University of Zurich Physics Institute

Monte Carlo Simulation of the Liquid Xenon Detector Response to Low-Energy Neutrons

July 2, 2014

Bachelor Thesis of Dario Biasini Supervisors: Dr. Alexander Kish Prof. Dr. Laura Baudis Abstract

The relative scintillation yield eff is an important quantity characterising a detec- L tion medium. It is dependent on the energy deposit of the beam particle. Several experiments have measured the scintillation yield to low-energy nuclear re- coils in liquid xenon (figure 4). Xurich II is a xenon two-phase detector designed to measure the yield at low recoil energies. At the time of writing this thesis, the experiment has not been done yet. Since the nuclear recoil energy is angle dependent, the experiment will be performed for a set of angles. The goal of this bachelor thesis is to provide a Geant4 model of the experimental setup and to perform a first Monte Carlo simulation for a sample angle of 45◦. As a cross check, the energy deposit is measured from the Monte Carlo Data. Further- more, a collimator has been introduced to examine the collimation of the neutron beam. It has been found to be of no use. Additionally, a lead plate was placed in the beam’s path to shield from background gammas. A lead thickness of 2 cm has been chosen.

1 Contents

1 Introduction 3 1.1 Dark Matter ...... 3 1.2 Direct Search for Dark Matter in the XENON experiment . . . . . 4 1.3 Neutron Interactions ...... 5 1.4 Energy Scale ...... 6

2 Experiment 8 2.1 The Xurich II Detector ...... 8 2.2 Principle of Measurement ...... 11

3 Implementation 12 3.1 Geometry Setup ...... 12 3.2 Features ...... 15 3.3 Monte Carlo Simulation ...... 17 3.3.1 Collimation ...... 17 3.3.2 Gamma Shielding ...... 17 3.4 Full Simulation of the Measurement ...... 20 3.4.1 Data Processing ...... 20 3.4.2 Outcome of the Monte Carlo Experiment ...... 20 3.4.3 Background ...... 22

4 Conclusions 23

5 Acknowledgements 24

2 1 Introduction

1.1 Dark Matter

Astronomical observations give rise to the assumption that most of the existing mass in the universe is not visible. This includes cosmic microwave background measure- ments [1], rotational velocity measurements of galaxy clusters [2] and gravitational lensing observations [3]. Only about 5% is luminous matter and therefore visible to telescopes [4]. To account for the missing mass, models suggest the existence of dark matter, that currently has only been detected indirectly through gravitational interaction with visible objects. Although the exact nature of dark matter is still subject of research, WIMPs (weakly interacting massive particle) are promising candidates [5]. There exist several models that propose WIMP particles. One of the most prominent theo- ries is supersymmetry [6], an extension to the standard model. Besides interacting gravitationally and weakly, WIMPs are predicted to be stable and electrically neu- tral. Additionally, they are considered to be non-relativistic (cold dark matter) [7] and predicted to interact with nuclei by weak interaction [6]. The current upper limit on the nucleon-WIMP cross section is seen in figure 1 with a minimum of 7.6 10−46 cm2 at a mass of 33 GeV/c2 [8]. A lot of effort exists to detect WIMPs ∼ · by non-gravitational means [9].

Figure 1: current upper limits on the spin-independent elastic WIMP-nucleon scattering cross section [8] Experiments Large Underground Xenon (LUX) 1σ interval (violet), Edelweiss II (dark yellow line), CDMS II (green line), ZEPLIN-III (magenta± line), XENON100 100 live-day (orange line, ’old’), and 225 live-day (red line, ’new’) results

3 1.2 Direct Search for Dark Matter in the XENON experiment

The goal of the XENON collaboration is to measure the WIMP-nucleon cross sec- tion and the WIMP mass [10]. The predicted rate of interaction is in the order a few interactions per target ton per year for cross sections in the order of the current limit. The XENON experiment is located at the Laboratori Nazionali del Gran Sasso (Italy) 1400 meters underground to shield from cosmic rays. The experiment XENON100 uses liquid xenon (LXe) as a detection medium, measuring scintillation light and ionisation charge created by interaction of traversing particles. It has a liquid xenon mass of 161 kg, thereof 62 kg target mass, the rest representing the surrounding veto volume [11]. The detector is designed as a time projection chamber (TPC). Particles traversing the target may interact with the shell electrons or with the nucleus. This leads to ionisation, excitation as well as heat. The de-excitation of the shell and recombi- nation of ionisation electrons with the xenon ions generate photons in the vacuum ultraviolet region ( 178 nm) [12]. ∼

Figure 2: Wednesday,mode December of operation 18, 13 of a time projection chamber [13] The prompt signal S1 and the secondary signal S2 get detected by arrays of PMTs. The cathode is at a negative high voltage (HV), the gate in the middle is grounded. The anode is at a positive HV. The drift-time together with the electron’s drift velocity indicates the z-position.

