1. AN ORIGINAL MODEL FOR THE SIMULATION OF LOW ENERGY ANTIPROTONS
S. Chauvie
On behalf of Geant4 Low Energy Electromagnetic Group
INFN, Sezione di Torino and Santa Croce e Carle Hospital, Cuneo, Italy
Antiprotons in the Space Environment
The first evidence of stopping power dependence on the particle charge dates back to Barkas in the ’50s; he measured different ranges for positive and negative pions at low energies (  < 0.5 ) and interpreted them as caused by the polarisation of the surrounding medium.
“The Barkas Effect”
Exotic sources
Primordial Black Holes
Annhilating/decaying Dark Matter in Galactic Halo WIMPS...
Simmetry Breaks, ...
Precise knowledge of
Antiproton/Proton ratio of
Cosmic Rays
Energy Loss and Range of Negatively Charged Particles
p: High Energy Cosmic Rays
A: Interstellar Medium
X: anything consistent with Charge and Baryonic number conservation
is important for various particle physics experiments
Status
Doesn’t exist simulation tools to account for charge dependence of Stopping Power.
Simulation without correction could lead to misunderstanding (e.g. 50% errors in range for 0.5 MeV Antiproton in Aluminum)
Geant4 Low Energy Electromagnetic Package take care of it
Algorithms encapsulated in objects
Physics models handled through abstract classes
Hadrons and ions
Interchangeable and transparent access to data sets
Hadron and ion processes in Geant4 Low Energy Electromagnetic Package
Variety of models, depending on energy range, particle type and charge
Positive charged hadrons
Density correction for high energy
Shell correction term for intermediate energy
Spin dependent term
Barkas and Bloch terms
Chemical effect for compound materials
Nuclear stopping power
Bethe-Bloch model of energy loss, E > 2 MeV
5 parameterised models, E < 2 MeV
based on Ziegler and ICRU reviews
3 models of energy loss fluctuations
Positive charged ions
Low energy extensions: hadrons and ions
Effective charge model
Nuclear stopping power
Scaling:
0.01 < b < 0.05 parameterisations, Bragg peak
based on Ziegler and ICRU reviews
b < 0.01: Free Electron Gas Model
Various models, depending on the energy range and charge
E > 2 MeV  Bethe-Bloch
1 keV < E < 2 MeV  parameterisationsZiegler 1977, 1985
ICRU 49
corrections due to chemical formulae of materials
nuclear stopping power
E < 1 keV free electron gas model
Negative charged hadrons
Parameterisation of available experimental data
Quantum Harmonic Oscillator Model
Model original to Geant4
Negative charged ions: required, foreseen
With the Generalised Oscillator Strength:
Stopping Power
Bethe Theory:
the Stopping Power is related to the Coulomb excitation and ionisation of the electron of the stopping medium
the interaction is treated within the first Born approximation
In the case of projectile velocity much greater than bounded electron
v >> ve
Stopping Number
Particle
Bethe formula
with the dimensionless Stopping Number L
Stopping Number with Harmonic Oscillator Model
is proportional to the conditional probabilitiy that the atom makes the transition to an excited state |n > upon receiving a momentum transfer q
Material
Harmonic Oscillator Model for Atoms
Born expansion in power of Zh
L0, L1, L2 terms have been calculated by the Theory Group at Aahrus University (Denmark)
Thanks!
implementation
T > 2 MeV  Bethe-Bloch formula
(50 keV) < T < 2 MeV  Quantum Harmonic Oscillator Model
T < (50 keV)  Electron Gas Model
Hp:
Oscillator Strength f = Occupation Number w
The atom is considered as an ensemble of j oscillators corresponding to the atomic shells
Model Validation Results
The Quantum Harmonic Oscillator Model is applied to calculate the energy loss of antiprotons in a material
Experimental data come from CERN Antiproton Decelerator (AD)
Stopping Number for Antiprotons in Silicon
Stopping Power for Antiprotons in Aluminum ...
Stopping Number (a.u)
Kinetic Energy (eV)
… Silicon ... L0 L L1 L2
Conclusions
From Protons to Antiprotons Stopping Power for Antiprotons (40-60% to 1-10%) che vuol dire?
Useful for various undergoing experiments and for space-related activities
Easy to implement Physics Processes in Geant4 (the iterative-incremental implementation of the class took 1 week)
Another alternative model (even for Protons)
...
... Gold.