We analyze data for ${}^{12}\mathrm{C}(e,e^{\text{'}}p)$ with $Q^2<2(\mathrm{GeV}/c){}^2$ 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 $1p_{3/2}$ orbital by short-range correlations. The total $1p$ and $1s$ strength for $E_m<80\mathrm{MeV}$ approaches 100% of IPSM (independent particle shell model), consistent with a continuum contribution for $30<E_m<80\mathrm{MeV}$ of about 12% of IPSM. Similarly, a scale factor of 1.12 brings RDWIA calculations into good agreement with ${}^{12}\mathrm{C}(e,e^{\text{'}}p)$ 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 $Q^2<0.2(\mathrm{GeV}/c){}^2$ are also smaller than obtained for $Q^2>0.6(\mathrm{GeV}/c){}^2$, 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.

• Received 1 February 2005

DOI:https://doi.org/10.1103/PhysRevC.71.064610