Muon Beam Intensity Monitor Using X-Ray Fluorescence

InstitutETHZ-IPP-2008-13 fur¨ Elektronik August 2008 Prof. G. Tr¨oster Wintersemester 2005/2006

Diplomarbeit DIPLOMA THESIS Verkehrsmessung mit MuonBildverarbeitung beam intensity monitor using X-ray ﬂuorescence

supervised by Prof. Urs Langenegger ETH Zürich Institute for Particle Physics IPP P-R. Kettle Paul Scherrer Institute PSI Laboratory for Particle Physics LTP

Verfasser: Betreuer: Remo Huber Bernhard M¨ader, SCS AG Reto B¨attig, SCS AG ETH Zürich, Switzerland Clemens Lombriser, ETH Abstract

This report presents a new method of measuring the particle rate of a muon beam using X-ray fluorescence. X-ray fluorescence is a common tool for non-destructive trace element analysis. Instead of irradiating a target with radioactive sources in order to induce X-rays, thin foils of Copper, Tantalum and other materials are placed in the muon beam. The X-rays are then measured using a silicon detector and the rate is compared with theoretical predictions. Finally the foil would be mounted permanently in the beam line and by measuring the X-ray rate the muon rate can be continuously monitored. The advantage of this method compared to others is that the muon beam is only affected at a minimum level in terms of energy loss and beam divergence induced by multiple scattering. Measurements using a Cockroft-Walton proton accelerator (at several energies reaching from 250 keV−1 MeV at ≈ 6.25·1012 Hz) as well as measurements using the muon beam (at a muon momentum of 27.75 ± 0.26 MeV/c at 7 + ≈ 3 · 10 Hz) are presented. In case of the proton beam a contamination of ≈ 25% H2 Ions has to be taken into account, whereas in the case of the muon beam the influence of decay positrons, originating from muons stopped in thick targets, must be considered. The method is shown to be viable at the required level of precision (≈ 1%) with modifications to the detector system. Hence with further tests the system can be implemented into one of the world’s most intense surface muon beams as an intensity monitor for the MEG experiment. Contents

1 Introduction 8 1.1 The standard model of particle physics ...... 8 1.2 Motivation and overview of the MEG experiment ...... 9 1.3 Diploma thesis in the context of the MEG experiment ...... 11

2 Theory of X-ray emission 13

3 Comparison of diﬀerent detectors 16 3.1 XR-123CR Si-detector ...... 16 3.1.1 Element analysis of a 5SFr coin ...... 17 3.2 XR-100CR Si-detector ...... 18 3.2.1 Rate measurement with the XR-100CR detector ...... 19 3.3 NaI(Tl) crystal detector ...... 23 3.4 Avalanche Photo Diode and Surface Barrier Detector ...... 27

4 Calculation of the X-ray emission rate 30 4.1 Ionization and emission cross-section results using ISICS06 ...... 31 4.2 Energy loss calculations with SRIM 2008 ...... 35 4.3 Rate calculation including attenuation in the target ...... 36 4.4 Calculation of the solid angle ...... 39 4.5 Error calculation ...... 42

5 Measurements with a proton beam 44 5.1 Cockcroft-Walton proton accelerator ...... 44 5.2 X-ray rate calculation / measurement ...... 46 5.3 Rate comparison to predictions ...... 51

1 6 Measurements with a muon beam 55 6.1 Pion production ...... 55 6.2 Pion-decay / Muon production ...... 56 6.2.1 "Surface" / "Sub-surface" muons ...... 56 6.2.2 "Cloud" Muons ...... 57 6.3 MEG muon beam line ...... 57 6.4 Muon induced X-ray rate measurements ...... 59 6.5 Consideration of the momentum window ...... 64 6.6 Rate prediction for the large Copper foil ...... 64 6.7 Rate prediction including positrons ...... 66 6.8 Comments on the positron induced X-ray rate ...... 68 6.9 Summary of the muon measurements ...... 68

7 Conclusion 69

Appendix 81

2 List of Figures

2.1 Schematic drawing of the X-ray emission process ...... 13 2.2 X-ray emission, Auger electron, Coster-Kronig transition ...... 14 2.3 Labeling of K-, L- and M-shell X-ray transitions ...... 14 2.4 Fluorescence yield for K- and L-shell ...... 15

3.1 Experimental setup for the Copper X-ray measurement ...... 16 3.2 Element analysis of a 5SFr coin ...... 17 3.3 XR-100CR Si-detector and PX2CR power supply/ampliﬁer ...... 18 3.4 Diagram of the readout scheme for the XR-100CR detector ...... 18 3.5 Copper spectrum with 55F e calibration ...... 19 3.6 Energy resolution versus X-ray energy of the XR-100CR Si-detector . . . 19 3.7 XR-100CR trigger check ...... 20 3.8 XR-100CR dead time ...... 21 3.9 Comparison of rate measurements: MCA / ICR connected to scaler . . . 22 3.10 Picture of the NaI(Tl) detector and pre-ampliﬁer ...... 23 3.11 Schematic drawing of the setup for the NaI(Tl) detector ...... 23 3.12 241Am spectrum with the NaI(Tl) detector ...... 24 3.13 P b spectrum with NaI(Tl) detector ...... 25 3.14 Energy resolution versus X-ray energy of the NaI(Tl) crystal detector. . . 26 3.15 Comparison of NaI(Tl) signal with and without TFA ...... 27 3.16 241Am and 109Cd spectrum with APD ...... 27 3.17 Disturbing signal for measurements with the APD ...... 28 3.18 109Cd spectrum with the SBD ...... 29

4.1 Ionization and emission cross-section for protons and muons as a function of the atomic number ...... 31 4.2 X-ray emission cross-section versus projectile energy ...... 32

