes with momentum transfer are rigorous predictions of QCD, modulo calculable logarithmic corrections from the behavior of the hadronic wave functions at short distances. These anomalous-dimension corrections are determined by evolution equations for process-independent meson and baryon "distribution amplitudes" $\ensuremath{\varphi}({x}_{i}, Q)$ which control the valence-quark distributions in high-momentum-transfer exclusive reactions. The analysis can be carried out systematically in powers of ${\ensuremath{\alpha}}_{s}({Q}^{2})$, the QCD running coupling constant. Although the calculations are most conveniently carried out using light-cone perturbation theory and the light-cone gauge, we also present a gauge-independent analysis and relate the distribution amplitude to a gauge-invariant Bethe-Salpeter amplitude.

Alpha inelastic scattering by 208Pb near the Coulomb barrier

Elastic scattering of 23.5 MeV α-particles by 208Pb and inelastic scattering to the 3 − state at 2.62 MeV have been measured. Good fits to the data using either the conventional deformed potential or folding-model descriptions of the interaction could be obtained, provided that the distorting potential and inelastic form factor were derived consistently. It was also found necessary to include an energy dependence in the imaginary potential. Both the EM transition rate and the tail of the nuclear form factor are well determined. They are consistent with equal proton and neutron deformation parameters for the 3 − state, although these latter quantities are model dependent and not strictly comparable. The isoscalar transition rate is poorly determined. In terms of the folding-model description, surface distributions of the nuclear matter and transition densities were derived which are in excellent agreement with theoretical calculation.

Elastic and inelastic charge form factors forLi36from electron scattering

A harmonic oscillator hard core plus residual two-body potential has been used to obtain the independent-particle shell-model wave functions for $_{3}^{6}\mathrm{Li}$. These wave functions have been utilized to calculate the theoretical elastic and inelastic electron scattering charge form factors. These are then compared with the experimental data.NUCLEAR REACTIONS Elastic and inelastic charge form factors for $_{3}^{6}\mathrm{Li}$ from electron scattering using harmonic hard core plus residual two-body potential.

Critical opalescence of the pion field and the M1 from factor of 12C: An investigation of the role of the rho meson

It is shown that the inelastic M1 form factor of 12C can be interpreted by nuclear polarization phenomena with inclusion of the rho meson in the polarizing interaction playing an essential role at large momenta. Whereas much of the observed anomaly can be attributed to standard core polarization effects, a large opalescence of the pion field (a factor 4.5 enhancement) would be needed to get full agreement with experiment.