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), 119991, Moscow Russia

Motivation New developments in digitization W. Wolszczak, P. Dorenbos, Nucl. Instrum. Meth. A857 (2017) pp.66-74. “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

Attempt to improve energy resolution by weighting signals from different time domains C I(t) t w1A+w2B+w3C

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

F. Gao, S.Keresit et al, PNNL-22859 Annual Report 2013 Science-Driven Candidate Search for New Scintillator Materials ; See also PNNL-23817 (2014); Nuclear Instruments and Methods in Physics Research A 652 (2011) 564–567

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-23817 (2014); Nuclear Instruments and Methods in Physics Research A 652 (2011) 564–567

Distribution of e-h concentration in track region 1

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

But … structure of the track strongly fluctuate

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

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

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

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

How fluctuation of concentration distribution is connected with fluctuations in kinetics

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

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

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

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

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

Decrease of efficiency of photon detection and emission

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

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

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

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

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

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

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

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

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