3 4.3 Proton and muon emission and ionization cross-section for Copper versus beta ...... 33 4.4 Comparison of ISICS06 calculations to experimental data ...... 33 4.5 Comparison of ISICS06 calculations to measurements for several elements 34 4.6 Energy loss in Copper calculated with SRIM ...... 35 4.7 Proton induced X-ray rate ...... 37 4.8 Muon induced X-ray rate ...... 38 4.9 Solid angle MC ...... 40 4.10 Proton beam spot ...... 41 4.11 Quartz crystal for proton beam spot measurements ...... 41

5.1 Picture of the C-W proton accelerator ...... 44 5.2 C-W accelerator column and ion source ...... 45 5.3 Experimental setup for the C-W measurements ...... 46 5.4 Proton induced Cu and Ta X-ray spectrum with XR-100CR ...... 47 5.5 Combined Cu and 55F e spectrum with NaI(Tl) ...... 47 5.6 Copper spectrum with NaI(Tl) ...... 48 5.7 Copper spectrum measured with C-W ...... 49 5.8 Comparison of proton induced X-ray measurements with predictions . . . 51 5.9 Radiation damage in a Copper target ...... 52 5.10 Radiation damage simulation with SRIM 2008 ...... 53 5.11 Measured X-ray rate as a function of the exposure time ...... 53

6.1 MEG beam momentum spectrum ...... 56 6.2 Secondary beam lines at PSI and MEG beamline ...... 57 6.3 Meg muon beam line ...... 58 6.4 Separation of positrons and muons ...... 59 6.5 Experimental setup for the muon beam ...... 60 6.6 Muon beam spot ...... 60 6.7 Muon induced Ag spectrum ...... 61 6.8 Comparison of proton and muon induced X-ray spectra ...... 62 6.9 Comparison of muon and positron induced X-ray spectra ...... 62 6.10 Rate calculation for the large Copper foil ...... 65 6.11 Muon measurement results ...... 67

4 6.12 Spin polarized muon decay ...... 68

1 Eﬃciency plot for the diﬀerent X-ray detectors ...... 72 2 K- and L- emission line lookup chart ...... 73 3 Relative abundance of K- and L-shell X-rays ...... 74 4 Schematic drawing of the C-W X-ray measurement setup ...... 77 5 Graphical comparison of C-W measurements with predictions ...... 78 6 Overview of muon induced X-ray measurements using thin foils . . . . . 81

5 List of Tables

1.1 Electromagnetic, weak and strong interaction and their respective gauge bosons...... 8 1.2 Lepton multiplets ...... 8 1.3 Lepton numbers for the Michel decay ...... 10 1.4 Lepton number violating muon decay ...... 10 1.5 Muon decay channels and probabilities ...... 11

3.1 Comparison of rate measurements: MCA / ICR and scaler ...... 22 3.2 Tabulated X-ray energies for the lead spectrum ...... 25

4.1 Comparison of SRIM 2008 calculations with experimental data ...... 36 4.2 Comparison of proton and muon induced X-ray production rate . . . . . 38

5.1 55F e X-ray lines and emission probabilities ...... 48 + 5.2 X-ray rate prediction for protons including a H2 contamination . . . . . 54

6.1 Delta resonance production ...... 55 6.2 Decay channels for the delta resonances ...... 56 6.3 Characteristic properties of the πE5 beam line ...... 58 6.4 Muon induced X-rays, comparison with predictions ...... 63 6.5 Labeling of the divisions on the large Copper foil ...... 65 6.6 X-ray rate prediction for muons including positrons ...... 67

1 Detector properties (active layer and entrance window) ...... 72 2 Detector eﬃciency table ...... 72 3 Relative abundance of K-shell X-rays ...... 74 4 Relative abundance of L-shell X-rays ...... 74 5 Comparison ISICS06 with exp.data from J.Phys.B, Vol.25, Nr.7 . . . . . 75 6 Comparison ISICS06 with exp.data from J.Phys.B, Vol.9, Nr.3 ...... 75

6 7 Comparison ISICS06 with exp.data from J.Phys.B, Vol.14, p.3153 . . . . 76 8 Comparison ISICS06 with exp.data from NIMB, Vol.249, pp.73-76 . . . . 77 9 C-W measurement results ...... 79 10 Comparison of muon induced X-ray measurements with predictions . . . 80 11 Measured X-ray energies with muon beam ...... 81

7 Chapter 1

Introduction

1.1 The standard model of particle physics

The standard model of particle physics (SM) includes the combined electroweak interaction, which is a combination of the electromagnetic and weak forces at high energies as well as quantum chromodynamics. Besides gravitation, there exist three know forces, namely the electromagnetic, the weak and the strong interaction, which have quite similar structures. In all cases the force is mediated via gauge bosons. The gauge bosons for the three forces, as well their couplings, are listed in tab.1.1:

Table 1.1: Electromagnetic, weak and strong interaction and their respective gauge bosons

Interaction couples to Exchanged particle Mass [ GeV/c2] strong colour charge 8 gluons (g) 0 electromagnetic electrical charge photon (γ) 0 weak weak charge W ±,Z0 bosons ≈ 102

Gluons themselves carry colour charge, hence they interact with each other. The exchange bosons for the weak interaction carry weak charge and therefore they also interact with each other, whereas photons are neutral and do not interact with each other. Besides these exchange bosons, further fundamental particles exist, which are assumed to be point like so 1 far, i.e. without any internal structure, namely quarks and leptons. Both, quarks and leptons are spin 2 particles, hence fermions. According to the SM these particles are arranged in three generations. Tab.1.2 shows the three lepton and quark generations as well as the lepton family numbers Ll (l = e, µ, τ) and the baryon number B respectively:

Table 1.2: The three known lepton and quark generations, as well as the lepton family numbers and the baryon number respectively. Note that anti-leptons + + + (e , µ , τ , νe, νµ, ντ ) carry the opposite lepton family number whereas anti- quarks (u, d, c, s, t, b) possess the opposite baryon number.