4 The immediate scintillation light signal (S1) is measured by 178 PMTs [11], distributed in two arrays at the top and bottom of the active volume(figure 2). Ad- ditionally, 64 PMTs are distributed in the veto for an anti-coincidence trigger. The ionised electrons that didn’t recombine get separated from the ions by an electric field, generated by applying high voltage to the cathode. A second field created by applying high voltage to the anode at the top of the TPC extracts the electrons from the liquid into the gas phase. Collisions with xenon atoms in the gas phase induce the emission of secondary scintillation light (S2) proportional to the charge signal. By looking at the drift-time between S2 and S1, the z coordinate can be calculated. With the top array of PMTs, the (x,y) coordinate can be reconstructed, using a neural network algorithm and comparison with Monte Carlo simulations. The ratio of S2/S1 has different values for electronic and nuclear recoils [14]. This is used to discriminate the relevant signal from the electronic recoil background [15].

1.3 Neutron Interactions

Neutrons produce the same signal as expected of a WIMP i.e. the same ratio of S2/S1. They may scatter elastically or inelastically with the target nucleus. In inelastic scattering, the nucleus recoils and gets excited to higher energy states, resulting in de-excitation gammas of energies in the hundreds of keV up to MeV range. Furthermore, a neutron can get captured by a nucleus. Subsequently, light nuclei are emitted such as nucleons or alpha particles as well as gammas of energy up to tens of MeV. The cross section of neutrons decreases with increasing nucleon number of the target material. The main energy depositing process is elastic scattering. The nuclear recoil energy for neutron elastic scattering Er is given by theory as

mnMXe Er 2En 2 (1 cosθ), (1) ≈ (mn + MXe) −

where En is the incident neutron energy, mn the neutron mass, mXe the xenon nucleus mass and θ the scattering angle (figure 3). Thus, one expects a recoil energy on the order of tens of keV for a neutron in in MeV range.

5 80 [keVr] r 70

60

recoil energy E 50

40

30

20

10

0 0 20 40 60 80 100 120 140 160 180 scattering angle θ [°]

Figure 3: nuclear recoil energy in the range of 0 to 180 ◦ for a neutron energy of 2.45 MeV

1.4 Energy Scale

The scintillation yield, defined as the number of photons detected per unit energy, depends on the type of particle under consideration and is an energy dependent quantity. Only a fraction of the energy loss of a particle is converted into measurable photons [16]. The deposit also manifests itself as heat and ionisation, as mentioned.

One defines the relative scintillation yield eff as the ratio of the scintillation yield L of nuclear recoils to that of electronic recoils (Ly) from photoabsorbed 122 keV rays from a 57Co source (at zero electric field) [17]. This has the advantage of being detector independent, absorbing any systematic errors connected to the setup.

eff is related to the nuclear recoil energy of single elastic neutron-nucleus scattering L by [18] See S1(Enr) eff (Enr) = (2) L Snr EnrLy

See where is a quenching factor depending on the electric field (See 0.5 for elec- Snr ≈ tronic recoils and Snr 0.9 for nuclear recoils at a field of 0.7 kV/cm) [19], Enr ≈ ≈ the nuclear recoil energy and Ly the reference light yield as described above. It is conventional to use keVr for nuclear recoil energy to distinguish it from the electron equivalent recoil energy keVee.

Measurements of eff have already been performed (figure 4). This experiment L will perform measurements of low recoil energies (small angles) and to reduce the

6 systematic uncertainties. 13 computed from the neutron generator yield at the op- 0.3 erating conditions. Since R is left as a free parameter Lebedenko 2009 2 Sorensen 2009 during the χ minimization, any additional contribution 0.25 Aprile 2005 to the resolution not accounted for will be absorbed in Aprile 2009 that parameter. Chepel 2006 0.2 Manzur 2010 The last step involves multiplying the simulated re- This Work coil energy spectrum by an overall, energy independent eff 0.15 efficiency ", taken as the same for all scattering angle L measurements, mostly due to the EJ301 energy threshold cut and to the uncertainty in the neutron generator yield. 0.1 This efficiency is computed during the χ2 minimization as an additional parameter for the measurement at the 0.05 recoil energies of 8.4, 10.7and14.8 keV. The best fit value from these three measurements is taken as the efficiency 0 1 10 100 for all measurements, while its uncertainty is taken as Nuclear Recoil Energy [keV] the maximum deviation in the measurements. The value +0.04 obtained is " =0.41 0.05. The 10% relative uncertainty FIG. 13: Measured values as function of nuclear recoil − eff on the efficiency reflects the fact that uncertaintiesFigure 4: Measured in the eff as of 2011 L Lenergy, together with measurements from other groups [11, neutron yield from the generator are at’This this level. Work’ in the figure12, 16 corresponds–19]. A possible to itsadditional source systematic paper [17]. uncertainty from the trigger efficiency roll-off alone, as described in the text,is indicated by the additional error markers. IV. RESULTS In order to interpret the detector response (response means the measured signal The values obtained for all scatteringof scintillation angles mea- photons) and to relate it to recoil energies, Monte Carlo simulations Leff sured are listed in Table I. Fig. 13 showsare required. the results The uncertainty on the nuclear recoil energy is significantly affected along with those of prior measurements at low ener- the measured values versus nuclear recoil energy. gies [11, 12, 16–19]. by the geometry of the experimentalLeff setup. Thus, the simulations are also needed The change in the inferred eff values due to the un- for an error estimation.certainties in the efficiency, andL the positions of the neu-

