Luminescence Response and Quenching Models for Heavy Ions of 0.5 keV to 1 GeV/n in Liquid Argon and Xenon
<p>(<b>a</b>) Quenching factor <span class="html-italic">q</span> for various ions as a function of linear energy transfer (LET) in liquid Ar. Measurements are as follows: 5.305 MeV <sup>210</sup>Po α-particles (▪), relativistic heavy ions (RHIs) of ~1 GeV/n (●) [<a href="#B12-instruments-05-00005" class="html-bibr">12</a>], 33.5 MeV/n <sup>18</sup>O and 31.9 MeV/n <sup>36</sup>Ar ions (closed diamonds) [<a href="#B14-instruments-05-00005" class="html-bibr">14</a>] and <sup>252</sup>Cf fission fragments (closed diamonds) [<a href="#B12-instruments-05-00005" class="html-bibr">12</a>]. Heavy fragments (HFs) and light fragments (LFs) are shown separately. Crosses (×,+) show the results calculated numerically for the hard-sphere cross-section divided by 4, σ<sub>HS</sub>/4. The previous result obtained for LFs with <span class="html-italic">T</span><sub>c</sub>/<span class="html-italic">T</span> = 1 is also shown (-). Dashed curves show Birks’ law applied to the numerical calculation for core quenching (Equation (27)) as shown in Figure 3b. RHIs and nonrelativistic ions (<sup>18</sup>O, <sup>36</sup>Ar and FFs) are treated separately. Open diamonds show <span class="html-italic">q</span> obtained by the sum of scintillation and charge signals [<a href="#B14-instruments-05-00005" class="html-bibr">14</a>] (see <a href="#sec4dot3-instruments-05-00005" class="html-sec">Section 4.3</a>). (<b>b</b>) Initial radial distribution of excited species, essentially the same as the prompt dose profile, in the cylindrical track core produced by various ions in liquid Ar (see <a href="#sec2dot1-instruments-05-00005" class="html-sec">Section 2.1</a>). The distribution for 30 keV Ar recoils (RC Ar) is also shown (dot-dashed curve). A Gaussian distribution is assumed.</p> "> Figure 2
<p>The stopping powers and the electronic LET for Pb ions: (<b>a</b>) in argon; (<b>b</b>) in xenon. <span class="html-italic">LET</span><sub>el</sub> was obtained by using a semi-empirical power-law approximation for <span class="html-italic">q</span><sub>nc</sub>.</p> "> Figure 3
<p>Calculated quenching in liquid argon. (<b>a</b>) Evolution of quenching in the track core produced by α-particles, Au, <sup>18</sup>O, <sup>36</sup>Ar and Ba ions (as heavy fission fragments). The ratio of the number of self-trapped excitons with and without quenching as a function of time is plotted. The initial radii are <span class="html-italic">a</span><sub>0</sub> = 0.39 and 5.8 nm for α-particles (dotted curve) and Au ions (dashed curve), respectively. <span class="html-italic">a</span><sub>0</sub> values for <sup>18</sup>O, <sup>36</sup>Ar and Ba ions (solid curves) are ~1.5 nm. (<b>b</b>) The inverse of <span class="html-italic">q</span><sub>c</sub> calculated for <sup>18</sup>O, <sup>36</sup>Ar, Mo (LF) and Ba (HF) ions plotted as a function of core LET. Birks’ law was used to fit values for <sup>18</sup>O and <sup>36</sup>Ar ions. Birks’ law applied for RHIs is also shown (<span class="html-italic">a</span><sub>0</sub> = 5.4–6.2 nm).</p> "> Figure 4
<p>Quenching factors <span class="html-italic">q<sub>T</sub></span> and <span class="html-italic">q</span><sub>nc</sub> for heavy recoils in α-decay. (<b>a</b>) Quenching factors in liquid Ar. Calculations are for <sup>208</sup>Pb ions. Symbols are <span class="html-italic">W</span><sub>α</sub>/<span class="html-italic">W</span><sub>NR</sub> measurements in gas for <sup>206</sup>Pb, <sup>208</sup>Tl and <sup>208</sup>Pb ions by Madsen (•) [<a href="#B27-instruments-05-00005" class="html-bibr">27</a>]. Points for 103 keV <sup>206</sup>Pb recoil ions by Cano (closed diamond) [<a href="#B29-instruments-05-00005" class="html-bibr">29</a>] and Jesse and Sadauskis (triangle) [<a href="#B28-instruments-05-00005" class="html-bibr">28</a>] are shifted for clarity. Numerical