Leptons Le Lµ Lτ Quarks B st − 1 1 generation e +1 0 0 u 3 1 νe +1 0 0 d 3 nd − 1 2 generation µ 0 +1 0 c 3 1 νµ 0 +1 0 s 3 rd − 1 3 generation τ 0 0 +1 t 3 1 ντ 0 0 +1 b 3

8 At each vertex, the lepton family number Ll given by the sum of leptons minus the sum of anti-leptons for a lepton family, is a conserved quantity:

Ll = N (l) − N l + N (νl) − N (νl) = const where l = e, µ, τ (1.1)

Since neutrinos are not completely massless and since the mass and ﬂavor eigenstates are not the same, oscillations occur, with the consequence that only the total lepton number L = Le + Lµ + Lτ , given by the sum of the lepton family numbers, is a conserved quantity.

The baryon number B as given in tab.1.2 is one third of the number of quarks Nq minus the number of anti quarks Nq:

N − N B = q q (1.2) 3 The reason to divide by three is that according to the laws of strong interaction all observed particles have to be colourless or white (due to confinement). There are three ways of combining the colours red, blue and green such that a colourless bound quark state results. The combination of three quarks with any flavour with different colour as well as the combination of three anti-quarks with different colour, yield colourless states called baryons and anti-baryons respectively:

0 00 Baryons: qrq q b g (1.3) 0 00 Anti baryons: qrqbqg

Note that the quark ﬂavour of q, q0, q00 does not need to be the same. The third way of creating a colourless states is by combining a colour with its anti-colour:

0 0 0 Mesons: qrqr or qbqb or qgqg (1.4)

Note that anti-quarks carry anti-colour. For reasons of better clarity only one bar is drawn (i.e. qr denotes the anti-quark q carrying the colour anti-red). In principle its possible to combine baryon and meson states to form so called pentaquarks. Although these pentaquarks are colourless states, such particles have been claimed to have been seen, though there is controversy about this. The baryon number is a conserved quantity for all reactions measured so far.

Although most particle reactions are predicted very precisely by the standard model of particle physics, there remain problems, one of which is that neutrinos are predicted to be massless which is not the case; Since neutrino oscillations have since been seen. However, the SM can be adjusted for neutrinos with non zero mass. In fact the SM does not predict any of the particle masses, which a good model should do. Another problem arises with dark matter. Only ≈ 4% of the total energy density can be seen directly. Another ≈ 25% is believed to be dark matter and the remaining part is dark energy. There are some promising candidate particles for dark matter, whereas there are no promising theories for dark energy so far. A more sophisticated particle physics model should also include dark matter particles.

1.2 Motivation and overview of the MEG experiment

This diploma work is part of the MEG experiment (which is an abbreviation for "Mu to e plus gamma") whose purpose it is to search for the lepton ﬂavor violating process µ+ → e+γ. The ﬁrst search for which was undertaken some 60 years ago by Hincks and Pontecorvo [1] using cosmic rays.

9 According to the Standard Model of Electro-Weak and Strong interactions the predicted branching ratio −50 BRµ+→e+γ is ≈ O(10 ) with respect to all muon decays, the dominant mode being the Michel decay + + µ → e νeνµ. Tab.1.3 and tab.1.4 show the lepton family numbers according to SM presented in the previous section (see tab.1.2) for the dominant Michel decay and the lepton number violating muon decay into a positron and a photon:

Table 1.3: Dominant muon decay and lepton numbers of all involved particles. Note that all lepton family numbers are conserved individually for the Michel decay

+ + µ −→ e νe νµ Le 0 -1 1 0 Lµ -1 0 0 -1 Lτ 0 0 0 0

Table 1.4: Lepton number violating muon decay into a positron and a photon. Note that both Le and Lµ are not conserved.

µ+ −→ e+ γ Le 0 -1 0 Lµ -1 0 0 Lτ 0 0 0

The motivation for measuring the branching ratio of the lepton ﬂavour violating muon decay into a positron and a photon is that such a signature, if found, would clearly signal "new physics" beyond the SM. Within the framework of the latter the decay is at least very unlikely, since higher order diagrams with neutrino oscillations have to be included. Also the SM is believed to be a low energy approximation of a more fundamental theory, at higher energies. Many Super Symmetric models (SSM), which predict a much larger branching ratio of the order of 10−15 − 10−11 [2], [3] which is accessible to the MEG experiment, whose planned goal is a two-orders of magnitude improvement in sensitivity over the present best upper limit by the MEGA collaboration [4] −11 (BRµ+→e+γ ≤ 1.2 · 10 at 90% CL). The MEG experiment, an Italian-Japanese-Swiss-Russian and American Collaboration at the Paul Scher- −13 rer Institute (PSI) aims to be sensitive to BRµ+→e+γ . 10 , which is of the order of the branching ratio predicted by SSM. Muons are stopped within a thin depolarizing target (see chapter 6), where the muon decays into a positron and a photon in a simple two body decay at rest. The following mandatory conditions for a pair of measured particles have to be satisﬁed to ensure that the measured reaction is indeed a muon decay into a positron and a photon:

• A simple condition is that one charged (positron) and one neutral particle (photon) are to be detected

• e+ and γ propagate back to back (momentum conservation)

• e+ and γ arrive coincident in time

+ 1 • e and γ carry each 2 mµ as energy (the photon energy is measured using a liquid Xenon calorimeter, while that of the positron comes from tracking chambers placed in a magnetic ﬁeld)

There are three key components [5] in the experiment that allow for such a sensitivity, namely the use of one of the highest intensity DC low energy muon beam (surface muons) existing so far (108 Hz