TABLE I: Values of eff obtained at the 8 angles used in this tron generator and of the EJ301 detectors, ∆ eff /∆", L L study, together with their errors as discussed in the text. ∆ eff /∆rg,and∆ eff /∆rs, respectively, were all calcu- latedL through a discreteL approximation by performing θ Enr (keV) eff L+0.014 additional Geant4 simulations where each parameter is 23◦ 3.0 0.60.088 0.015 varied by small amounts. ± −+0.015 26.5◦ 3.9 0.70.095 0.016 ± −+0.014 30◦ 5.0 0.80.098 0.015 The largest contribution to the total uncertainty in ± − 34.5◦ 6.5 1.00.121 0.010 eff comes from the spread in recoil energy. At energies ± ± L 39.5◦ 8.4 1.30.139 0.011 below 6.5 keV, this is followed by the uncertainty in the ± ± efficiency ". This is expected as in this region, varies 45◦ 10.7 1.60.143 0.010 eff ± ± most with nuclear recoil energy, and since the meanL of the 53◦ 14.8 1.30.144 0.009 ± ± pure single elastic recoil peak is in the roll-off of the trig- 120◦ 55.2 8.80.268 0.013 ± ± ger efficiency curve. For energies of 6.5 keV and above, the statistical uncertainty from the fit is the next-to lead- The total uncertainty on eff is given by a combination ing contribution to the total uncertainty. This is likely L of statistical and systematic factors with the statistical caused by the smaller statistics acquired for the higher uncertainty taken from the fit to the data. The system- recoil energy datasets. atic uncertainties include contributions from the spread in nuclear recoil energies, σEnr , and uncertainties associ- The systematic uncertainty in eff coming from the 57 L ated with the Co light yield, σLy ,theefficiency of the uncertainty in the trigger efficiency roll-off has been in- liquid scintillator threshold cut, σ!, and the positions of vestigated by varying the trigger efficiency function. If the neutron generator, σrg ,andoftheEJ301detectors, one assumes the measured trigger efficiency as the true

σrs . Explicitly efficiency, then its statistical uncertainty has a neglige- able effect on the inferred eff values. However, if one 2 2 L σ2 = σ2 + ∂ eff σ2 + ∂ eff σ2 assumes that a systematic effect is responsible for the eff eff ,fit ∂LL Ly ∂LE Enr L L y nr discrepancy between the mesured and simulated trigger ∆ 2 2 ∆ 2 2 ∆ 2 2 + Leff σ! + " Leff σ! + " Leff σ . (8) ∆! ! ∆rg rg ∆rs rs efficiencies and takes the simulated efficiency as the true efficiency, then the effect on the values below 6.5 keV ! " ! " ! " 7 Leff The change in eff with nuclear recoil energy, ∂ eff /∂Enr, is substantial. The effect is indicated by the additional is computed inL closed form from a logarithmicL fit to error indicators in in Fig. 13. 2 Experiment

2.1 The Xurich II Detector

Xurich I is a two-phase xenon TPC built to measure the scintillation and ionization yield of low-energy electronic recoils. The detector was also used to study energy calibrations with 83mKr photons [20]. Its successor Xurich II is built to study the light yield of low-energy neutrons in liquid xenon (LXe) at definite energies. Since neutrons, that only scatter once in the active volume, cannot be distinguished from WIMPs experimentally, they are suited to examine the properties of the xenon de- tector medium. It is much more compact than XENON100 with only two PMTs at the top and bottom of the target. Great effort was placed to reduce accidental scattering off non-sensitive material by reducing the amount of material used. A CAD model of the Xurich II detector is shown in figure 5. The target liquid xenon volume lies inside the drift spacer (4). Its interior has a height of 28 mm and a diameter of 17.5 mm. At the bottom of the drift spacer lies the cathode (3) with a copper-beryllium wire mesh. The drift field needed to drift the electrons upward extends up to the grounded gate, followed by a stronger electric field to the anode to accelerate the electrons and to get secondary scintilla- tion light (S2). The drift spacer is surrounded by copper wire rings that ensure a uniform electric field. The field values can be adjusted during operation. The drift field will be on the order of kV/cm [21]. The drift velocity of electrons in liquid xenon is approximately 2 105cm s−1 at 1 kV/cm electric field voltage. ·

