Nuclear Transparency in a Relativistic Quark Model

Abstract

We examine the nuclear transparency for the quasi-elastic ($e, e'p$) process at large momentum transfers in a relativistic quantum-mechanical model for the internal structure of the proton, using a relativistic harmonic oscillator model. A proton in a nuclear target is struck by the incident electron and then propagates through the residual nucleus suffering from soft interactions with other nucleons. We call the proton "dynamical" when we take into account of internal excitations, and "inert" when we freeze it to the ground state. When the dynamical proton is struck with a hard (large-momentum transfer) interaction, it shrinks, i.e., small-sized configuration dominates the process. It then travels through nuclear medium as a time-dependent mixture of intrinsic excited states and thus changing its size. Its absorption due to the soft interactions with nuclear medium depends on its transverse-size. Since the nuclear transparency is a measure of the absorption strength, we calculate it in our model for the dynamical case, and compare the results with those for the inert case. The effect of the internal dynamics is observed, which is in accord with the idea of the "color transparency". We also compare our results with the experimental data in regard of $q^2$-dependence as well as A-dependence, and find that the A-dependence may reveal the color-transparency effect more clearly.