10 muon stopping rate in the target). A special positron spectrometer consisting of a gradient magnetic field superconducting solenoid magnet COBRA (COnstant Bending RAdius, 1.27 T magnetic field at the center and 0.49 T at both ends) together with 16 planar radial ultra-thin drift chambers. Lastly, a liquid Xenon scintillation gamma-ray detector (0.8 m3 liquid Xenon and 800 PMTs for the light readout) with good spatial, timing and energy resolution. Furthermore, there are scintillation counter arrays consisting of scintillator bars and orthogonal fibres placed at either end of the magnet allowing for fast timing and triggering of positrons. There are several background processes producing similar signals to that expected from muon decay into a positron and a photon. Besides the dominant Michel decay, roughly 1.4% of all muons decay via radiative muon decay (RMD), see tab.1.5:

Table 1.5: Dominant Michel decay, radiative muon decay (RMD) and the hypothetical muon decay into a positron and a photon including their probabilities

+ + µ −→ e νeνµ Michel decay: 98.6% + + µ −→ e νeνµγ Radiative muon decay, RMD: 1.4% + + −13 µ −→ e γ Muon decay into positron and photon: 0(. 10 )

In the case that the neutrinos from the RMD are produced almost at rest, the conditions are similar to the direct decay into a positron and a photon (positron and photon back to back, coincident in time, carrying half of the muon mass as energy). The RMD therefore produces a so-called "physics background". However, the most likely background comes from so-called "accidental background", where a Michel decay positron can, together with a photon originating from either a RMD or annihilation-in-ﬂight (e+e− → γγ, forward going!) or a Bremsstrahlung photon from conversion in materials of the detector, mimic a µ+ → e+γ decay. Neutrons may also induce accidental background.

1.3 Diploma thesis in the context of the MEG experiment

In order to reach the planned unprecedented sensitivity of the MEG experiment, not only high precision innovative detectors are needed, but also a high intensity, high quality muon beam, as well as understanding the systematics of the whole detector. Apart from minimizing background events in the detector, related to unwanted material interactions, it is crucial to have a high quality muon beam to suppress beam-related background, since the accidental background increases quadratically with beam rate. The normalization of the experiment relies on a knowledge of the number of stopped muons which is obtained from measuring the number of secondary Michel positron tracks reconstructed in the drift chambers and timing counters. Under the assumption of equivalent acceptances and eﬃciencies of positrons in the detector coming from Michel and µ+ → e+γ decays the method is self-normalizing. However, if this is not the case then a precise understanding of the various eﬃciencies and acceptances is necessary. In view of this and the fact that in a precision experiment such as MEG it is advisable to measure important quantities independently - it would therefore seem reasonable to have a continuous and independent measure of the muon beam intensity.

The goal of this diploma thesis is to test the possibility of using muon induced X-ray fluorescence to monitor the muon beam rate. Since the muons are stopped within a small polyethylene target, the rate measurement must not influence the muon trajectory too much. Because of the small muon energy (Ekin = 3583 keV) normal scintillators would be too thick, i.e. the muons either stop or undergo significant multiple scattering inside the scintillator instead of decaying within the polyethylene target.

11 Another problem is that due to the high muon beam rate of roughly 108 Hz, very fast counters would be needed. These problems can be solved by using muon induced X-ray fluorescence. In order to monitor the muon beam using this new method of muon induced X-ray fluorescence, a thin foil (thickness of a few microns) is placed in the beam (see fig.6.5 for the experimental setup). Incoming muons ionize some target atoms (K-,L-,M- shell ionization) in the foil, and while de-exciting to the ground state the target atoms release the difference in the binding energy as X-rays and Auger electrons. The ratio is given by the fluorescence yield and depends on the target material. The X-rays are measured with an X-ray detector where the number of measured muon induced X-rays is directly proportional to the muon rate. Therefore, monitoring the muon induced X-ray rate provides a method of monitoring the muon beam intensity continuously in a non-destructive way. In this diploma thesis the opposite was done, in so much as to test the principle, the muon rate derived from the proton signal gives the X-ray rate as a prediction which is then compared to measurements. Note that even if the predictions do not agree with the measurements at the percent-level, once calibrated, this method provides a precise and good muon rate measurement.

12 Chapter 2

Theory of X-ray emission

X-Rays where first discovered by Roentgen in the year 1895 for which he was awarded the first Nobel Prize in 1901. Proton induced X-ray emission (PIXE) has received considerable attention in recent years as a useful method for non-destructive trace element analysis [6]. Knowing the characteristic X-ray emission lines from different elements, PIXE can be used in order to identify the chemical composition of materials and by comparing the intensity of the characteristic X-ray lines the abundance of the different elements can be determined. X-rays may be produced following the excitation of target atoms induced by primary energetic protons. The exited target atoms regain a stable energy state by returning to their original electron configuration. This process can be accompanied by characteristic X-ray emission. Different transitions are possible depending on the primary proton’s ability to either knock out a K,L,M,... shell electron. Fig.2.1 shows an incident proton knocking out a K-shell electron. The excited target atom relaxes (de-excites) to its original electron configuration by producing a K-shell X-ray.

Figure 2.1: Incident proton exiting a target atom followed by the relaxation producing an X-ray.

An initial ionization can also be followed by an ejection of an electron, where the two cases, namely the emission of an Auger electron and the Coster-Kroning transition, are distinguished. Fig.2.2 shows the diﬀerent processes that may follow the ionization of a target atom. a) shows the K-shell ionization of the target atom, b) a following X-ray emission. Instead of emitting an X-ray an electron de-exciting from the L-shell to the K-shell can transfer the diﬀerence of the two energy states to another electron which is then ejected. This ejected electron, shown in Fig.2.2 c), is called an Auger electron. Since this process moves the vacancies to higher shells, it may still be accompanied by X-ray emissions (in this case an L-shell X-ray emission, i.e. an electron de-exciting from a higher shell to the L-shell producing an X-ray). Coster-Kroning transitions are similar processes that take place amongst atomic sub-shells with the same principal quantum numbers. A schematic drawing of a Coster-Kroning transition is shown in Fig.2.2 d).