8 Xurich2 TPC Overview

Pos. 21

Pos. 10

Pos. 12

Pos. 16

Pos. 9 Pos. 6

Pos. 1

Pos. 3 Pos. 8 Pos. 2 Pos. 7 Pos. 3

Pos. 13 Pos. 4 Pos. 3

Pos. 5

Pos. 14

Pos. 11

Pos. NameFigure 5: CAD model of the TPC, the mostPos. relevant Name parts are: 1 Levelmeter(1) grid holder, & Grid (2) Holder level-control cup, (3) cathode12 (bottom),Levelcontrol gate (middle) Feed Trough and anode Connector (top), (4) drift 2 Levelcontrolspacer (active Cup volume), (7) capacitor plates,13 (9) level-controlTPC Holding pipe Rod with bellow, (black cylinders) 3 GridPMTs 14 Bottom PMT Holding Rod 4 Dift Spacer 15 Top Flange (not visible) 5 Bottom PMT Holder 16 TPC Fixation Rod 6 Top PMT Holder 17 9 7 Capacito Plate Bottom 18 8 Capacitor Plate Top 19 9 Levelcontrol Pipe Assembly 20 10 Top PMT Holder 21 Holding Adapter Plate 11 Bottom PMT Holder The liquid xenon level resides between the grid and the cathode in (1). It can be varied in a range of 0.9 mm. By measuring the capacitance between the plates (7), the liquid xenon level can be determined with µm precision. The top part of the TPC is surrounded by gaseous xenon. The level-control pipe (9) has a built-in bellow to regulate the xenon height. Xenon first spills into the level-control cup (2), that allows for a smooth level adjustment of the liquid surface. There are two 200-diameter Hamamatsu R9869/R6041 PMTs located at the top and bottom [22]. The TPC has a total height of 170 mm and a diameter of 90 mm. All parts but the level control components (brass) and steel holders (11/12) are made out of PTFE (Polytetrafluoroethylene, known as Teflon). PTFE has suitable insulator properties and is a good reflector for the VUV scintillation light. The cooling to operating temperature shrinks PTFE by about 1.5% [11]. The LXe temperature is held at a constant temperature of 175 K and a pressure of 1.8 bar by a specifically designed vacuum cryostat. The cooling is provided by a copper finger immersed in a liquid nitrogen bath. Utility pipes for electrical wiring, pumps and inlet/outlets for Xe circulation are attached to the top flange [20].

Figure 6: The Xurich II TPC during its assembly.

10 2.2 Principle of Measurement

The main goal of the experiment is to measure eff of liquid xenon at low recoil L energies. The recoil energy distribution of neutrons scattered elastically at an angle θ with respect to the beam axis (figure 8) is simulated. Two organic scintillators will detect the scattered neutrons leading to an energy selection criterion (equation 1). The detector is placed in front of the exit of the NSD-1e7-DD-C neutron generator by NSD-Fusion GmbH. It provides a monoenergetic beam of neutrons with a kinetic energy of 2.45 MeV produced by deuterium-deuterium fusion. It has a measured Neutron flux of 1.25 105s−1 according to manufacturer (at 1% of the maximum · flux, which will be the main operating mode) [23].

2H +2 H 3 He(0.82 MeV) + n(2.45 MeV) (3) → The NSD Neutron Generator consists of a reaction chamber which is housed in a aluminum cylinder. The source is enclosed by a borated polyethylene shield and a concrete block. The neutrons exit through a 100 mm diameter window. The organic liquid scintillator detectors are 300 diameter Eljen Technologies M510 detectors filled with EJ301. EJ301 is especially adapted to fast neutron detection in the presence of γ radiation due to its excellent pulse shape discrimination (PSD) characteristics [17].

The neutrons are generated isotropically in the generator volume. The goal is to obtain a beam of small cross section, definite energy and small angular spread. The effect of two types of collimators is analysed (figure 7) in three sample config- urations. They have a shape of a cylinder with a conical hole in the middle, the material is chosen to be polyethylene.

