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Register a new userOn the role of the effective interaction in quasi-elastic electron scattering calculations
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Antonio Miguel Lallena Rojo
Publication date
1997
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English
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The role played by the effective residual interaction in the transverse nuclear response for quasi-free electron scattering is discussed. The analysis is done by comparing different calculations performed in the Random--Phase Approximation and Ring Approximation frameworks. The importance of the exchange terms in this energy region is investigated and the changes on the nuclear responses due to the modification of the interaction are evaluated. The calculated quasi-elastic responses show clear indication of their sensibility to the details of the interaction and this imposes the necessity of a more careful study of the role of the different channels of the interaction in this excitation region.
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We present theoretical predictions for electron scattering on the N = 14, 20, and 28 isotonic chains from proton-deficient to proton-rich nuclei. The calculations are performed within the framework of the distorted-wave Born approximation and the proton and neutron density distributions are evaluated adopting a Relativistic Hartree-Bogoliubov (RHB) approach with a density dependent meson-exchange interaction. We present results for the elastic and quasi-elastic cross sections and for the parity-violating asymmetry parameter. Owing to the correlations between the evolution of the electric charge form factors along each chain with the underlying proton shell structure of the isotones, elastic electron scattering experiments on isotones can provide useful informations about the occupation and filling of the single-particle levels of protons.
Conventional coupled-channels analyses, that take account of only the collective excitations of the colliding nuclei, have failed to reproduce the different behavior of the experimental quasi-elastic barrier distributions for the $^{20}$Ne + $^{90,92}$Zr systems. To clarify the origins of this difference, we investigate the effect of non-collective excitations of the Zr isotopes. Describing these excitations in a random-matrix model, we explicitly take them into account in our coupled-channels calculations. The non-collective excitations are capable of reproducing the observed smearing of the peak structure in the barrier distribution for $^{20}$Ne + $^{92}$Zr, while not significantly altering the structure observed in the $^{20}$Ne + $^{90}$Zr system. The difference is essentially related to the closed neutron shell in $^{90}$Zr.
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the Dirac equation with a Coulomb potential. Convergence is rapid at energies above about 250 MeV. Analytical results for the eikonal wave functions are obtained for a simple analytical form of the Coulomb potential of a nucleus. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. Focusing factors are shown to arise from the corrections to the eikonal approximation. A precise form of the effective-momentum approximation is developed by use of a momentum shift that depends on the electrons energy loss.
The role of the pion in the parity-conserving and parity-violating quasi-elastic nuclear response functions is analyzed within a relativistic model which fulfills gauge invariance.
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