fishing for positronic compounds
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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) - PowerPoint PPT PresentationTRANSCRIPT
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Fishing for positronic compoundsDario Bressanini
QMC in the Apuan Alps QMC in the Apuan Alps VII 2012 VII 2012
TTI Vallico SottoTTI Vallico Sotto
Università dell’Insubria, Como, ITALY
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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
• Two spin states •Singlet (para-positronium) – 0.125 ns•Triplet (ortho-positronium) – 142 ns
Annihilation via photons is inevitable…
“resistance is futile”…but a lot can happen on the way
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Time scales
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e+ and Ps spectroscopy• Used in
► Polymer science► Medical research► Solid state, electronics► hope to build a -ray laser
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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)
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Current status for atoms
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Computational techniques
• CI► slow convergence► frozen core► many atoms
• ECG-SVM► very accurate► slow optimization► 4 e-
• VMC-DMC► Compact ► VMC can be unbound► statistical error
Bressanini and Morosi: JCP Bressanini and Morosi: JCP 119119, 7037 (2003), 7037 (2003)
)()()()()ˆ1(),2,1( 112 ee rgPsrfHPe
HPs
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Polyleptons
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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
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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
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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…
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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
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Pse+ Ps-
Ps+ Ps2-Ps2
Ps3Ps2+ Ps3
-
e-
Ps3+ Ps4
10 32 4
1
2
3
4
0
e-e+
Higher systems? Psn, Ps-n
• Ps2-
► Ps2 + e- Ps2-
► Ps + Ps- Ps2-
► L=0 unbound (ECG)► What about L>0 ?
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Ps2- and beyond: general
strategy• Problems with Monte Carlo:
► No starting (R) from HF/DFT
• Use a “Valence Bond-like” (R)► (R)=A[(Ps) (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+))► (R)=A[(Ps) (Ps-) (interaction)]► Consider the limit for g1
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Ps2- total energy
• E(L=1) < E(L=0)
0 0.2 0.4 0.6 0.8 1g
-1 .2
-1
-0.8
-0.6
-0.4
Ener
gy (a
.u.)
Ps+Ps-
Ps2+e-Ps2
- L=1
Ps2- L=0
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Ps2- binding energy
• L=0 is unbound• L=1 is probably
unbound…• …but with
better nodes?
0 0.2 0.4 0.6 0.8 1g
-0.05
0
0.05
0.1
0.15
0.2
0.25
Bin
ding
ene
rgy
(a.u
.)
Ps2- L=0
Ps2- L=1
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Ps3 and Ps3-
0.2 0.4 0.6 0.8 1g
-0.2
0
0.2
0.4
0.6
Bin
ding
ene
rgy
(a.u
.)
Ps3
Ps3-
• Preliminary results
• Ps3 and Ps3-
unbound so far• Not explored yet
all excited states
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Z=3 e+ Li
• 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+Li
Li+2Li+3 LiLi+
10 32 4
1
2
0
e-
e+
Li-
5 6
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Z=3 e+ Li
• 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+Li
Li+2Li+3 LiLi+
10 32 4
1
2
0
e-
e+
LiPs
Li-
5 6
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Z=3 e+ Li
• Li+ + Ps2 → Li+Ps2 • SVM-FC BE = 0.009 a.u. • DMC BE = 0.012 a.u. (preliminary)• +Z=3, 4e- 2e+
e+Li
Li+2Li+3 LiLi+
10 32 4
1
2
0
e-
e+
LiPs
Li+Ps2
Li-
5
Li-Ps
LiPs2 Li-Ps2
6
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e+ Z=1
HPs-HPs
HPs2e+HPs
H
10 32 4
1
2
0
e-
e+
H-Ps2
5
H+ H-
e+H
H+Ps3 HPs33 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 ?
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H -Ps2• (H-)(Ps2) unbound• (Ps-)(HPs)
unbound• c+ (1-c)
bound
0 0.2 0 .4 0.6 0.8 1c mixing
-1 .060
-1.056
-1.052
-1.048
-1.044
-1.040
E (a
.u.)
H - + Ps2
HPs + Ps-
H -Ps2
Dissociation
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Fishing for positronic compounds
Which atom?
How many e-?
How many e+?
Which state?
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e+ Z=2
• He (1s2 1S) does not bind e+
• He (1s2s 3S) binds e+ (very weakly)• He- (1s2s2p 4Po) and He- (2p3 4So) do not bind
e+
e+He
He+Ps
He+
10 32 4
1
2
0
e-
e+
HePs2
5
He+2 He He-
HePs He-Ps
He-Ps2
Excitedstate
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LiPs
1s
2s
2p
ePpsLi 32221
1s+
2s+
2p+
oPpe 22
x
oSLiPs 4
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
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Molecules
2 4 6 8 10R (a.u.)
-8 .2
-8
-7 .8
-7 .6
-7 .4
Ener
gy (a
.u.) LiH
e+LiH
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H2 em+ en
-
• H2Ps H2 + Ps H + HPs• H2Ps- H2 + Ps- H- + HPs
H2Pse+H2
H2Ps+ H2Ps2-
H2+ H2
-
10 32 4
1
2
0
e-
e+
H2Ps-
H2Ps2
5
H2
Unbound
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H2Ps-
2 4 6 8 10R (a.u.)
-1.5
-1.4
-1.3
-1.2
-1.1
Ener
gy (a
.u.) H2 + Ps -
H- + HPs
H 2Ps -
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Thank youStill a lot of work to do