Generator Screen d1 d2 d2 d1 configuration 2 configuration 3

Figure 7: schematic cut through the collimator in configuration 2 and 3 Configuration one is without a collimator. The screen is where the particles get registered in the simulation.

Thursday, December 19, 13

11 3 Implementation

The code was written in Geant4.9.6.2 [24] using ROOT 5.34.10 [25] as an analysis tool. A photon counter is implemented for the PMTs, but not used in this sim- ulation. The photon response can in principle be simulated with Geant4, but a different physics implementation would be needed for proper scintillation. Addi- tionally, there exists an option to make every material/volume in the setup active, such as the generator enclosure or the cryostat.

3.1 Geometry Setup

generator

2120 mm

a

Cryostat b ϑ Scintillator 1 Scintillator 2

Friday, January 3, 14 Figure 8: experimental setup The generator part constists of a concrete block (grey), containing a borated polyethylene (BPE) neutron shield (cyan) and a paraffin container (magenta). The cryostat is cylindrical, seen is only the quadratic base plate.

First, the particles are tracked at a virtual screen of 1 µm thickness just after the collimator. The simulation was performed for three configurations, that are config- uration 1 without a collimator, r1=50 mm and r2=15 mm for configuration 2, and r1=15 mm and r2=50 mm for configuration 3.

12 A sample of primary particles is recorded at screen position for a suitable col- limation and gamma shielding configuration. The cryostat is placed at a distance a = 1 m from the generator exit. The scintillators are placed at an angle θ and at a distance b = 1 m from the cryostat. The height of the cryostat is adjusted to z = 1.1 m, such that the center of the neutron beam hits the center of the active volume. Figure 3.1 shows the Geant4 model of the Cryostat, figure 3.1 the model of Xurich II.

(a) cryostat (b) TPC

Figure 9: Geant4 models of the (a) cryostat and (b) TPC (colors and transparencies just for visualisation purposes) (a) One can see the (here transparent) vacuum aluminium can containing the TPC (grey) (b) The xenon spills into the brass cup (orange). The target resides in the drift spacer (transparent blue). The PMTs are coloured in dark green.

Inside the TPC, there are several sensitive volumes, as shown in figure 10. The layer of liquid between cathode and bottom PMT is charge insensitive, since it is outside of the drift field. A photon scattering once in region 2 or 3 and once in region 1 might get confused as a nuclear recoil event. It can be excluded by a cut in

13 the z-coordinate. Regions 4 and 5 contain gaseous xenon, thus only volumes 2 and 3 are considered to be active. The information recorded in these volumes includes the energy, position, time, type of particle, creation processes and energy depositing process.

5 GXe 4 3 LXe

2 Drift Field

1

Figure 10: labeling on the TPC sensitive regions The numbers correspond to the code internal numbering of the xenon active regions, that is stored in the output file.

Wednesday, December 11, 13

14 3.2 Features

The code provides a set of user interface commands. Apart from visualisation options, one may

enable/disable the use of a collimator • set the two inner radii of the collimator • set the material of the collimator • set the length of the collimator • set the angle of the organic scintillators • choose from primary generators neutron generator, particle gun or screen source • define various variables for particle source control such as setting the energy, • particle type, direction, distribution etc.

toggle between normal mode and screen mode to activate/deactivate sensitive • detectors

toggle general mode to make every volume sensitive • the hadronic physics list • The primary generators provided includes a neutron generator, as described above, featuring a monoenergetic isotropic distribution of neutrons with an energy of 2.45 MeV and a Geant4 built-in particle gun, consisting of a simple beam of definite direction with no randomization. Additionally, the screen particle source is designed to take input from a .root file filled with particles at screen position and convert them into primaries. It reades out a random particle from the file for each event. The information registered is the type of particle (gamma or neutron), momentum, energy and position. The hadronic physics list can be chosen from the predefined QGSP BERT (QGSP stands for quark-gluon string precompound [26]) for fast test calculations, and QGSP BERT HP as well as QGSP BIC HP for high neutron transport precision in the actual run. These are recommended physics lists that are well suited for low-energy neutron simulations [27]. The last two differ by the hadronic cascade model used (Bertini cascade and binary cascade respectively). The addition of HP adds high precision data for a precise transportation of neutrons below 20 MeV.

15 In the source code, one can change easily

the liquid xenon level between gate and anode • the electromagnetic physics list • The program can be evoked with command line options

-o [path to output file] • -f [path to run macro] • -i [path to initalization macro] • -s [path to screen input files] • -i interactive mode • -v visualisation mode • -n [number] run with a number of n events • A macro to merge the screen output to input files for the main simulation exists in addition to the Geant4 source code. Additional code may be used to analyse the simulation for an arbitrary configuration.

