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Fishing for positronic compounds

Fishing for positronic compounds. Dario Bressanini. Università dell’Insubria, Como, ITALY. QMC in the Apuan Alps VII 2012 TTI Vallico Sotto. Theory ahead of experiments. e + 1930: Dirac theory e + 1933: Carl Anderson experiment (cosmic radiations)

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Fishing for positronic compounds

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  1. Fishing for positronic compounds Dario Bressanini Università dell’Insubria, Como, ITALY QMC in the Apuan Alps VII 2012 TTI Vallico Sotto

  2. Theory ahead of experiments • e+ 1930: Dirac theory • e+ 1933: Carl Anderson experiment (cosmic radiations) • Ps (e+ e-) 1937 (1946): Ruark theory(coined the name) • Ps (e+ e-) 1946: Wheeler theory(polyelectrons) • Ps (e+ e-) 1951: Martin Deutsch experiment Annihilation via g photons is inevitable… “resistance is futile” …but a lot can happen on the way • Two spin states • Singlet (para-positronium) – 0.125 ns • Triplet (ortho-positronium) – 142 ns

  3. Time scales

  4. e+ and Ps spectroscopy • Used in • Polymer science • Medical research • Solid state, electronics • hope to build a g-ray laser

  5. Theory ahead of experiments • Ps- (e+ e- e-) and Ps+ (e+ e+ e-) • inconsistent nomenclature • A- means Ae- , an added electron (as usual) • A+ means Ae+ , an added positron (but not always) • 1946, 1947: Wheeler, Hylleraas theory • 1981 Ps- seen in experiment by Mills • HPs (p+ e+ e- e-) • 1947, Hylleraas & Ore theory • Seen in experiment 1992 Schrader • Many calculations on atomic bound states, very few experimental results (more with molecules)

  6. Current status for atoms

  7. Computational techniques HPs • CI • slow convergence • frozen core • many atoms • ECG-SVM • very accurate • slow optimization • 4 e- • VMC-DMC • Compact Y • VMC can be unbound • statistical error Bressanini and Morosi: JCP 119, 7037 (2003)

  8. Polyleptons

  9. Ps2 : e-e-e+e+ • 1946: Wheeler, unbound • 1946: Ore, unbound • 1947: Hylleraas & Ore: bound • -0.504 a.u. • 1947-1996: what is the energy? • Energy did not converge with time 0.001 a.u. = 0.027 eV

  10. The energy of Ps2 • 1996-1997: Energy controversy resolved • -0.51601(1) DMC (1997, Bressanini et al.) • agrees with Frolov & Smith, hylleraas (1996) • -0.516003788 Matyus & Reiher ECG 2012 0.001 a.u. = 0.027 eV

  11. Ps2 : e-e-e+e+ • 2007: finally seen in experiment • Cassidy & Mills, Nature 449 195 (2007) • 60 years after theoretical prediction • Open the possibility to study BEC of Ps • Not the end of the story…

  12. Ps2 : e-e-e+e+ • Symmetry of Ps2 must include charge conjugation: e-  e+ • problems with early calculations • 1993: isomorph to D2h group (Kinghorn & Poshusta) • 0+(A1) ground state • 0+(B2), 0+(E) excited states • 1998: Varga, Usukura, Suzuki ECG • 1-(B2) bound L=1 state E = -0.334408 a.u. • 2012: L=1 state detected experimentally

  13. Higher systems? Psn, Ps-n Ps2- Ps2 + e- Ps2- Ps + Ps- Ps2- L=0 unbound (ECG) What about L>0 ? 0 1 2 3 4 e- e+ 0 e- 1 e+ Ps Ps- 2 Ps+ Ps2 Ps2- 3 Ps2+ Ps3 Ps3- 4 Ps3+ Ps4

  14. Ps2- and beyond: general strategy • Problems with Monte Carlo: • No starting Y(R) from HF/DFT • Use a “Valence Bond-like” Y(R) • Y(R)=A[Y(Ps) Y(Ps-)] or for other fragments • VMC and DMC unbound. Dissociation • Use a modified potential (preserving symmetry) • V(R) = V(e-,e+) + g (V(e-,e-) + V(e+,e+)) • Y(R)=A[Y(Ps) Y(Ps-) Y(interaction)] • Consider the limit for g1

