Positronium molecule

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1 Positronium molecule e + e - e - (0γ) 2γ (4γ) (1γ) 3γ (5γ) e + PSAS 2008 University of Windsor, July 26, 2008 Andrzej Czarnecki University of Alberta

2 Outline Positronium, its ion, and the molecule Positronium atom Ion: theoretical prediction for the decay rate. Comparison with experiment. Molecule: spectrum. Dipole transition vs. annihilation.

3 Positronium and its ion e + e _ Very similar to hydrogen, except no hadronic nucleus annihilation reduced mass reduced me m 2 e Two spin states: singlet (para-ps) triplet (ortho-ps)

4 Positronium ion: a new test of bound-state QED e - e - Predicted 1946 Wheeler Observed 1981 Mills 2γ (4γ) (1γ) 3γ (5γ) e + Unique for the ion but very suppressed New positronium-ion source at the FRM II reactor in Munich: measurements of branching ratios.

5 Theory of the Ps ion: the wavefunction r ψ ( r, r ) = φ ( r, r, r) r 1 r 2 The wave function is not known analytically, but can be found using the variational method. Ground state: symmetric 1 2

6 Example of a variational calculation Test function: φ ( r, r, r) = exp k( r + r ) φ H φ E φφ With this very simple ansatz we do find a positive k but the binding energy is smaller than for positronium. The ion would not be stable.

7 A better fit to the wavefunction ( r, r, r) exp( k r k r ) exp( k r k r ) φ One finds that k1 2k2 Drachman & Bhatia We can picture the ion as a positronium shell and a loosely-bound electron. Now we can easily estimate the dominant decay channels.

8 For comparison: decays of positronium (atoms) e - γ ortho-ps e + γ γ Γexp o-ps = μs ( ) ( ) para-ps ( ) ( ) -1 Γ exp p-ps = ns 210 4

9 Recent measurement of the ion decay rate ( ) ( ) 1 μ Γexp Ps = s (factor 4-5 improvement expected)

10 Recent measurement of the ion decay rate ( ) ( ) 1 μ Γexp Ps = s (factor 4-5 improvement expected) We wanted to improve this

11 Positronium ion decay: refinements Corrections O(α) single hard photon loops Corrections O(α 2 ); challenge: divergences lnα soft hard O(k 2 ) corrections to the amplitude M Breit hamiltonian correction to ψ(r=0) Short-distance two-loop photon exchange Real photon radiation

12 Decay rate prediction + corrections ( ) 1 Ps ( 12) ns Γ = with M. Puchalski and S. Karshenboim PRL 99, (2007)

13 Ratio of three- to two-photon annihilation

14 Dipositronium Ps 2 e + e - e - (0γ) 2γ (4γ) (1γ) 3γ (5γ) e +

15 Discovery of dipositronium 2007 Molecule formation kills long-lived positronia. At higher temperature, fewer atoms on the surface, fewer molecules formed. Indeed: at high-t, more long-lived positronia observed. Cassidy & Mills, Nature 2007

16 Spectrum of the molecule Ps 2 From Suzuki & Usukura, 2000

17 A direct signal of the molecule: transition line. From Suzuki & Usukura, 2000 Autodissociation forbidden by Bose-Einstein statistics

18 A direct signal of the molecule: transition line. From Suzuki & Usukura, 2000 Observable UV transition

19 Two questions about this transition: What is its accurate energy? How often does it appear (before annihilation)? Results: arxiv: in press in PRL; with M. Puchalski

20 Energy levels: ground state and P-excitation Wave function determined variationally, using Coulomb potential; M. Puchalski Hylleraas & Ore, 1947 Relativistic corrections: perturbations. Annihilation dominates. Interval P-S determined with 5 x 10-6 accuracy (slightly smaller than in Ps, dielectric effect").

21 Competition: dipole transition vs. annihilation S-state annihilates quite rapidly. Assume it consists of two weakly-interacting Ps atoms, with random spins: There is a para-positronium pair with probability = 4 2 The decay rate: P-state: half of this rate ΓS = 2 τ 0.25ns pps

22 Competition: dipole transition vs. annihilation Quiz: if an isolated P-excited Ps atom lives ~3.2 ns, what do we expect in Ps 2? Let s assume the atoms interact very weakly in the molecule.

23 Competition: dipole transition vs. annihilation Quiz: if an isolated P-excited Ps atom lives ~3.2 ns, what do we expect in Ps 2? Let s assume the atoms interact very weakly in the molecule. datom = S d P PS+PS dmolecule = SS d = 2d 2 atom Transition in the molecule is twice faster. Branching ratio 1 P S 19% ~ ( ) BR = with M. Puchalski

24 Summary New states of positronium-like systems, ions and molecules: opportunity to test threeand four-body QED. The Coulomb wave functions not known analytically for e + e - e - and e + e - e + e -. Variational methods very accurate. O(alpha 2 ) corrections computed for the ion decay rate and the Ps 2 P-S interval. Both are being measured.

25 Breakdown of corrections to the Ps ion width

High-Order QED Calculations in Physics of Positronium

current status and future perspectives of High-Order QED Calculations in Physics of Positronium Alexander A. Penin II. Institut für Theoretische Physik, Universität Hamburg, Germany and Institute for Nuclear