1. Kamil Fedus, Andrzej Karbowski, Jan Franz*
2nd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics
Cracow, 06 June 2017
Positronium formation in atoms and molecules – from experiment to modelling
Grzegorz Karwasz,
Kamil Fedus, Andrzej Karbowski, Jan Franz*
Institute of Physics
Nicolaus Copernicus University
Toruń, Poland
*Gdańsk Technical University, Institute of Physics

2. Outline
Why we need cross sections?
Positron scattering in gases by beam methods
Total (& elastic cross sections)
Positron annihilation in (degassed) liquids
? Conclusions

3. Główny cel – pokazać, że tlen znacząco redukuje czasy życia orto-pozytu w cieczach nie zmieniając intensywności
Modelowanie propagacji pozytonów w materii biologicznej wymaga znajomości przekrojów czynnych
Problem ze definiowaniem przekrojów czynnych pozytu dla dużych molekuł organicznych– bezpośrednie pomiary Ps formation dla dużych molekuł tylko z jednego laboratorium ANU
Problem z wyznaczaniem przekrojów czynnych w zakresie bardzo niskich energii (benzen, Franz), poniżej Ps formation
Inne dziwactwa w zakresie niskich energii– np. rezonansowe wzmocnienie sygnału anihilacji dla dużych molekuł

4. TOF - PET diagnostic tool in biological tissues
Rationale (0):
TOF - PET diagnostic tool in biological tissues
The concept of time-of-flight means simply that for each annihilation event, we note the precise time that each of the coincident photons is detected and calculate the difference.
Applying the energy thresholds for measured photons as in traditional lifetime measurements should, in principle, to allow for 3D monitoring of positronium lifetimes.
3D monitoring of oxygen level should be possible.
J – PET in Cracow
plastic scintillators allow to improve time resolution

5. Protonoterapia (C) G. Kontrym-Sznajd
W przypadku zastosowania cząstek, jonizacja polega na tym, że przechodząc przez tkankę, przykładowo protony, wybijają elektrony krążące wokół jąder atomowych. Robią to tym skuteczniej, im wolniej się poruszają - w efekcie dawka jonizacji posiada ostre maksimum na końcu zasięgu protonu. Ilustruje to pik Bragga, którego położenie zależy od energii wiązki, przykładowo: 3 cm dla protonów o energii E=60 MeV i aż 30 cm dla protonów o E=230 MeV. Dzięki temu, regulując ich energię, określamy obszar, w którym najwięcej komórek będzie zniszczonych - „celujemy” w obszar nowotworu.
(C) G. Kontrym-Sznajd

6. What cross-sections do we need?

7. Modeling of positron/ electron/ proton tracks in condensed matter
or positron
generaton 7

8. Rationale (1): unexpected results for positron scattering in gas phase

9. Trento low-energy gas-phase positron beam experiment
G. P. Karwasz, R.S. Brusa, M.Barozzi and A.Zecca, Nuclear Instr. and Methods in Physics B 171, 178 (2000)

10. Rationale (1): positron scattering in gases

11. Rationale (2): liquids vs. gases
Positron annihilation is the fundamental process in PET, and also in radiation therapies.
60 and over yrs of positron annihilation studies (in condensed) matter match very poorly with experiments in gas phase (*1977)
Till recently (2004) positron scattering at low energies did not match with theories, particularly at thermal energies (reasons will be shown here)
Studies of annihilation in liquid phase are usually limited to the long lifetime component, that is used to be attributed to o-positronium formation. The lifetime of o-Ps in vacuum is 143 ns and it annihilates in three γ-quanta.
Note that studies of o-Ps are to be considered methodologically „pure” only in large really free volumes, like in some double-matrix glasses, like so-called vycor (lifetimes up to 50 ns, or so).
In liquids (or polymers) measured lifetimes are of few (2-3) ns. Several processed are called in help, like o-Ps→p-Ps transition and/or electron capture from the medium.
Numerous models allow to relate the lifetime to the volume (Eldrup, Consolati, Goworek). We like the most the model of quantum well by Radek Zalewski.

