1. Fluctuation of track structure in terms of distribution of excitations and fractal dimensions
A.Vasil’ev   Skobeltsyn Institute of Nuclear Physics of Lomonosov Moscow State University, Leninskie Gory, 1(2), , Moscow Russia

2. Motivation New developments in digitization
W. Wolszczak, P. Dorenbos, Nucl. Instrum. Meth. A857 (2017) pp “Shape of intrinsic alpha pulse height spectra in lanthanide halide scintillators”
V. Gayshan, A. Gektin, S. Vasyukov, S. Gridin, D. Onken, R. Williams, SCINT2017, Chamonix, “Pulse shape analysis of individual gamma events – correlation to resolution and the possibility of its improvement”
Attempt to make a theoretical background for enhancing of scintillator energy resolution

3. Attempt to improve energy resolution by weighting signals from different time domainsC
I(t) t
w1A+w2B+w3C

4. Concentration and kinetics
High efficiency of emission and detection of photons
Part of excitations do not produce photons
Part of photons are not detected

5. F. Gao, S.Keresit et al, PNNL-22859
Annual Report 2013
Science-Driven Candidate Search for New Scintillator Materials ;
See also PNNL (2014); Nuclear Instruments and Methods in Physics Research A 652 (2011) 564–567

6. Fano factor (variance of the number of electron-hole pairs produced), F
F. Gao, S.Keresit et al, PNNL-22859
Annual Report 2013
Science-Driven Candidate Search for New Scintillator Materials ;
See also PNNL (2014); Nuclear Instruments and Methods in Physics Research A 652 (2011) 564–567

7. Distribution of e-h concentration in track region1

8. Decay curves from regions with different e-h concentration
w(n)
YAG
660keV
30keV
YAG decay kinetics
n, cm-3
t, ns
INTELUM project data

9. But … structure of the track strongly fluctuate

10. Origin of large fluctuations in track structure for CsI (Generalized Landau fluctuations in large energy scale)
Ionization from core levels
δ-electron production

11. Origin of large fluctuations in track structure for CsI (Generalized Landau fluctuations in large energy scale)
Ionization from core levels
δ-electron production
Less than one event per track
Less than one event per track
More than one event per track
More than one event per track
Auger electrons from K, L and M edges and δ-electrons with energy >1 keV result in track branching and therefore the modification of track structure

12. Example of fluctuation of concentration distribution due to different branching of the track
w(n)
̴30keV
̴30keV
̴30keV
e- 100keV
e- 100keV

13. Efficiency of photon emission and registration from regions with different concentrations
F(n)
Losses due to long tails
Losses due to concentration
quenching

14. How fluctuation of concentration distribution is connected with fluctuations in kinetics

15. w(n) ̴30keV ̴30keV ̴30keV e- 100keV e- 100keV e- 100keV ̴30keV ̴30keV

16. w(n)
̴30keV
̴30keV
̴30keV
e- 100keV
Fluctuations of excitation concentration distribution results in energy resolution degradation and decay fluctuations
e- 100keV
e- 100keV
̴30keV
̴30keV
̴30keV
e- 100keV

17. How to measure fluctuations of track structure – fractal dimensions?
Two-particle distribution function Fee(r), Feh(r), Fhh(r)
3D uniform random distribution (plasma-like) Dee(r)=3
2D uniform random distribution in plane Dee(r)=2
1D uniform random distribution along line Dee(r)=1

18. How to define “concentration”?
For uniform random distribution:
For track structure:
“Concentration” which “feel” a particle:
for three closest particles

19. 20 keV track
e-e, h-h and e-h correlation functions
e-e, h-h and e-h “fractal” dimensions
e-e, h-h and e-h distribution functions
e-h closest distance distribution
e-h “concentration” distribution

20. Decrease of efficiency of photon detection and emission

21. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

22. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

23. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

24. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

25. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

26. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
emitted and detected photons
n, cm-3
Fractal dimensions
h-h
e-e
e-h
r, nm

27. Distribution of “concentrations” and fractal dimensions for ee, hh and eh distribution function
excitations
Fano factor for number of e-h excitations for 100 keV track is about 0.2
Fano factor for emitted and detected photons (assuming PMT efficiency = 1) is much higher (about 0.8 for our calculations)
emitted and detected photons
n, cm-3
h-h
e-e
e-h
r, nm

28. Conclusions
Fluctuations of excitation concentration distribution results in energy resolution degradation and decay fluctuations
Digital pulse shape analysis is a promising way for make the energy resolution better

29. Thank you for your attention!
AV thanks the support by the Ministry of Education and Science of the Russian Federation (state contract no. RFMEFI61614X0006)