13 Figure 2.2: a) Ionization of a target atom followed by: b) X-ray emission, c) ejection of an Auger electron, d) Coster-Kroning transition

Fig.2.3 shows a schematic drawing for the labelling of the most frequent X-ray transitions:

Figure 2.3: Labeling of K-, L- and M-shell X-ray transitions (left) [7] and a more detailed graph for Copper X-ray transitions (right) [8].

The parameter that determines the probability for an X-ray emission after an initial ionization is referred to as the ﬂuorescence yield parameter ω. It increases gradually with the atomic number Z for K- as well as for L-shell X-ray emission. Fig.2.4 shows the ﬂuorescence yield parameter ω as a function of the atomic number Z for incoming protons at 500 keV kinetic energy.

14 Figure 2.4: Fluorescence yield parameter ω for K- and L-shell X-ray emission as a function of the atomic number Z for incident protons

The calculation of the ﬂuorescence yield parameter was made with the C++ program ISICS06. In order to perform absolute PIXE measurements, the X-ray emission cross-section, which is connected to the ionization cross-section via the ﬂuorescence yield, has to be known. This can be directly computed via ISICS06.

15 Chapter 3

Comparison of diﬀerent detectors

Before starting the proton/muon induced X-ray fluorescence measurements, various suitability tests were performed on several types of X-ray detectors, namely two different commercial Silicon detectors (XR-100CR and XR-123CR), a NaI(Tl) detector, an APD (Avalanche Photodiode) and a SBD (Surface Barrier Detector). The main criteria studied were the signal to noise ratio, dead time, energy resolution, the detector active area and the detection efficiency for X-ray energies of possible target elements in the range of 5 − 25 keV.

3.1 XR-123CR Si-detector

First X-ray measurements were performed with an Amptek XR-123CR Si-detector, which is very similar to a newly purchased XR-100CR Si-detector (see sec.3.3). The XR-123CR detector is easy to operate since it contains a MCA (which the XR-100CR detector does not) and an USB port to connect the detector directly to a computer. After taking first X-ray spectra of radioactive sources (55F e, 241Am and 109Cd), X-ray fluorescence measurements on Ni, Cu, Ag and T a targets (for the energy of the material specific K- and L-shell X-rays see X-ray lookup chart, fig.2 in the appendix), using an 241Am source to induce the fluorescence X-rays in the target material, were performed. Fig.3.1 shows the experimental setup and the measured spectrum for the X-ray fluorescence measurement of Copper.

Figure 3.1: Left: Experimental setup for the Copper X-ray ﬂuorescence measurement (241Am is used as a source to induce Copper X-rays. The energy calibration is performed with the 55F e), Right: Measured spectrum of Copper. The tabulated Copper X-ray lines of 8.05 keV for the Kα and 8.9 keV for the Kβ are clearly visible.

16 The 241Am source (see ﬁg.3.1 on the left) is completely hidden inside the iron shielding during the measurement in order to ensure that no X-rays from the source can hit the detector directly (only for reasons of clarity the 241Am is not hidden in ﬁg.3.1). The measured energies for the Copper K-shell X-ray lines of 8.054 keV and 8.93 keV agree very well with the tabulated values (see X-ray lookup chart,

ﬁg.2) of 8.05 keV for the Kα and 8.9 keV for the Kβ X-ray line.

3.1.1 Element analysis of a 5SFr coin

As a simple performance test an element analysis on a 5SFr coin was performed. 5 coins were used as a target instead of just one in order to increase the X-ray production rate. Fig.3.2 shows the experimental setup as well as the measured spectrum:

Figure 3.2: Left: Picture of the experimental setup for the 5SFr coin measurement, right: Spectrum of the 5SFr coin (241Am is used as a source and for the energy calibration)

The spectrum contains three signal peaks. The ﬁt of the spectrum is performed using the sum of three gaussian functions and a linear background:

2 x−x 2 x−x2 x−x 2 1 − 2 3 − σ σ − σ fit = c1 + c2x + c3e 1 + c4e 2 + c5e 3 (3.1)

Using the fit function, the three signals are identified as Ni-Kα, Cu-Kα and Cu-Kβ X-ray lines. In order to determine the relative abundance of Nickel and Copper in a 5SFr coin, the area of the gaussian peaks (after subtracting the linear background) has to be compared. Initially a first order approximation was made by assuming equal cross sections for Nickel and Copper K-shell X-ray emission. This results in a relative abundance of 77.8 ± 1% Copper and 22.2 ± 1% Nickel. This result can however be improved. Looking at the spectrum of a pure Nickel target, two closely spaced K-Shell X-ray emission lines (Kα and Kβ) are found. The Nickel spectrum is very similar to the Copper spectrum presented in figure 3.5. As in the case of the Copper spectrum, the Kα-line (at smaller energy) is more intense than the Kβ emission line. Since the Kβ Nickel emission line at 8.26 keV is close to the intense Kα Copper line at 8.05 keV, it is not visible in the spectrum. A fit including a fourth gaussian function does not converge. Therefore the intensity of the Kβ Nickel emission line at 8.26 keV with respect to the Nickel line at 7.48 keV (≈16% Kα and ≈84% Kβ X-ray emissions) is calculated using the spectrum resulting from a pure Nickel target. This amount is then subtracted fom the Copper K-Shell emission line at 8.05 keV and added to the area of the Nickel Kα-line in order to get the total area of the Nickel peaks. This results in a relative aboundance of 74.2 ± 1% Copper and 25.8 ± 1% Nickel, whereas the manufacturer "Swissmint" states that a 5SFr coin consists of 75% Copper and 25% Nickel which is consistent with the measurements.

17 3.2 XR-100CR Si-detector

Fig.3.3 shows a picture of the newly purchased XR-100CR detector, which was used for the remaining measurements (since the XR-123CR Si detector was on-loan for a short period).