12. Positronium formation in gas-phase organic molecules

13. Positron cross-sections for simple targets
EPs = I – 6.8eV

14. Cross-sections for positronium formation in noble gases

15. Cross-sections for positronium formation in large organic systems
EPs=( )eV ?
Where is
the positronium ?
EPs=( )eV ?
G.P. Karwasz, et al.., Acta Phys. Pol. 107 (2005) 666.

16. Benzene - angular resolution correction!θ
rcycl= mv┴/ eB
v┴= vosin θ vo
vo=√(2E/m) R
Ps signal?
Karwasz et al., NIM B, 266/3 (2008) 471

17. Quantum phenomena at low-energy interaction (below Ps)
Resonant annihilation for large organic molecules
Znaleźć problemy
C. Surko et al. (San Diego University)

18. Theoretical analysis of benzene cross sections
Bayesian analysis and DFT calculations of elastic scattering cross-sections
Surko et al..
(bound state)
(virtual state)

19. Positronium formation in liquid-phase organic molecules

20. The results of analyses of lifetime spectra for different liquids
τ2= 3.2 – 4.6 ns
I2 = 30-48%
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 3.

21. The results of analyses of lifetime spectra for different liquids
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 3.

22. The results of analyses of lifetime spectra for benzene (C6H6)
1 [ns]
I1 [%]
2 [ns]
I2 [%]
3 [ns]
I3 [%]
4 [ns]
I4 [%]
0.142
20.5
0.440
36.4
3.18
43.1 -
Mogensen (1995), degassed
64.2
3.10
35.8
Gray (1967), degassed
0.148
18.1
0.416
37.4
3.26
39.2
1.18
5.3
Consolati (1991), degassed
0.100
12.0
0.360
44.0
2.56
37.0
1.08
7.2
Bisi (1991), air saturated
0.130
41.0
3.25
38.0
8.6
Bisi (1991), air degassed
0.38
60.0
3.1 40
Merrigan (1972) 70
2.65 30
Singh (1971) 59
2.50 41
Hatcher (1960)
3.24
Lee (1965), degassed
2.62
Lee (1965), air saturated
1.75
Lee (1965), oxygen saturated
2.60
Berko (1955) in air?
0.20
65.2
2.39
34.8
Blonde (1972) in air?
3.14
Brown (1974)
O. E. Mogensen, Positron Annihilation in Chemistry, Springer-Verlag, Berlin 1995.
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 1145.
G. Consolati, D. Gerola, F. Quasso, J. Phys.: Condens. Master 3 (1991) 7739.
A. Bisi, G. Consolati, N, Gambara and L. Zappa, Nuovo Cimento D 13 (1991) 393.
J. A. Merrigan, J. H. Green, S. J. Tao: In Physical Methods of Chemistry, ed. by A. Weissberger (Wiley, New York 1972) Vol. 1, Pt. IID.
K. P. Singh, R. M. Singru, C. N. Rao, J. Phys. Atom. Molec. Phys. 4 (1971) 261.
C. R. Hatcher, T. W. Falconer, W. E. Millett, J. Chem. Phys. 32 (1960) 28.
J. Lee, and G. J. Celiitans, J. Chem. Phys., 42 (1965) 437
S. Berko, A. J. Zuchelli, Phys. Rev. 102 (1955) 724.
G. R. A de Blonde, PhD thesis: Positron annihilation in condensed hydrocarbons, The University of Manitoba (1972).
B. J. Brown, Aust. J. Chem. 27 (1974) 1125.
3= 3.1 – 3.3 ns
air lowers 3 to ns

