A.Voronin a J.Carbonell b a) P.N. Lebedev Physical Institute, Moscow b) Institute des Sciences Nucleaires, Grenoble HYDROGENANTIHYDROGEN at sub-Kelvin Temperatures

Hydrogen-Antihydrogen Why interesting? n 1. Intriguing physics of atom-antiatom What does CPT violation mean for HH ?

Hydrogen-Antihydrogen Why interesting? n 2. Can we use H for fast deexcitation of H ? n 3. How long survive? n 4. Collisional shift and broadening of H

HH -molecule and fundamental symmetries HH -molecule and fundamental symmetries C-symmetry P-symmetry CP-symmetry

CPT and HH-molecule CPT violation induces C-violation in HH hamiltonian: C forbidden transitions: C in =-1, C fin =+1 C in =1 C fin =-1

Kinematics n Quantum numbers of opened channels

FORMALISM: 2 component Wave-function  is the quantum numbers set of opened Protonium channels

FORMALISM: Equations

Effective potential

Model H r1r1 r2r2 R R r  Pr Ps Variational calculation

In the simplest approximation we consider Pr and Ps relative motion as free, using free motion Green functions 32 final states are taken into account. MODEL: SIMPLE APPROXIMATION

Model: Final equation For R>1 a.u. : All information about inelastic transitions is within complex operator W eff, which vanishes for R>1 a.u. U nucl (R)-complex potential, describing nuclear absorption -C 6 /R 6 Quasibound states with inelastic width 1a.u.

Imaginary part of effective interaction

Annihilation cross-section Scattering length: a=6.1-i2.7 a.u., a at =5.2-i1.8 a.u.

Quantum features  max /  min ~ 10

Isotope effect

Oscillations with C 6

The effect of nuclear potential

Weakly-bound metastable states.

Scattering length oscillations

Analytical expression for scattering length Short range potential W eff + “long range”C 6 /R 6 r 0 is the range of W eff, about 1 r B,  is phase shift produced by short-range complex interaction. W eff -C 6 /R 6 r0r0 Im  black sphere Im  <<1-oscillations, Re  is very important Semitransparent Im a/Im a at =1.5

Excitation transfer reactions

CONCLUSIONS n 1. Nearthreshold weakly bound states is a key to dynamics. n 2. Magnifying glass – enhancemant of short range (nuclear) effects in n 3. Excitation transfer reactions can be a tool for antihydrogen deexcitation. n 4. Fundamental symmetries of molecule- can we check CPT with it? can we check CPT with it?

Some Refferences: 1. M.Amoretti et al. Nature 419 (2002) G. Gabrielse et al. Phys. Rev. Lett. 89, (2002); Phys. Lett. B 507, 1 (2001) 3. D.L. Morgan Jr. and V.W. Hughes: Phys. Rev. D2, 1389 (1970); W. Kolos et al.: Phys. Rev. A11, 1792 (1975) 4. G.V. Shlyapnikov et al.: Hyp. Int. 76, 31 (1993) 5. A.Yu. Voronin, J. Carbonell: Phys. Rev. A57, 4335 (1998); Nucl. Phys. A689(2001) 529c-532c 6. J. Carbonell et al.: Few-Body Systems Suppl. 8, 428 (1995) 7 S. Johnsel, A.Saenz,P. Froelich, B.Zygelman, A.Dalgarno, Phys. Rev.A 64, (2001);Phys. Rev.A 63, (2001)

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