16 3.3 Monte Carlo Simulation

3.3.1 Collimation

The collimation has been simulated for 107 events per configuration. This corre- sponds to a lifetime of 80 seconds. Figure 11 shows the relevant histograms.

1 configuration rate [s− ] mean energy [MeV] mean pz/p γ to n ratio [%] 1: without collimator 119.6 1.2 1.84 0.009 0.974 0.001 37 0.9 ± ± ± ± 2: r1 = 50 mm, r2 = 15 mm 12.1 0.4 1.57 0.03 0.923 0.005 112 5 3: r = 15 mm, r = 50 mm 30.7±0.6 1.76±0.02 0.967±0.002 75 ±2 1 2 ± ± ± ±

In conf. 3, the angular spread is 18 mm as opposed to the collimator inner ≈ radius of 15 mm. Comparing conf. 3 to conf. 1, the rate of 2.45 MeV neutrons (highest bin) is reduced by about one order of magnitude, the rate of lower energy neutrons (energy < 2 MeV) does not change significantly. For both types of colli- mators, one can note that the neutron rate decreases notably when introducing a collimator. As a side effect, a number of unwanted gammas get produced.

3.3.2 Gamma Shielding

In practice, it is not always possible to distinguish between electronic and nuclear recoil. Some signals might overlap, covering relevant peaks that the readout software cannot tag. Therefore, it is necessary to reduce the electronic recoil background. To decrease the gamma rate, a plate of high-Z material can be placed at the exit of the generator. This setup is simulated for a lead plate with thicknesses ranging from 0 to 5 cm in 1 cm steps. A number of 108 events has been simulated for each configuration. Figure 12 shows the relevant data. Looking at the number of neutrons with an energy higher than 2.4 MeV, one clearly wants a minimum thickness of lead. On the other hand, a minimum ratio of gamma to neutron rate is required. Note, that at 2 cm the ∼ ratio of gammas to neutrons is reaching a constant value.

17 particle type kinetic energy of gammas ] ] -1 -1 102 rate [s rate [s

1 10

-1 1 10

-1 10 10-2

neutron gamma anti_nu_e e- nu_e 0 1 2 3 4 5 6 7 8 9 10 particle Type kinetic Energy [MeV]

kinetic energy of neutrons neutron rate conf. 1 [s-1] (x,z) rate ] 60 -1 Entries 71120.25 Mean x 0.07722

rate [s Mean y 0.3331 40 RMS x 25.13 RMS y 24.910.2 10 z coordinate [mm] 20

0.15 0 1 0.1 -20

0.05 -40 10-1

-60 0 0 0.5 1 1.5 2 2.5 3 -60 -40 -20 0 20 40 60 kinetic Energy [MeV] x coordinate [mm]

neutron rate conf. 2 [s-1] neutron rate conf. 3 [s-1] 60 (x,z) rate 60 (x,z) rate Entries 968 Entries 1488 Mean x 0.15030.2 Mean x 0.1880.14 Mean y 0.5401 Mean y -0.2842 40 0.18 40 RMS x 10.38 RMS x 18.350.12 RMS y RMS y 9.8150.16 18.1 z coordinate [mm] z coordinate [mm] 20 0.14 20 0.1

0.12 0.08 0 0 0.1

0.08 0.06 -20 -20 0.06 0.04

-40 0.04 -40 0.02 0.02

-60 0 -60 0 -60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60 x coordinate [mm] x coordinate [mm]

Friday, January 3, 14 Figure 11: data output for collimation tracked at the virtual screen (from left to right, top to bottom) color coding: conf. 1 (blue), conf. 2 (red) and conf. 3 (green) The first histogram shows the rate of particles detected at screen position for the three configu- rations. The second histogram shows the kinetic energy distribution for gammas, the third for neutrons. 1 The other three plots show the neutron rate [s− ] in conf. 1-3 at the screen (x,z) plane.

18 25 98

20 /p> in percent z 96

94 15

92 10

90 ratio of gamma to neutron rate in percent

5 88

0 86 0 1 2 3 4 5 0 1 2 3 4 5 lead thickness [cm] lead thickness [cm] ] ] -1 90 -1 rate [s rate [s 85 10

80

1 75

70 10-1

65

-2 60 10

55 10-3 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 lead thickness [cm] neutron energy [MeV]

Figure 12: screen output for gamma shielding as a function of lead thickness (from left to right, top to bottom) The first plot shows the ratio of gamma/neutron rate in percent, the second the mean pz/p, the third graph shows the neutron rate. In the last plot, one can see the energy distributions of the neutrons for a lead thickness of 0 cm (red) and 3 cm (blue). The statistical error bars not shown here are too small to be visualised.

