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

## Abstract

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.

- Authors:

- Laboratoire des Collisions Atomiques et Moleculaires (CNRS UMR 8625), Batiment 351, Universite Paris-Sud, 91405 Orsay Cedex (France)
- (Spain)
- Departamento de Fisica de Materiales, Facultad de Quimicas UPV/EHU, Apartado 1072, 20080 San Sebastian (Spain)
- Donostia International Physics Center DIPC, P. Manuel de Lardizabal 4, 20018 San Sebastian (Spain)

- Publication Date:

- OSTI Identifier:
- 20786724

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.012901; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 36 MATERIALS SCIENCE; ANTIPROTONS; CHARGED PARTICLES; COMPARATIVE EVALUATIONS; DENSITY FUNCTIONAL METHOD; ELECTRON GAS; ELECTRONS; EXCITATION; HOLES; NONLINEAR PROBLEMS; PLASMONS; TIME DEPENDENCE; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Borisov, A. G., Donostia International Physics Center DIPC, P. Manuel de Lardizabal 4, 20018 San Sebastian, Juaristi, J. I., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Muino, R. Diez, Sanchez-Portal, D., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Echenique, P. M., Departamento de Fisica de Materiales, Facultad de Quimicas UPV/EHU, Apartado 1072, 20080 San Sebastian, and Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian.
```*Quantum-size effects in the energy loss of charged particles interacting with a confined two-dimensional electron gas*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Borisov, A. G., Donostia International Physics Center DIPC, P. Manuel de Lardizabal 4, 20018 San Sebastian, Juaristi, J. I., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Muino, R. Diez, Sanchez-Portal, D., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Echenique, P. M., Departamento de Fisica de Materiales, Facultad de Quimicas UPV/EHU, Apartado 1072, 20080 San Sebastian, & Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian.
```*Quantum-size effects in the energy loss of charged particles interacting with a confined two-dimensional electron gas*. United States. doi:10.1103/PHYSREVA.73.0.

```
Borisov, A. G., Donostia International Physics Center DIPC, P. Manuel de Lardizabal 4, 20018 San Sebastian, Juaristi, J. I., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Muino, R. Diez, Sanchez-Portal, D., Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian, Echenique, P. M., Departamento de Fisica de Materiales, Facultad de Quimicas UPV/EHU, Apartado 1072, 20080 San Sebastian, and Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian. Sun .
"Quantum-size effects in the energy loss of charged particles interacting with a confined two-dimensional electron gas". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786724,
```

title = {Quantum-size effects in the energy loss of charged particles interacting with a confined two-dimensional electron gas},

author = {Borisov, A. G. and Donostia International Physics Center DIPC, P. Manuel de Lardizabal 4, 20018 San Sebastian and Juaristi, J. I. and Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian and Muino, R. Diez and Sanchez-Portal, D. and Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian and Echenique, P. M. and Departamento de Fisica de Materiales, Facultad de Quimicas UPV/EHU, Apartado 1072, 20080 San Sebastian and Unidad de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, P. Manuel de Lardizabal 3, 20018 San Sebastian},

abstractNote = {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.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 1,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}