  15. Ps2- total energy • E(L=1) < E(L=0)

  16. Ps2- binding energy • L=0 is unbound • L=1 is probably unbound… • …but with better nodes?

  17. Ps3 and Ps3- • Preliminary results • Ps3 and Ps3- unbound so far • Not explored yet all excited states

  18. Z=3 e+ Li 6 0 1 2 3 4 5 • 1976: Hylleraas CI, e+Li unbound(Clary) • 1996: DMC, e+Li unbound(Yoshida & Miyako) • 1997: ECG, e+Li bound(Ryzhikh & Mitroy, Strasburger & Choinacki) • Li+ + Ps → e+Li BE=0.0025 a.u. (first neutral atom to bind e+) • 1999: DMC, e+Li bound(Mella, Morosi & Bressanini) e- e+ 0 Li+3 Li+2 Li+ Li Li- 1 e+Li 2

  19. Z=3 e+ Li 6 0 1 2 3 4 5 • 1996: DMC, LiPs unbound, BE = -0.011(4) a.u. (Harju, Barbiellini & Nieminen) • 1997: DMC, LiPs bound, BE = 0.028(5) a.u. (Yoshida & Miyako) • 1998: DMC, LiPs bound, BE = 0.0096(8) (Bressanini, Mella & Morosi) • 1998: ECG-SVM, LiPs bound BE = 0.01051 (Ryzhikh & Mitroy) • Li + Ps→ LiPs BE=0.01237 a.u. e- e+ 0 Li+3 Li+2 Li+ Li Li- 1 e+Li LiPs 2

  20. Z=3 e+ Li 6 0 1 2 3 4 5 • Li+ + Ps2→Li+Ps2 • SVM-FC BE = 0.009 a.u. • DMC BE = 0.012 a.u. (preliminary) • +Z=3, 4e- 2e+ e- e+ 0 Li+3 Li+2 Li+ Li Li- 1 e+Li LiPs Li-Ps 2 Li+Ps2 LiPs2 Li-Ps2

  21. e+ Z=1 0 1 2 3 4 5 e- e+ 0 H H+ H- 1 HPs HPs- e+H 2 e+HPs HPs2 H-Ps2 3 H+Ps3 HPs3 H-Ps3 • +Z=1, 4e- 2e+ H- + Ps2→H-Ps2 Ps- + HPs→H-Ps2 • ECG-SVM (Varga not converged) BE = 0.004 a.u. • DMC BE = 0.006 a.u. (preliminary) • What about Z=2 HePs2 ?

  22. H -Ps2 • Y(H-)Y(Ps2) unbound • Y(Ps-)Y(HPs) unbound • Y=cY1+ (1-c) Y2bound

  23. Fishing for positronic compounds Which atom? How many e+? How many e-? Which state?

  24. e+ Z=2 0 1 2 3 4 5 • He (1s21S) does not bind e+ • He (1s2s3S) binds e+ (very weakly) • He- (1s2s2p4Po) and He- (2p34So) do not bind e+ Excited state e- e+ 0 He+ He+2 He He- 1 e+He HePs He-Ps 2 He+Ps HePs2 He-Ps2

  25. LiPs 2p+ 2s+ x 1s+ 2p 2s 1s UNBOUND Stable with respect to dissociation into Li(2Po) + Ps(2Po) Ethr = -7.472656532 Preliminary DMC: BE = 0.47 mH, SVM = 0.21 mH, CI-FC = 0.02 mH

  26. Molecules

  27. H2 em+ en- 0 1 2 3 4 5 • H2Ps  H2 + Ps  H + HPs • H2Ps- H2 + Ps-  H- + HPs Unbound e- e+ 0 H2+ H2- H2 1 e+H2 H2Ps H2Ps- 2 H2Ps+ H2Ps2 H2Ps2-

  28. H2Ps-

  29. Thank you Still a lot of work to do

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