19 3.4 Full Simulation of the Measurement

Following the previous considerations, configuration 1 and a lead plate of 2 cm is chosen. A set of 109 events is sampled at the screen position for further use. The coincidence of an energy deposit in one of the scintillators and the active liquid xenon volume serves as a trigger. The liquid xenon level is set to 4.5 mm relative to the bottom of the grid holder in figure 5.

3.4.1 Data Processing

Since the detector has a finite position resolution, not all energy deposits for an interacting neutron can be told apart. The time difference between two S2 peaks must be greater than 2 µs for a successful readout. The minimal z-distance has been measured to be 3 mm in average. This distance depends on the drift velocity and on the readout software. Taking this into account, the energy depositing events in the TPC are first ordered by height z. Beginning with the topmost, the energy deposits get written to a histogram. Additionally, if the neutron didn’t deposit energy in any material other than the active liquid xenon and the scintillator, the event is considered as true coincidence. The data can further be refined, by applying a time-of-flight cut. This excludes slower neutrons that scattered in other materials and contribute to background. To figure out at which time to cut, the time-of-flight is evaluated with a single collinear beam of definite neutron energy 2.45 MeV.

3.4.2 Outcome of the Monte Carlo Experiment

Figure 13 shows the time-of-flight (TOF) and energy deposition distributions in the liquid xenon for a sample angle of 45 degrees and a number of 107 events. Electronic recoils are excluded in this analysis. A TOF cut of 50 ns is chosen, such that the peak is fully contained in this region. A more precise cut value results in less contamination of the data, resulting in a smoother distribution. A more precise positioning of the cut value is thus not relevant. For generator neutrons as a primary source, the results are as shown in figure 14. A number of 108 events has been simulated.

20 energy deposit time of arrival ] ] -1 4.5 -1 9

rate [s 4 rate [s 8 3.5 7 3 6 2.5 5 2 4

1.5 3

1 2

0.5 1

0 0 0 5 10 15 20 25 30 35 40 45 50 0 20 40 60 80 100 120 140 160 180 200 energy deposit [keVr] time [ns]

Figure 13: sample output for a neutron beam of energy 2.45 MeV and energy deposit in LXe nuclear recoil (green), true coincidence (red), TOF cut (dashed orange line)

energy deposit time of arrival ] ] -1 -1 0.07 Monday, January 6, 14 0.12 rate [s rate [s 0.06 0.1

0.05 0.08 0.04

0.06 0.03

0.04 0.02

0.01 0.02

0 0 0 5 10 15 20 25 30 35 40 45 50 0 20 40 60 80 100 120 140 160 180 200 energy deposit [keVr] time [ns]

Figure 14: sample output for a neutron beam of energy 2.45 MeV nuclear recoil (green), TOF cut (blue), true coincidence (red), energy interval for calculating the mean value and deviation (dashed orange lines)

Monday, JanuaryThe 6, 14 peak is clearly visible and can be taken to calculate the mean recoil energy as well as the standard deviation. This corresponds to (11.1 0.1) keVr. The ± predicted value of 11.0 keVr is well within the error range.

21 3.4.3 Background

Events outside of peak on the left in figure 14 originate from neutron inelastic scattering with energy deposits of the recoiling xenon atoms comparable to the elastic scattering deposits or from neutrons with additional deposits in non-active material. Neutrons travelling directly from the generator to the scintillators are excluded by requiring coincidence, slow neutrons (as in conf. 1 of figure 11) get excluded by the TOF cut. Gammas originating from neutron capture may have energies higher than 2.45 MeV (up to 10 MeV). Figure 15 shows the materials responsible for neutron capture and inelastic scattering. For neutron capture, concrete is the most relevant material, inelastic scattering happens mainly in concrete, steel and aluminium. energy deposit neutron capture ] -1 105

3 10 rate [s 10 10

10-1

10-3 1

-5 total energy deposited [MeV] 10

10-7 10-1 10-9

10-11

10-13 10-2 10-15 G4_AIR SSteel Vacuum AluminiumG4_CONCRETEGXe LXe Copper Teflon G4_Ni BPE G4_PARAFFINQuartz G4_CONCRETESSteel Copper BPE Aluminium G4_AIR LXe Teflon Quartz GXe G4_Ni material material

Figure 15: inelastic scattering (red) and neutron capture (blue) rate sorted by material

For inelastic scattering, Geant keeps track of the resulting xenon isotopes. It is interesting to look at their relative distribution.