results (dashed curve) and the power-law approximation (dot-dashed curve) for <span class="html-italic">q</span><sub>nc</sub> by Lindhard et al. are shown [<a href="#B23-instruments-05-00005" class="html-bibr">23</a>]. The dotted curve shows <span class="html-italic">q</span><sub>nc</sub> estimated by Ling and Knipp [<a href="#B30-instruments-05-00005" class="html-bibr">30</a>]. Measured <span class="html-italic">q</span><sub>T</sub> values by Xu et al. [<a href="#B35-instruments-05-00005" class="html-bibr">35</a>] are shown with open diamonds (corrected for <span class="html-italic">L</span><sub>γ</sub><sub>0</sub>) together with present calculation (solid curve). (<b>b</b>) Quenching factors in liquid Xe. <span class="html-italic">W</span><sub>α</sub>/<span class="html-italic">W</span><sub>NR</sub> measurements for <sup>206</sup>Pb in gas by Cano (closed diamond) [<a href="#B29-instruments-05-00005" class="html-bibr">29</a>]. Calculated values for <span class="html-italic">q</span><sub>nc</sub> are the power-law approximation (dot-dashed curve) by Lindhard et al. and the present approximation (dotted curve). The present calculation for <span class="html-italic">q</span><sub>T</sub> is shown by the solid line.</p> "> Figure 5
<p>Quenching factors in liquid Xe: (<b>a</b>) The electronic quenching factor <span class="html-italic">q</span><sub>el</sub>, estimated for Xe and Pb recoils as a function of <span class="html-italic">LET</span><sub>el</sub>. A closed circle shows <span class="html-italic">q</span><sub>c</sub> = 0.70 for 5.49 MeV α-particle. Curves show Birks’ law. Horizontal scales show the energy of Xe and Pb recoils in keV; the diamond show a value corrected for core expansion: (<b>b</b>) Quenching factors calculated for Xe recoils in liquid Xe as a function of the energy. The solid curve shows Lindhard <span class="html-italic">q</span><sub>nc</sub>, the dotted curve is an extrapolation. The dot-dashed curve shows the total quenching factor <span class="html-italic">q<sub>T</sub></span> = <span class="html-italic">q</span><sub>nc</sub>·<span class="html-italic">q</span><sub>el</sub>. The dashed curves show uncertainties due to the estimated <span class="html-italic">T<sub>c</sub></span>/<span class="html-italic">T</span> ratio, 0.76±0.04, in α track. The <span class="html-italic">q<sub>T</sub></span> curve may approach to Lindhard <span class="html-italic">q</span><sub>nc</sub> curve faster than the dot-dashed curve as the energy decreases below about 2 keV (see <a href="#sec4dot1-instruments-05-00005" class="html-sec">Section 4.1</a> and <a href="#sec4dot2-instruments-05-00005" class="html-sec">Section 4.2</a>). The result obtained previously by the α-core approximation is shown with a dot-dot dashed curve [<a href="#B25-instruments-05-00005" class="html-bibr">25</a>].</p> "> Figure A1
<p>Schematic drawing of quenching. Level 1 is the excited level involved in quenching, level 2 gives fluorescence and level 3 is the quencher. (<b>a</b>) Pseudo-first-order reaction. (<b>b</b>) Second-order reaction under diffusion.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Track Structure
2.2. Biexcitonic Collision Kinetics
2.3. Recoil Ions for Dark Matter Searches
2.4. Heavy Recoil Ions in α-Decay
3. Results
3.1. Fast Ions in Liquid Argon
3.2. Heavy Recoils in α-Decay in Liquid Argon
3.3. Xe Recoils and Heavy Recoils in α-Decay in Liquid Xenon
4. Discussion
4.1. Fast Ions in Liquid Argon
4.2. Recoil Ions in Dark Matter Searches
4.3. General Remarks on Dark Matter Searches
4.4. Birks’ Law and Second-Order Reaction Kinetics
- The radius of the initial ion track core should be regarded as constant since the reaction kinetics include the density n, not the specific number N.
- The boundary for kinetics, the track structure of heavy ions, has to be considered.
- LETel, not Se or ST, should be used in place of dE/dr in Birks’ law for slow recoils.