Figure 3.3: Left: XR-100CR detector, right: PX2CR power supply/ampliﬁer system. Speciﬁcations: Si-PIN detector, 500 µm thick, 13 mm2 active area, thermal cooling. Energy Resolution for 55F e (5.9 keV): ∆E = 4.5% E FWHM

X-ray spectra from the XR-100CR detector were recorded using a digital oscilloscope by generating a histogram (counts versus integral of the analogue waveform equivalent to charge). Histograms were also generated by taking the amplitude instead of the charge, but the energy resolution was found to be worse in this case. The histogram data was stored in ascii ﬁle for later analysis. Fig.3.4 shows a diagram for the readout of the XR-100CR detector:

Figure 3.4: Diagram of the readout scheme for the XR-100CR detector. X-ray spectra are recorded with the digital oscilloscope and stored as an ascii ﬁle for later analysis, whereas X-ray rate measurements are performed using the ICR-gate and scaler system, see sec.3.2.1.

The characteristics of X-ray spectra recorded with the XR-100CR detector are very similar to those recorded with the XR-123CR detector. Fig.3.5 shows the X-ray fluorescence spectrum for a Copper target using the XR-100CR detector (compare to the measurements using the XR-123CR detector in fig.3.1): The experimental setup is equivalent to that used for the measurements of the Copper fluorescence X- rays with the XR-123CR detector presented in fig.3.1. The Copper target is again irradiated with the 241Am source and the energy calibration is made with the 55F e source with known X-ray lines at 5.9 keV and 6.5 keV (see fig.3.5). The measured Copper X-ray line energies agree with the tabulated values, as well as with the measurements using the other X-ray detector.

18 Figure 3.5: Measurement of the Copper spectrum using 241Am as source for the X-ray ﬂuorescence and 55F e for the energy calibration.

The energy dependence of the energy resolution was also measured using known calibration sources of 55 241 109 F e, Am and Cd, as well as the ﬂuorescence Kα-line of Copper. This allows the prediction of the energy resolution of the detector over a wide range of possible X-ray energies, see ﬁg.3.6.

Figure 3.6: Energy resolution versus X-ray energy of the XR-100CR Si-detector

The measured energy resolution for the 5.9 keV 55F e X-ray line is 4.6%, in good agreement with the value of 4.5% stated by the manufacturer (see caption of fig.3.3). The fit for the energy resolution is performed using the following fit function:

∆E p0 = √ (3.2) E FWHM E + p1 Several ﬁt functions were tested for their ability to reproduce the experimental data. Since the resolution plot is used to predict the resolution for some given energy and not to compare to some theoretical detector model, the type of the ﬁt function is secondary.

3.2.1 Rate measurement with the XR-100CR detector

The XR-100CR detector has three signals available from the ampliﬁer unit: an analogue waveform output, a pile-up gate (PU) and an input count rate signal (ICR). Of the three, two signals were used

19 for the measurement of X-ray ﬂuorescence spectra and X-ray rates. The analogue signal - a triangular shaped linear signal with a 6 µs shaping time and the ICR-signal, a fast low-threshold discriminator logical output signal, set to trigger just above the noise level of the detector. The output pulse-width of the ICR-signal varied depending on the input pulse-height, up to a maximum limit of 2 µs. In order to measure the X-ray rate, the ICR gate was connected to a scaler and the number of counts were compared to the number of histogram entries generated by using the digital oscilloscope. Since a sizable disagreement (more than 50% deviation) was found further tests were performed. A comparison of the discriminated analogue waveform with the direct ICR output of the XR-100CR detector (both rates measured with a scaler) showed that these values agree very well with each other, whereas they do not agree with the number of entries in the histogram. Both ICR and the discriminated analogue signals could therefore be used to measure the correct rates, whereas the spectrum taken with the digital oscilloscope due to dead-time and digitization eﬀects could only be used to determine the spectral composition i.e. the percentage of real signal X-rays in the spectrum (for example Copper Kα / Kβ X-rays), i.e. the fraction:

signal 100% · where noise e.g. could be Bremsstrahlung background (3.3) signal+noise Fig.3.7 shows the three output signals of the XR-100CR Si-detector for an 55F e source placed very close to the detector (i.e. one can check the behavior for high X-ray rates).

Figure 3.7: Screen shot of the digital oscilloscope showing the analogue waveform (blue), the pileup gate (red) and the ICR gate (green, short square pulse for every analogue signal) of the XR-100CR detector.

The 55F e source produces closely spaced K-shell X-rays (5.9 keV and 6.5 keV, see ﬁg.3.5) and therefore the large analogue pulses in ﬁg.3.7 (blue curve), having approximately double the amplitude of the smaller pulses, are actually two X-rays arriving almost at the same time. Using the pileup gate (red) these X-rays are not counted. Looking at the ICR-gate (green) one can see that the internal trigger of the XR-100CR detector works well since these large analogue signals are actually treated as two independent X-rays (two ICR-gates are generated). Therefore if only the X-ray rate is required without any energy information, the ICR-gate signal can simply be counted. In order to calculate the true X-ray rate, pileup pulses must be taken into account. The true X-ray rate

RT is given by the observed X-ray rate RO and the dead time of the detector (i.e. the length τ of the ICR-gate) via:

RO RT = (3.4) 1 − τ · RO

20 A closer look at the length of the ICR-gate clearly shows that it’s length is not constant (see fig.3.7, where the third ICR-gate is significantly longer than the other ones). Since the dead time of the detector is given either by the double-pulse resolution of the discriminator of if larger than the dead-time, the width of the output pulse. In order to measure this shortest possible time difference between the leading edge of two consecutive ICR-gates, a histogram at very high X-ray rate was recorded, where the number of entries as a function of time difference between the leading edges of two consecutive ICR-pulses was measured. A continuous distribution of the time difference with a sharp edge at the minimum time difference is expected. Fig.3.8 shows the measured distribution between consecutive X-rays.

