A project of an experiment benefits from a full simulation of it (when possible)

1. CTMC Simulation of H-bar formation by chargeexchange reaction with PsG. Testera on behalf of C. Canali INFN GenoaAEGIS meeting CERN june 2006

2. A project of an experiment benefits from a full simulation of it (when possible) • Several types of simulations are needed in AEGIS • 1) detection (“standard” for particle physics, see Andrea F. talk at last meeting) • 2) Ps*- pbar interaction and Hbar formation, Hbar in E, B fields • 3) Measurement setup (Sinisa…) • We have just started addressing point 2) • (about 2 months ago) • Open projet, needs collaboration from expert people

3. Simulation of Hbar formation • Simulate our production setup and geometry (Ps* laser excited reacts with cold pbar stored in a trap) No plasma simulation: assume that pbars form a cloud with given dimensions and temperature • Simulate charge exchange and understand the Hbar final state distribution • Follow formed Hbar* in given electric (and magnetic) fields • Find the Hbar final energy distribution, trapping efficiency ..

4. Some related works • J. Lu et al. “Antihydrogen formation by collisions of antiprotons with positronium in a magnetic field” PRA 68 024702 (2003) • J. Lu phd Thesis University of Bielefeld (2003) “Classical trajectory simulations of Ions-Rydberg atoms collisions” supervisor prof. H. O. Lutz • J-H. Choi, J. R. Guest, G. Raithel (Dep of Physics ,University of Michigan) papers about magnetic trapping of Rydberg atoms and classical (CTMC) calculations • M.L. Wall, C.S. Norton, F. Robicheaux “Two stage Rydberg charge exchange in a strong magnetic field” PRA 72 052702 (2005) Cs* + e+--Ps* +… Ps*+ p- Hbar*+e- CTMC calculations OK for Rydberg states

5. Charge exchange cross section for collision of p-bar with Ps : No magnetic field : ▲▼ B=5T: ● ■ * B=4T: ♦ The presence of B decrease the cross section Relative Velocity [3] J. Lu et al - Phys. Rev. A 68, (2003)

6. Charge Exchange interaction between Ps and p-bar: • Use of a CTMC (Classical Trajectory Monte Carlo) method • cross-section study • B-dependence of σ • B + E-dependence of σ • final states distribution (n,l) / (n,k) for H-bar • produced by charge exchange with laser excited positronium ? ? • CTMC works for high-n states of positronium/antihydrogen

7. After collision: e- remains bound to e+ e+ captured by other ionization Charge exchange simulation strategy • Choose the initial state of Ps* • Follow classical motion of bound (e+,e-) and pbar • (3 bodies CTMC) e+ e- Ps in Rydberg states

8. Positronium in magnetic field (and Electric field) [1],[2] Hamiltonian of an e+ and e- in homogeneous static Electric E and magnetic field B: e- e+ The total momentum is p=p1-p2 The centre-of-mass motion and the relative motion of e+ e- cannot be separated. The pseudo-momentum is a conserved quantity [3]: High n-states (classical description) Hamiltonian of the internal motion (p=p1-p2) [1] J. Shetzer - Phys. Rev. A 58, 2 (1998) [3] J.E. Avron - Ann. Phys. (N.Y.) 114 431 (1978) [2] O. Dippel – Phys. Rev. A 49, 4415 (1994)

9. Still open questions: • What is the final states distribution of produced H-bar ? (n, l) can be obtained from classical considerations for Rydberg states Follow motion of (pbar e+)* in given external fields Raithel: 2 bodies CTMC • What is the Cross Section in presence of E and B field ?