0.3

0.25 relative abundance

0.2

0.15

0.1

0.05

0 Xe124 Xe126 Xe128 Xe129 Xe130 Xe131 Xe132 Xe134 Xe136 isotope

Figure 16: distribution of the xenon isotopes after inelastic scattering

22 4 Conclusions

In the course of this bachelor thesis, several tasks have been accomplished. A sample simulation of 45◦ has been performed. The simulations based on this code will be continued by the group. They will be performed with a much higher number of events and for a set of angles, corresponding to the measured angles in the experiment. As a conclusion, the key accomplishements are listed here.

In the scope of this thesis, a Geant4 model for the Xurich II experiments has • been developed.

A suitable user interface is provided for further simulations. • The predicted curve of the nuclear recoil energy is well within the error of the • simulated data.

The use of different types of neutron collimators has been simulated and was • found to be of no relevance.

Gammas have been found to originate from inelastic scattering and neutron • capture. Neutron capture is mostly found in aluminium, steel and concrete, inelastic scattering in concrete.

Gamma shielding has been examined by introducing lead plates and compared • for different thicknesses. A lead shield with thicknesses of 2 cm has been chosen for the experiment.

23 5 Acknowledgements

I would like to thank Dr. Alexander Kish for his incredible help, patience and time invested on teaching me. I would also like to thank Prof. Dr. Laura Baudis for making this bachelor project possible. Additionally, I’d like to thank Francesco Piastra for showing me how to simulate on the cluster.

24 List of Figures

1 current upper limits on the spin-independent elastic WIMP-nucleon scattering cross section [8] Experiments Large Underground Xenon (LUX) 1σ interval (violet), ± Edelweiss II (dark yellow line), CDMS II (green line), ZEPLIN-III (magenta line), XENON100 100 live-day (orange line, ’old’), and 225 live-day (red line, ’new’) results ...... 3 2 mode of operation of a time projection chamber [13] The prompt signal S1 and the secondary signal S2 get detected by arrays of PMTs. The cathode is at a negative high voltage (HV), the gate in the middle is grounded. The anode is at a positive HV. The drift-time together with the electron’s drift velocity indicates the z-position...... 4 3 nuclear recoil energy in the range of 0 to 180 ◦ for a neutron energy of 2.45 MeV ...... 6

4 Measured eff as of 2011 L ’This Work’ in the figure corresponds to its source paper [17]. . . . 7 5 CAD model of the TPC, the most relevant parts are: (1) grid holder, (2) level-control cup, (3) cathode (bottom), gate (middle) and anode (top), (4) drift spacer (active volume), (7) ca- pacitor plates, (9) level-control pipe with bellow, (black cylinders) PMTs ...... 9 6 The Xurich II TPC during its assembly...... 10 7 schematic cut through the collimator in configuration 2 and 3 Configuration one is without a collimator. The screen is where the particles get registered in the simulation...... 11 8 experimental setup The generator part constists of a concrete block (grey), containing a borated polyethylene (BPE) neutron shield (cyan) and a paraffin container (magenta). The cryostat is cylindrical, seen is only the quadratic base plate...... 12

25 9 Geant4 models of the (a) cryostat and (b) TPC (colors and trans- parencies just for visualisation purposes) (a) One can see the (here transparent) vacuum aluminium can con- taining the TPC (grey) (b) The xenon spills into the brass cup (orange). The target resides in the drift spacer (transparent blue). The PMTs are coloured in dark green...... 13 10 labeling on the TPC sensitive regions The numbers correspond to the code internal numbering of the xenon active regions, that is stored in the output file...... 14 11 data output for collimation tracked at the virtual screen (from left to right, top to bottom) color coding: conf. 1 (blue), conf. 2 (red) and conf. 3 (green) The first histogram shows the rate of particles detected at screen position for the three configurations. The second histogram shows the kinetic energy distribution for gammas, the third for neutrons. The other three plots show the neutron rate [s−1] in conf. 1-3 at the screen (x,z) plane...... 18 12 screen output for gamma shielding as a function of lead thickness (from left to right, top to bottom) The first plot shows the ratio of gamma/neutron rate in percent, the

second the mean pz/p, the third graph shows the neutron rate. In the last plot, one can see the energy distributions of the neutrons for a lead thickness of 0 cm (red) and 3 cm (blue). The statistical error bars not shown here are too small to be visualised...... 19 13 sample output for a neutron beam of energy 2.45 MeV and energy deposit in LXe nuclear recoil (green), true coincidence (red), TOF cut (dashed or- ange line) ...... 21 14 sample output for a neutron beam of energy 2.45 MeV nuclear recoil (green), TOF cut (blue), true coincidence (red), energy interval for calculating the mean value and deviation (dashed orange lines) ...... 21 15 inelastic scattering (red) and neutron capture (blue) rate sorted by material ...... 22 16 distribution of the xenon isotopes after inelastic scattering . . . . . 22

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