Quantum-size effects in the energy loss of charged particles interacting with a confined two-dimensional electron gas

Time-dependent density-functional theory is used to calculate quantum-size effects in the energy loss of antiprotons interacting with a confined two-dimensional electron gas. The antiprotons follow a trajectory normal to jellium circular clusters of variable size, crossing every cluster at its geometrical center. Analysis of the characteristic time scales that define the process is made. For high-enough velocities, the interaction time between the projectile and the target electrons is shorter than the time needed for the density excitation to travel along the cluster. The finite-size object then behaves as an infinite system, and no quantum-size effects appear in the energy loss. For small velocities, the discretization of levels in the cluster plays a role and the energy loss does depend on the system size. A comparison to results obtained using linear theory of screening is made, and the relative contributions of electron-hole pair and plasmon excitations to the total energy loss are analyzed. This comparison also allows us to show the importance of a nonlinear treatment of the screening in the interaction process. © 2006 The American Physical Society.
This work was supported, in part, by the Basque Departamento de Educación, Universidades e Investigación, the University of the Basque Country UPV/EHU (Grant No. 9/UPV 00206.215-13639/2001), the Spanish Ministerio de Educación y Ciencia (Grant No. FIS2004-06490-C03-00), and the EU Network of Excellence NANOQUANTA (Grant No. NMP4-CT-2004-500198). A.G.B. acknowledges financial support by the DIPC.