23. The results of analyses of lifetime spectra for cyclohexane (C6H12)
1 [ns]
I1 [%]
2 [ns]
I2 [%]
3 [ns]
I3 [%] -
3.90
Lee (1965), degassed
2.40
Lee (1965), air saturated
1.81
Lee (1965), oxygen saturated
3.20
30.5
Gray (1967), degassed
0.39 58
3.08
34.0
Blonde (1972), degassed
0.214
26.1
0.469
36.3
3.25
37.6
Mogensem (1995), degassed
Zgardzińska (2013), degassed
J. Lee, and G. J. Celiitans, J. Chem. Phys., 42 (1965) 437
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 1145.
G. R. A de Blonde, PhD thesis: Positron annihilation in condensed hydrocarbons, The University of Manitoba (1972).
O. E. Mogensen, Positron Annihilation in Chemistry, Springer-Verlag, Berlin 1995.
B. Zgardzińska, T. Goworek, Chemical Physics, 421 (2013) 10.
What we do not like in reported data is that they
do not refer to other than τ3 lifetimes…

24. The results of analyses of lifetime spectra for methanol (CH3OH)
1 [ns]
I1 [%]
2 [ns]
I2 [%]
3 [ns]
I3 [%] -
3.47
Lee (1965), degassed
2.88
Lee (1965), air saturated
1.84
Lee (1965), oxygen saturated
3.94
19.0
Gray (1967), degassed
3.50
Brown (1974), degassed
0.150
17.6
0.464
60.8
3.53
21.6
Mogensen (1995), degassed
J. Lee, and G. J. Celiitans, J. Chem. Phys., 42, 437 (1965).
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 1145.
B. J. Brown, Aust. J. Chem. 27 (1974) 1125.
O. E. Mogensen, Positron Annihilation in Chemistry, Springer-Verlag, Berlin 1995.

25. ORTEC Positron Lifetime System

26. ORTEC Positron Lifetime System

27. ORTEC Positron Lifetime System
- plastic scintilators (St. Gobain BC418) and photomultipliers RCA,
- data acquisition MAESTRO by ORTEC,
measured time resolution (in metals) FWHM = 180 ps
degassing system with rotary pump (10-3 LN2 freezing)
temperature regulation (Peltier) º C
positron source 22Na (15 μCi) in kapton 7 μm thick foil,
250k-1000 k data in one run
data analysis - LT 9 programme by J. Kansy,
3:1 ratio between o-Ps and p-Ps fixed (the latter 124 ps)
χ2 better than 1.01; some runs repeated
A. Karbowski, J. D. Fidelus, G. Karwasz, Materials Science Forum, 666 (2011) 155

28. Results for methanol
Quite in line with previous measurements: τ3 of some ps
In other words: nihil novae sub Sole

29. Cancer and oxygen
The link between oxygen and cancer is clear. In fact, an underlying cause of cancer is usually low cellular oxygenation levels.
In 1931 Dr. Warburg won his first Nobel Prize for proving cancer is caused by a lack of oxygen respiration in cells. He stated in an article titled "The Prime Cause and Prevention of Cancer... the cause of cancer is no longer a mystery, we know it occurs whenever any cell is denied 60% of its oxygen requirements..."
Source:

30. Results for benzene Solid benzene
so, it is oxygen in air which lowers o-Ps lifetime

31. Results for benzene Within error bar I3 is constant.
This is non in-line with predictions, that oxygen makes quenching o-Ps→p-Ps
Re-analysis to be done: 3:1 ratio is to be released…

32. Results for benzene: τ2
No clear conclusion: 380 ps is too close to the source component …
However, the intensity is much more than the source itself,
and it changes when benzene gets solid

33. The results of analyses of lifetime spectra for benzene (C6H6)
1 [ns]
I1 [%]
2 [ns]
I2 [%]
3 [ns]
I3 [%]
4 [ns]
I4 [%]
0.142
20.5
0.440
36.4
3.18
43.1 -
Mogensen (1995), degassed
64.2
3.10
35.8
Gray (1967), degassed
0.148
18.1
0.416
37.4
3.26
39.2
1.18
5.3
Consolati (1991), degassed
0.100
12.0
0.360
44.0
2.56
37.0
1.08
7.2
Bisi (1991), air saturated
0.130
41.0
3.25
38.0
8.6
Bisi (1991), air degassed
0.38
60.0
3.1 40
Merrigan (1972) 70
2.65 30
Singh (1971) 59
2.50 41
Hatcher (1960)
3.24
Lee (1965), degassed
2.62
Lee (1965), air saturated
1.75
Lee (1965), oxygen saturated
2.60
Berko (1955) in air?
0.20
65.2
2.39
34.8
Blonde (1972) in air?
3.14
Brown (1974)
Lee: no „I3” is given
0.125
~14%
390±5 ps
~42%
3.0±0.1 ns
43±1%
degassed
380±5 ps
2.4 ns
in air
15%
430±10ps
38±1%
1.5 ns
46±1%
oxygen

