1. How to Simulate Anti-Matter – Matter Interactions?2
Simulation of light antinucleus-nucleus interactions
A.Galoyan and V. Uzhinsky, 22/06/2012
Anti-Matter at Accelerators
Anti-Proton 1955, Emilio Segre and Owen Chamberlain (Nobel Prize in Physics)-
Anti-Neutron, 1956, Bruce Cork and colleagues (BNL)
Anti-Deuterium, 1965, Antonino Zichichi et al. (CERN), D.E. Dorfan et al. (BNL)
Anti-Helium-3, , Y.M. Antipov et al. (IHEP)
Anti-Helium-4, March 2011, Star Collab, H. Agakishiev et al. (RHIC)
Observation of the antimatter helium-4 nucleus, arXiv: , Au+Au, 200
18 Anti-He-4
ALICE Collab.
LHC
5 Anti-He-4
Discovery of Anti-Nuclei in cosmic rays? - > PAMELA,BESS,AMS,CAPRICE
How to Simulate Anti-Matter – Matter Interactions? 1

2. Task: estimate antinucleus-nucleus interaction cross
sections, elastic scattering and multi-particle production
● Apply of the Glauber theory for the cross section calculations
● Apply the Glauber amplitudes and black disk model with diffuse boundary for a simulation of the elastic scattering
● Apply the Quark-Gluon String Model for a simulation of the multi-particle production processes
● Our parametrization of Pbar-P total and elastic cross sections
● Our parametrization of antinucleus-nucleus total and elastic cross sections
● Results of simulation of inelastic Pbar-P, Pbar-A interactions
We use well known
Glauber theory 2

3. Glauber theory for antiproton-nucleus interactions
For the first time a good description of Pbar D interactions was reached in the paper by V. Franco, R.J. Glauber, Phys. Rev. 142 (1966) High-energy deuteron cross-sections.
adTa_Fig8
Amplitude of hadron-nucleus elastic scattering
Differential elastic scattering cross section
Amplitude of elastic hN scattering in impact parameter representation
ß is the slope parameter of hN differential elastic cross section
Square module of the wave function is written as:
Diagen: Generator Of Inelastic Nucleus-nucleus Interaction Diagrams. S. Shmakov, V.Uzhinsky, A.Zadorozhny, Comp. Phys. Comm., 54 (1989) 125 3

4. Our parameterization of PbarP cross sections
σel/σtot=1/(2 Csh)≈1/3, according to the quasi-eikonal approach of the reggeon field theory
(K.A. Ter-Martirosyan, A.B. Kaidalov) 4

5. The Glauber approach works well!
V. Uzhinsky, J. Apostolakis, A. Galoyan et al., Phys. Lett B705 (2011) 235
Geant4 class G4ComponentAntiNuclNuclearXS for Pbar – Nucleus and light
Anti-Nucleus – Nucleus cross sections.
Physics List – FTF_BERT
The Glauber approach works well! 5

6. Glauber theory for nucleus-nucleus interactions
Amplitude of nucleus-nucleus elastic scattering in Glauber theory
Generator of inelastic nucleus-nucleus interaction diagrams
Computer Physics Communications, V 54, 1989, Pages
S. Yu. Shmakov, V. V. Uzhinskii, A. M. Zadorozhny - DIAGEN 6

7. Nuclear cross sections – absorption X’s
The Glauber approach works well! 7 7

8. Nuclear cross sections – absorption X’s6 8

9. Parameterization of Glauber Anti-Nucleus-Nucleus cross sections
Radii for total Anti-Nucleus-Nucleus cross sections 9

10. Simulation of Anti-Nucleus-Nucleus Elastic Scattering
Calculation results for Profile functions in Glauber model
Generator of inelastic nucleus-nucleus interaction diagrams, Computer Physics Communications, 54 (1989)125, S. Yu. Shmakov, V. V. Uzhinskii, A. M. Zadorozhny
Profile functions P(b) for pbar+Pb at Plab=0.1, 1, 1000 GeV/c
According to black disk model approximation 2-dimensional
Fourie transform of P(b):
(1)
W.E. Frahn, R.H. Venter// Ann. Phys. 24 (1963) 234;
D.C. Choudhury// Phys. Rev. C22 (1980) 1848; 10
Yu.A. Berezhnoy, V.Yu. Korda// Inter. J. Mod. Phys. 7 (1998) 723