Figure 3.8: Screen shot of the digital oscilloscope showing the time diﬀerence distribution between the leading edge of two consecutive ICR pulses (red) and the ICR signal (blue). The thin red lines correspond to calibration points using a clock at a frequency of 100 kHz, 1 MHz and 100 MHz. The dead time of the XR-100CR detector is given by the leading edge of the histogram at ≈ 1.65 µs.

The spectrum was calibrated with a clock at frequencies of 100 kHz, 1 MHz and 100 MHz (i.e. 10 µs, 1 µs and 10 ns between neighboring pulses see thin red lines in ﬁg.3.8. The clock signal at 100 MHz is in good approximation to the zero value in the histogram. The measured dead-time τ for the XR-100CR detector, given by the half-height of the leading edge of the time diﬀerence distribution is ≈ 1.65 µs this together with the observed rate and eqn.3.4 allows the true X-ray rate to be evaluated. All proton induced X-ray rate measurements undertaken initially used the ICR signal and scaler system.

Alternatively, a multi-channel analyzer (MCA) was also used to measure the particle induced X-ray rate directly. This has the advantage of being able to perform a rate measurement and taking a spectrum at the same time. The rate consistency of the MCA system was also checked against that of the ICR system. Fig.3.9 shows the measured relative X-ray rate for an 55F e source using the MCA, with the source placed at diﬀerent distances to the XR-100CR detector.

21 Figure 3.9: X-ray rate for an 55F e source, placed at diﬀerent distances to the detector, measured with the MCA and compared to the rate measurement with the ICR signal.

The rates in ﬁg.3.9 are pileup corrected. In case of the rate measurement with the ICR signal the true rate is given by eqn.3.4. For the MCA the true rate RT is obtained from the observed RO rate via:

Real-time R = R · (3.5) T O Live-time Within the rate interval 30 Hz-2 kHz (measured with the ICR signal) the two measurements agree. For higher X-ray rates (55F e source close to the detector) the two measurements disagree. This is due to the large pileup using the MCA (see tab.3.1) and cannot be properly corrected by eqn.3.5.

Table 3.1: Comparison of the X-ray rate (55F e source) measured with the MCA and the ICR signal connected to a scaler. The high rate disagreement is due to pileup problems with the MCA whereas the low rate disagreement could be due to multiple triggering of single cosmic muons (several ICR signals are generated for a single cosmic ray).

ICR MCA MCA MCA MCA Percentage: counts counts Real time [s] Live time [s] Pileup MCA of ICR rate 1041402 673628 60.18 29.8 101.9 % 126.9 ± 0.2 % 374427 321900 60.3 47.36 27.3 % 108.3 ± 0.3 % 99072 95541 61.76 57.92 6.6 % 102.6 ± 0.5 % 14917 14821 60.52 59.66 1.4 % 100.7 ± 1.2 % 14749 14553 300.52 298.56 0.7 % 99.3 ± 1.2 % 5432 5157 305.74 304.1 0.5 % 95.4 ± 1.9 % 3379 2733 726.4 723.6 0.4 % 81.2 ± 2.1 %

As shown in ﬁg.3.7 the ICR gate seems to be generated correctly with the internal trigger even for high X-ray rates. However, looking at the analogue and ICR signal on the digital oscilloscope without any source in front of the detector one can see that several ICR gates are generated for single higher energetic cosmic rays (these large analogue signals are therefore treated as many single low energetic X-rays). For very low rates the number of counts measured with the ICR signal is signiﬁcantly higher than the number of incoming particles (for high X-ray rates, the number of cosmic rays is negligible even

22 if they are counted as several X-rays). This eﬀect could be the reason for the disagreement between the two rate measurements for very low rates. In order to be independent of rate eﬀects, X-ray measurements were performed in the rate-region where the two methods gave agreement i.e. 30 Hz − 2 kHz. All measurements after May are performed using the MCA system.

3.3 NaI(Tl) crystal detector

Besides measuring X-rays with the XR-100CR Si detector, measurements using a sodium iodide detector from Saint-Gobain were performed. The advantages of the NaI(Tl) detector compared to the XR-100CR Si detector are the detector’s large active area (1.500 diameter for NaI(Tl) detector and only 13 mm2 active area for the XR-100CR detector) and thickness (1 mm thick NaI(Tl) layer). Especially for X- ray energies above 20 keV the efficiency (absorption probability) of the NaI(Tl) detector is significantly higher than that of the XR-100CR detector (see tab.2 in the appendix). Unfortunately, the energy resolution of the NaI(Tl) detector is worse than that of the XR-100CR detector (compare fig.3.14 to fig.3.6), this however is not of primacy importance since we are not performing trace element analysis. Due to the poorer energy resolution of low X-ray energies as well as the susceptibility to magnetic fields, all measurements with the muon beam were made with the XR-100CR Si detector.

Figure 3.10: Picture of the NaI(Tl) detector including it’s pre-amplifier. Specifications: Saint-Gobain NaI(Tl) X-ray detector 1XM 0.4/1.5B with PA- 12 pre-amplifier. Be-window, optically coupled 1 mm thick NaI(Tl) crystal, mounted on a 1.5” diameter Photomultiplier. Energy resolution for 55F e (5.9 keV): ∆E = 41.9%. E FWHM

The NaI(Tl) detector is operated at +800 V high voltage. The variable gain is changed on the pre- amplifier. The analogue output signal of the pre-amplifier is either monitored directly with the digital oscilloscope or processed with a Timing Filter Amplifier (TFA) to shorten the fall time (see fig.3.15) and therefore reduce pileup. Fig.3.11 shows a schematic drawing of the setup for the NaI(Tl) detector:

Figure 3.11: Schematic drawing of the setup for the NaI(Tl) detector

As in case of the XR-100CR detector, the digital oscilloscope is used as an MCA by generating a histogram of the analogue waveform (counts versus integrated area of the analogue waveform). First

23 measurements were done with an 55F e source. Looking at the value for energy resolution for 55F e (5.9 keV) of 41.9% as stated by the manufacturer (see caption of fig.3.10) it is obvious, that the two X- ray lines at 5.9 keV and 6.5 keV completely overlap and therefore only one peak appears in the spectrum. The measured energy resolution of 42% (see fig.3.14) is in very good agreement with that stated by the manufacurer. Next measurements were performed with an 241Am source (see fig.3.12).

