Relativistic distorted-wave impulse approximation analysis ofC12(e,e'p)forQ2<2 (GeV/c)2

Abstract

We analyze data for $^{12}\mathrm{C}(e,{e}^{'}p)$ with ${Q}^{2}<2\phantom{\rule{0.3em}{0ex}}(\mathrm{GeV}/c){}^{2}$ using the relativistic distorted-wave impulse approximation (RDWIA) based upon Dirac-Hartree wave functions. The $1p$ normalization extracted from data for ${Q}^{2}>0.6$ (GeV/c)${}^{2}$ is approximately 0.87, independent of ${Q}^{2}$, which is consistent with the predicted depletion of the $1{p}_{3/2}$ orbital by short-range correlations. The total $1p$ and $1s$ strength for ${E}_{m}<80\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ approaches 100% of IPSM (independent particle shell model), consistent with a continuum contribution for $30<{E}_{m}<80\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ of about 12% of IPSM. Similarly, a scale factor of 1.12 brings RDWIA calculations into good agreement with $^{12}\mathrm{C}(e,{e}^{'}p)$ data for transparency. We also analyzed low ${Q}^{2}$ data from which a recent nonrelativistic RDWIA analysis suggested that spectroscopic factors might depend strongly upon the resolution of the probe. We find that the momentum distributions for their empirical Woods-Saxon wave functions fit to low ${Q}^{2}$ data for parallel kinematics are too narrow to reproduce data for quasiperpendicular kinematics, especially for larger ${Q}^{2}$, and are partly responsible for reducing fitted normalization factors. Although the RDWIA normalization factors for ${Q}^{2}<0.2\phantom{\rule{0.3em}{0ex}}(\mathrm{GeV}/c){}^{2}$ are also smaller than obtained for ${Q}^{2}>0.6\phantom{\rule{0.3em}{0ex}}(\mathrm{GeV}/c){}^{2}$, the effect is smaller, and we argue that it should be attributed to the effective single-nucleon current operator instead of to spectroscopic factors, which are probe-independent properties of nuclear structure. However, remediation of the failure of RDWIA calculations to reproduce low ${Q}^{2}$ data for parallel kinematics will require a more sophisticated modification of the current method than a simple multiplicative factor.