1. Salamanca, July 2002
Geant4 simulation of the energy loss of slow negatively-charged hadrons
Stephane Chauvie
José M. Fernández-Varea
Vladimir N. Ivanchenko
Petteri Nieminen
Maria Grazia Pia
(for the Geant4 low-energy e.m. group)

2. Energy loss of heavy charged particles
Salamanca, July 2002
Energy loss of heavy charged particles
Electronic stopping power (1st Born approx.)
Stopping number
Inelastic form factor

3. If the ground state is isotropic
Salamanca, July 2002
If the ground state is isotropic
High-energy behaviour (Bethe formula)
Born-series expansion
Antiprotons: Z = -1 (no charge-exchange effects)

4. The quantal harmonic oscillator model
Salamanca, July 2002
The quantal harmonic oscillator model
Stopping number of an atom (= ensemble of oscillators)
Frequencies & oscillator strengths
Constraints
These quantities are normally obtained from available optical
or dielectric data

5. Nominal plasma frequency
Salamanca, July 2002
Simplified model
Nominal plasma frequency
Sternheimer parameter a ~ e1/2 = 1.65
For other heavy negative hadrons

6. Geant4 implementation of the model
Salamanca, July 2002
Geant4 implementation of the model

7. Salamanca, July 2002
Results (i)
Continuous curve: antiproton; dashed curve: proton; symbols: exp.;
dot-dashed curve: non-linear calculation.

8. Salamanca, July 2002
Results (ii)
Continuous curve: antiproton; dashed curve: proton; symbols: exp.;
dot-dashed curve: non-linear calculation.

9. Salamanca, July 2002
Results (iii)
Continuous curve: antiproton; dashed curve: proton; symbols: exp.