In this work, the problem of the quantum optical model is considered where an one-mode quantized radiation field interacts with a two-level atom (TLA). Also, the atomic position distribution is taken into account, i.e., the atom passing through the length of the optical cavity. We believe that the atomic position affects the matter-field interaction and can be realized in several multiple experiments, such as ultracold atoms and trapped ions. We take into consideration the atom is moving along the cavity field in the x-direction so that the time-position Schrödinger equation for the atom in the x-direction is obtained. We suppose that the field is initially prepared in a coherent state optical field and the atom is initially prepared in an excited state. Also, the atomic motion along the cavity length vanishes in the cavity wall. By using the Laplace transformation method, an exact analytical solution for the coupled partial differential Schrödinger equation for the wave function is calculated. Some non-classical statistical aspects such as the atomic inversion and the photon distributions are discussed in detail. The collapses-revivals, the Poissonian distributions of the photon by Mandel Q parameter, the degrees of the entanglement, and the fidelity have been investigated. The effect of the atomic position distribution in the x-direction on these phenomena is examined. We observed that the atomic position distribution along the cavity has an effective effect on the quantum statistical properties of these phenomena. Minutely, the influence of the atom location distribution on the amount of quantum entanglement has been obtained.
The nucleus–nucleus reaction cross-sections of [Formula: see text]C and [Formula: see text]C at 240[Formula: see text]MeV/u are calculated using the optical limit of the Glauber model. The deformation and radii of a deformed Fermi density are calculated from the relativistic mean field (RMF). The results are compared with the recent experimental data. It is found that the Fermi density whose quadrupole deformation parameters and radii are derived from RMF, using TMA effective interaction in the RMF Lagrangian, provide a satisfactory explanation of the experimental data of Na isotopes, except for [Formula: see text]Na, which are expected to be strongly deformed. For F isotopes, the deformed Fermi density adjusted to the radii derived from RMF, using TMA interaction, presents a lower reaction cross-section. The Lagrangian parameters set NL3* gives a good description of the data which is better than that predicted by TMA. On the other hand, the two forces cannot describe the reaction cross-section of [Formula: see text]F since it is expected to have a deformed halo structure. The radius deduced from the data is found to be of the order 3.5[Formula: see text]fm.
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