# Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions

## Abstract

We present theoretical calculations of the energy-loss straggling of C, Al, Si, and Cu targets for H, He, and Li ions in the range of intermediate to high energies (0.01-10 MeV/u). These calculations have been done by employing the dielectric formalism and by considering the different equilibrium charge states of the swift ion inside the solid as a function of its energy. Two different models are used: the Mermin energy-loss functions combined with generalized oscillator strengths (MELF-GOS) and the shellwise application of the local plasma approximation (SLPA). The MELF-GOS describes the target outer-electron excitations through a fitting to experimental data in the optical limit, employing a linear combination of Mermin-type energy-loss functions; the excitations of the inner-shell electrons are taken into account by means of generalized oscillator strengths. The SLPA employs a free-electron-gas model for the target valence electrons and the local density approximation for each shell of target electrons separately by using Hartree-Fock atomic wave functions. The results of the energy-loss straggling obtained by the two independent models show good agreement with the available experimental data. The calculated energy-loss straggling tends at high energies to the Bohr value and takes values below it at intermediate energies. The Bethe-Livingston shouldermore »

- Authors:

- Instituto de Astronomia y Fisica del Espacio, Casilla de correo 67, Sucursal 28, 1428 Buenos Aires (Argentina)
- (Argentina)
- (Spain)

- Publication Date:

- OSTI Identifier:
- 20982137

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022903; (c) 2007 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; ALUMINIUM; ATOMIC IONS; CARBON; CHARGE STATES; COMPUTER CALCULATIONS; COPPER; DENSITY FUNCTIONAL METHOD; ELECTRON GAS; ENERGY LOSSES; EXCITED STATES; HARTREE-FOCK METHOD; HELIUM IONS; HYDROGEN IONS; ION-ATOM COLLISIONS; KEV RANGE; LITHIUM IONS; MEV RANGE 01-10; OSCILLATOR STRENGTHS; SILICON; WAVE FUNCTIONS

### Citation Formats

```
Montanari, C. C., Miraglia, J. E., Heredia-Avalos, Santiago, Garcia-Molina, Rafael, Abril, Isabel, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Departamento de Fisica - CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia, and Departament de Fisica Aplicada, Universitat d'Alacant, Apartat 99, E-03080 Alacant.
```*Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.022903.

```
Montanari, C. C., Miraglia, J. E., Heredia-Avalos, Santiago, Garcia-Molina, Rafael, Abril, Isabel, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Departamento de Fisica - CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia, & Departament de Fisica Aplicada, Universitat d'Alacant, Apartat 99, E-03080 Alacant.
```*Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions*. United States. doi:10.1103/PHYSREVA.75.022903.

```
Montanari, C. C., Miraglia, J. E., Heredia-Avalos, Santiago, Garcia-Molina, Rafael, Abril, Isabel, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Departamento de Fisica - CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia, and Departament de Fisica Aplicada, Universitat d'Alacant, Apartat 99, E-03080 Alacant. Thu .
"Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions". United States.
doi:10.1103/PHYSREVA.75.022903.
```

```
@article{osti_20982137,
```

title = {Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions},

author = {Montanari, C. C. and Miraglia, J. E. and Heredia-Avalos, Santiago and Garcia-Molina, Rafael and Abril, Isabel and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Departamento de Fisica - CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia and Departament de Fisica Aplicada, Universitat d'Alacant, Apartat 99, E-03080 Alacant},

abstractNote = {We present theoretical calculations of the energy-loss straggling of C, Al, Si, and Cu targets for H, He, and Li ions in the range of intermediate to high energies (0.01-10 MeV/u). These calculations have been done by employing the dielectric formalism and by considering the different equilibrium charge states of the swift ion inside the solid as a function of its energy. Two different models are used: the Mermin energy-loss functions combined with generalized oscillator strengths (MELF-GOS) and the shellwise application of the local plasma approximation (SLPA). The MELF-GOS describes the target outer-electron excitations through a fitting to experimental data in the optical limit, employing a linear combination of Mermin-type energy-loss functions; the excitations of the inner-shell electrons are taken into account by means of generalized oscillator strengths. The SLPA employs a free-electron-gas model for the target valence electrons and the local density approximation for each shell of target electrons separately by using Hartree-Fock atomic wave functions. The results of the energy-loss straggling obtained by the two independent models show good agreement with the available experimental data. The calculated energy-loss straggling tends at high energies to the Bohr value and takes values below it at intermediate energies. The Bethe-Livingston shoulder (or overshooting) at intermediate energies does not appear in the present calculations. We find that the energy-loss straggling normalized to Z{sub P}{sup 2} is almost independent of the ion atomic number Z{sub P}; therefore, the results for H, He, and Li projectiles in each target can be approximated by a universal curve at high energies.},

doi = {10.1103/PHYSREVA.75.022903},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}