34. Results for cyclohexane
τ3 lifetime drops down by a factor of 2 in presence of oxygen!
(and intensity slightly rises!)

35. Results for cyclohexane: τ2
τ2 for degassed cyclohexane not much different from that in benzene,
but intensity I2 much higher (50% vs 40%)

36. The results of analyses of lifetime spectra for cyclohexane (C6H12)
1 [ns]
I1 [%]
2 [ns]
I2 [%]
3 [ns]
I3 [%] -
3.90
Lee (1965), degassed
2.40
Lee (1965), air saturated
1.81
Lee (1965), oxygen saturated
125
13%
380±10
49±1%
3.1
38%
degassed
390±10
48%
2.4
with air
14%
440±10
45%
1.4±0.1
41%
with oxygen
J. Lee, and G. J. Celiitans, J. Chem. Phys., 42 (1965) 437
P. R. Gray, C. F. Cook, G. P., Sturm, J. Chem. Phys. 48 (1968) 1145.
G. R. A de Blonde, PhD thesis: Positron annihilation in condensed hydrocarbons, The University of Manitoba (1972).
O. E. Mogensen, Positron Annihilation in Chemistry, Springer-Verlag, Berlin 1995.
B. Zgardzińska, T. Goworek, Chemical Physics, 421 (2013) 10.

37. Results for methanol
τ3 lifetime (again) drops down by a factor of 2 in presence of oxygen!

38. Results for methanol: τ2

39. Conclusions @ 25ºC: present vs Mogensen
Molecule
1 (ns)
I1 (%)
2 (ns)
I2 (%)
3 (ns)
I3 (%)
I1+I3 (%)
Benzene
0.142
20.5
0.440
36.4
3.18
43.1
63.6
0.125
14.7
0.390
41.1
3.0
44.2
58.9
c-hexane
0.214
26.1
0.469
36.3
3.25
37.6
63.7
12.9
0.377
48.2
3.07
38.9
51.8
methanol
7.2
0.401
70.3
3.11
22.5
29.7
Mogensen
Present
Pretty good agreement with Mogensen for τ3 and I3
τ1 and τ2 require further analysis (with no 3:1 fix)
1 (ns)
I1 (%)
2 (ns)
I2 (%) 3
I3 (%) x2
Counts
Description
0.154
18.1
0.451
60.6
3.27
21.3
1.01
223k
degassed
0.103
11.6
0.427
63.9
1.64
24.8
oxygen

40. Conclusions
Oxygen reduces strongly the ortho-positronium lifetimes (not intensities) in all studied liquids
τ2 (in degased liquids): 400 ps (methanol) > 390 ps (benzene) > 380 ps (cyclohexane)
I2 (in degassed): 70% methanol > 48% cyclohexane > 41% benzene
I3 (in degassed): 44% benzene > 39% cyclohexane > 22% methanol
Does it reflect a higher (??) relative positronium formation cross section in gas-phase benzene?
First, we need calculations of the elastic part of total cross section
Little dependence on temperature in C6H6 and C6H12, stronger in CH3OH (? effect of rising pressure in the sample cell → higher concentration of O2 dissolved?/ polar character of CH3OH? )

41. Perspectives Re-calculation of τ3 and I3 releasing 3:1 ratio
Futher ab-initio calculation: cyclohexane and methanol
More liquids to be measured
More precise measurements in gas eV
Positron scattering in gas phase – the low-energy beam machine at testing with UMK

42. Thank you for your attention!