Spectroscopic factors inCa40andPb

Abstract

We present results for spectroscopic factors of the outermost shells in 40 Ca and 208 Pb, which have been derived from the comparison between the available quasielastic (e, e ′ p) data from NIKHEF-K and the corresponding calculated cross-sections obtained within a fully relativistic formalism. We include exactly the effect of Coulomb distortion on the electron wave functions and discuss its role in the extraction of the spectroscopic factors from experiment.Without any adjustable parameter, we find spectroscopic factors of about 70%, consistent with theoretical predictions. We compare our results with previous relativistic and nonrelativistic analyses of (e, e ′ p) data. In addition to Coulomb distortion effects we discuss different choices of the nucleon current operator and also analyze the effects due to the relativistic treatment of the outgoing-distorted and bound nucleon wave functions.

Coulomb corrections for quasielastic scattering: eikonal approximation

“…We have developed an approximate description -the eikonal approximationthat is more transparent and numerically easier to deal with than the exact treatments (solution of the full Dirac equation) previously employed [6,7,8]. At the same time, the eikonal approximation is much more realistic than the effective momentum approximation often employed in the absence of results from exact calculations.…”

“…The corresponding expression for the physical situation where electrons and nucleons are treated as particles with spin can be found, e.g., in [8].…”

“…Calculations with exact Dirac wave functions have been performed by Kim et al [6] in the Ohio group and Udias et al [7,8]; the present eikonal approximation has the advantage that it is relatively simple to implement and that it avoids large computational costs. The eikonal method and its higher approximations, which can be obtained from an iterative procedure, is expected to lead to an asymptotic, rather than a convergent expansion [9].…”

Scaling and isospin effects in quasielastic lepton–nucleus scattering in the relativistic mean field approach

“…Due to this, the ratio between upper and lower components of the fully relativistic calculation is quite different from the one for free spinors or implied in the NR or SR approaches [15][16][17]. In order to assess the influence of the enhancement of the lower components (also called spinor distortion [18]) the fully relativistic calculation is compared here with the effective momentum approach (EMA) [9,15,17,18]. In the EMA the relationship between upper and lower components is forced to be the same as for free spinors.…”

“…In contrast, the study presented in [6,7] has shown that the asymmetry can in fact be obtained within the relativistic impulse approximation (RIA), given that a description of final-state interactions (FSI) using strong relativistic mean field (RMF) potentials is assumed. Recently, we have shown [8] that an asymmetrical scaling function can be also obtained within the framework of a semi-relativistic (SR) model, based on improved NR expansions of the on-shell electromagnetic current, provided that the FSI are described by the Dirac equation-based (DEB) potential [9] derived from the RMF. Note that, in the SR model, the nonlocalities arising from the NR reduction of the Dirac equation-and incorporated into the wave functions through the Darwin factor-are essential to reproduce the asymmetric shape of the scaling function.…”