Effect of the Optical Potential on the Nucleon Momentum Distribution in Nuclei. The Pickup Reaction

The effect of the optical potential on the nucleon momentum distribution in nuclei is discussed in this work. The idea of McCarthy et al., that the refraction and localization effects caused by the real and imaginary parts of the optical potential smears the single-particle momentum distribution, is amplified and applied to nucleon momentum distribution experiments. The assertion is made here that it seems impossible to directly measure in any manner the momentum distribution of nucleons in nuclei. Further it is proposed that much or all of the large discrepancy between the experimental momentum determinations and the shell-model predictions is due to the neglect of these important sources of high-momentum components. The high-energy ${\mathrm{C}}^{12}(p, d){\mathrm{C}}^{11}$ pickup reaction data are re-analyzed in the light of these considerations. It is shown that for $\frac{q^2}{{\beta }^2}\lesssim 8$, the $1p$-shell harmonic oscillator distribution, $\left(\frac{q^2}{{\beta }^2}\right)\exp (-\frac{q^2}{{\beta }^2})$, has sufficient high-momentum components to fit the data. The lack of agreement for $\frac{q^2}{{\beta }^2}>8\mathrm{}$ is possibly due more to a failure in the distorted-wave approximation calculation used here than to lack of high-momentum components in the wave function.