11. Glauber amplitudes and black disk model approximation
Pbar+Pb elastic scattering Glauber amplitudes at P=0.1 and 1000GeV/c
(blue lines) and J1(Rq)/(Rq) (black lines)
First zero of F(q) can be used for determination of R, R=3.832/q_zero
F(0)=πR2 at such choice of R 11

12. Interpolation of effective parameters of black disk model12

13. Differential Cross sections of Elastic Pbar Nucleus interactions13

14. Differential Cross sections of Elastic Pbar Nucleus interactions14

15. Differential Cross sections of elastic interactions of Dbar with C, Ca and Pb15

16. Dual Parton Model (Quark-Gluon String Model)
Calculation procedure:
V.V. Uzhinsky and A.S. Galoyan, hep-ph/
Cross-sections of various processes in anti-P P
interactions.
Implementation:
A.Galoian and V.Uzhinsky,AIP Conf.Proc.796:79,2005
New Monte Carlo implementation of quark-gluon
string model of anti-p p interactions.
FTF (Geant4), DPM (Panda), UrQMD +SMM 16

17. 12
Annihilation at rest 17

18. Inclusive Spectra in Antibaryon-Baryon Interactions
The situation is as
usual!
Some experimental
data agree well with
our approach.
Some data which
do not agree are
probably suspect! 18

19. Simulation of pbar-A at Plab= 608 MeV/c
Annihilation of antineutrons at Plab=1.4 GeV/c 19

20. Energy distributions of produced neutrons in Pbar-A interactions20

21. 15
Simulation of anti-deuteron-Ta interactions
Anti-deuteron momentum 12.2 GeV/c
Parameter variations. 21

22. Conclusion
New parametrization of Pbar-P total and elastic cross sections has
is proposed. Results of our parametrization are in agreement with
known exp.data.
2. Method for calculations of Light Anti-Nucleus– Nucleus cross
sections has been developed and implemented in Geant4.
Good description of known exp. data on cross sections is obtained.
3. Simulation of annihilation Nbar-N processes based on Dual Parton
model has been implemented in Geant4.
Simulation of Light Anti-Nucleus – Nucleus Inelastic interactions
is also presented in Geant4. Some exp. data agree well with
our approach.
4. Method of simulation of Anti-Nucleon – Nucleus and
Light Anti-Nucleus – Nucleus Elastic scatterings has been
created and also implemented in Geant4. The method is based on
Black Disk Model with Diffuse Boundary and Coulomb - Wentzel
model. Exp. data on elastic scatterings have been reproduced. 22

23. Class: G4VHadronElastic G4AntiNuclElastic Data of class: Base class
FTFP+Bert Physics List
GEANT4
G4VHadronElastic
Base class
Class for elastic Pbar-P, Pbar-A simulations
G4AntiNuclElastic
G4double SampleInvariantT (
const G4ParticleDefinition* p,
G4double plab, G4int Z, G4int A);
Derived methods
Sampling of polar angle Theta
Methods:
G4double SampleThetaCMS( particle, plab, Z, A);
G4double SampleThetaLab( p, plab, Z, A);
and other methods
cs, fTeta1, fTetaCMS, fThetaLab, fRa, fRef et al.
Data of class: 23

24. 24 Simulation of Anti-Nucleus-Nucleus Elastic Scattering
Strong Absorption Model, or Black Disk Model 24

25. SampleInvariantT (p, plab, Z, A);
G4AntiNuclElastic::
SampleInvariantT (p, plab, Z, A);
Coulomb – Wentzel scattering ( V.M. Grishine/ CPC 181 (2010) 921 )
Hadronic part
─ Magorant function 25

26. Description of the Totem data and our predictions for other LHC En.
V. Uzhinsky, A. Galoyan, Nov e-Print: arXiv:
"Description of the Totem experimental data on elastic pp-scattering at sqrt(s)=7 TeV in the framework of unified systematic of elastic scattering data.“
Description of the Totem data and our predictions for other LHC En. 26