5. Conclusions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
CEνNS | coherent elastic neutrino-nucleus scattering |
CSDA | continuous slowing down approximation |
FFs | fission fragments |
FWHM | full width at half maximum |
HFs | heavy fragments |
keVee | electron recoil equivalent energy in keV |
LAr | liquid argon |
LET | linear energy transfer (−dE/dx) |
LETc | linear energy transfer in the track core |
LETel | electronic linear energy transfer |
LFs | light fragments |
LXe | liquid xenon |
NR | nuclear recoil |
PET | positron emission tomography |
PID | photoionization detector |
PMT | photomultiplier tube |
RC Ar | recoil argon |
RHI | relativistic heavy ion |
TPC | time projection chamber |
VUV | vacuum ultraviolet |
WIMPs | weakly interacting massive particles |
Appendix A
Birks’ Law and Reaction Kinetics
- Pseudo-first-order reaction
- 2.
- Second-order reaction under diffusion
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Units | 18O | 36Ar | Mo (LF) | Ba (HF) | |
---|---|---|---|---|---|
Energy | MeV/n | 33.5 | 31.9 | 0.98 | 0.56 |
Range | μm | 3200 | 1270 | 44 | 37 |
LET | MeVcm2/mg | 1.35 | 6.47 | 24.1 | 21.7 |
Tc/T | 0.75 | 0.75 | 0.88 | 0.90 | |
a0 | nm | 1.53 | 1.49 | 1.52 1 | 1.46 1 |
qc | 0.64 | 0.27 | 0.083 | 0.087 | |
q | 0.73 | 0.46 | 0.19 | 0.18 | |
q expt. | 0.59 2 | 0.46 2 | 0.17 3 | 0.16 3 |
Source | 210Po | 212Bi | 214Po | 212Po | |
---|---|---|---|---|---|
Recoil Ion | Units | 206Pb | 208Tl | 210Pb | 208Pb |
Energy | keV | 103 | 116 | 146 | 169 |
R | μm | 0.09 | 0.10 | 0.12 | 0.13 |
LETel | MeVcm2/mg | 1.85 | 2.03 | 2.41 | 2.68 |
a0 | nm | 0.45 1 | 0.47 1 | 0.51 1 | 0.54 1 |
qnc | 0.23 | 0.24 | 0.27 | 0.29 | |
qel | 0.38 | 0.36 | 0.33 | 0.31 | |
qT | 0.086 | 0.087 | 0.089 | 0.090 | |
EL | keV | 8.9 | 10 | 13 | 15 |
EL | keVee | 10 | 11 | 14 | 17 |
EL expt. | keVee | ~5 2 | 7.4 ± 0.4 2 |
Source | 210Po | 212Po | 241Am | |||
---|---|---|---|---|---|---|
Recoil Ion | Units | Xe | Xe | 206Pb | 208Pb | α-Core |
Energy | keV | 6 | 20 | 103 | 169 | 5490 × 0.76 |
R | μm | – | – | 0.08 | 0.12 | 43 |
LETel | MeVcm2/mg | 0.30 | 0.53 | 0.60 | 0.88 | 0.33 |
a0 | nm | 0.48 1 | 0.51 2 | 0.55 2 | 0.66 2 | 0.48 1 |
qnc | 0.20 | 0.23 | 0.14 | 0.18 | 1 | |
qel | 0.72 | 0.59 | 0.56 | 0.50 3 | 0.70 | |
qT | 0.14 | 0.14 | 0.08 | 0.09 | – | |
EL | keV | 0.8 | 2.8 | 8 | 15 | – |
EL | keVee | 0.9 | 3 | 9 | 17 | – |
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Hitachi, A. Luminescence Response and Quenching Models for Heavy Ions of 0.5 keV to 1 GeV/n in Liquid Argon and Xenon. Instruments 2021, 5, 5. https://doi.org/10.3390/instruments5010005
Hitachi A. Luminescence Response and Quenching Models for Heavy Ions of 0.5 keV to 1 GeV/n in Liquid Argon and Xenon. Instruments. 2021; 5(1):5. https://doi.org/10.3390/instruments5010005
Chicago/Turabian StyleHitachi, Akira. 2021. "Luminescence Response and Quenching Models for Heavy Ions of 0.5 keV to 1 GeV/n in Liquid Argon and Xenon" Instruments 5, no. 1: 5. https://doi.org/10.3390/instruments5010005