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Fishing for positronic compounds

This paper by Dario Bressanini from Università dell'Insubria delves into the intricate world of positronic compounds. It covers the theoretical frameworks established by Dirac, Anderson, and Wheeler, alongside experimental accomplishments in positronium spectroscopy that aid in diverse fields such as polymer science and medical research. The challenges of computational techniques are highlighted, with discussions on recent findings related to polyleptons and binding energies. The study opens avenues for constructing gamma-ray lasers and advances knowledge of atomic interactions involving positrons.

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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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