Figure 3.12: Spectrum of 241Am with the NaI(Tl) detector. The two X-ray lines at 13.95 keV and 17.74 keV are not resolvable and therefore only the overlap at 16.2 keV is visible. Besides this peak and the strong 241Am line at 59.54 keV (used for the energy calibration) an escape peak at 27.6 keV appears.

The 241Am spectrum (fig.3.12) looks quite different to that of the XR-100CR detector. First of all the spectrum line intensity is different due to different efficiencies, particularly the 59.5 keV line which is much more intense because of the detector thickness and hence the efficiency is much higher compared to the XR-100CR detector. Moreover, the two X-ray lines at 13.95 keV and 17.74 keV are not resolvable, whereas they are completely separated in case of the XR-100CR detector. A new feature is the so-called "escape peak" of Iodide which can be explained as follows: 241Am 59.54 keV X-rays can knock out a K-shell electron of Iodine. The electron having the energy

Ee =(59.5 keV-Eb), where Eb = 33.2 keV is the binding energy of Iodine, can then stop in the detector and deposit 26.3 keV. While de-exciting to the ground state the Iodine ion releases the binding energy of

33.2 keV predominantly as Kα = 28.6 keV and Kβ = 32.3 keV X-rays. The remaining energy difference is emitted as low energetic L- and M-shell X-rays which are difficult to measure with the NaI(Tl) detector. Therefore if the K-shell X-rays are absorbed within the detector, the full amount of 59.54 keV is deposited whereas if they escape, only 26.3 keV are measured, assuming the low energetic L- and M-shell X-rays are not detected. The measured value of 27.6 keV agrees well with the predicted value of 26.3 keV considering the fact that eventually some of the low energetic L-shell X-rays will also be detected which then increase the value for the theoretical prediction. Simulations and measurements (with a prototype NaI(Tl) detector) for the GLAST detector (Gamma ray large area space telescope) presented at Gamma-Ray Bursts in the Afterglow Era 4th Workshop Rome in Italy [9] show the same characteristics for the 241Am spectrum as the measurements presented in fig.3.12. Such escape peaks are also observed for other elements, see for example [10].

24 Another interesting spectrum taken with the NaI(Tl) detector was that of a lead shielding brick (normally used to shield radioactive sources), which was irradiated with 137Cs (see ﬁg.3.13). The energy calibration is performed using the "zero" of the spectrum (measurement without any source and trigger of the digital oscilloscope on auto trigger) and the tabulated value of 74.96 keV for the P b

Kα X-ray line. The mean energy for the other peaks is determined using gaussian fits. The first peak at 10.56 keV is due to P b L-shell X-rays, whereas the second one at 28.74 keV is probably due to Antimony (Sb), which is used to harden the lead. Similar to the escape peak in the 241Am spectrum in fig.3.12 due to the 241 59.54 keV Am X-rays, there is an escape peak due to the P b Kα X-rays at 45.3 keV.

Figure 3.13: Spectrum of a lead shielding brick which is normally used to shield radioactive sources. The lead brick is irradiated with 137Cs. Besides the P b K- and L- shell X-rays two other peaks are visible. The ﬁrst one is probably due to Sb (Antimony) which is used to harden lead and the other one is probably an escape peak due to the P b Kα X-rays

The tabulated energies for the X-ray lines in the lead spectrum of ﬁg.3.13 are listed in tab.3.2.

Table 3.2: Tabulated X-ray energies for the lead spectrum

X-ray line X-ray energy [keV] P b, Lα 10.55 P b, Lβ 12.61 Sb, Kα 26.36 Sb, Kβ 29.72 Escape from P b Kα 41.72 P b Kα 74.96 P b Kβ 84.92

Since the Sb Kα and Kβ X-ray line completely overlap, a rough theoretical estimation for the mean value of the gaussian peak involving the K-shell X-rays is given by:

meanSb = cKα · EKα + cKβ · EKβ = 0.79 · 26.36 keV + 0.21 · 29.72 keV = 27.1 keV (3.6)

Where EKα (EKβ ) is the X-ray energy for the Kα (Kβ) X-ray line and cKα (cKβ ) is the percentage of Kα X-rays with respect to the total amount of K-shell X-rays. The prediction of 27.1 keV for the Sb

25 X-ray line is in the range of the measured value of 28.74 keV. Therefore this peak probably originates from the Sb content in the lead brick. A similar calculation for the P b L-shell X-rays yields 11.4 keV which is in agreement with the measured value of 10.6 keV. The peak at 45.3 keV is consistent with an escape peak due to the 74.96 keV P b

Kα X-rays knocking out a K-shell electron of Iodine. The theoretical prediction for the escape peak of 41.7 keV (see tab.3.2) is most likely too low since low-energy X-rays might also deposit energy in the NaI(Tl) detector (see discussion about the escape peak in the 241Am spectrum, fig.3.12). The relative abundances of specific X-ray lines are evaluated using a web page of the Berkeley LAB [11], which contains an interactive periodic table with X-ray spectra for most elements. The relative abundance is determined by comparing the peak height for the Kα/Kβ (Lα/Lβ) X-ray lines, also fig.3 and tab.7 in the appendix show the relative abundance of X-rays for some chosen elements.

As in case of the XR-100CR Si detector we are interested to have an energy resolution plot for the NaI(Tl) detector in order to be able to predict the resolution for some given X-ray energy (this is for example useful to predict whether two closely spaced X-ray lines will be resolvable or not). Fig.3.14 displays the relative energy resolution for the NaI(Tl) detector.

Figure 3.14: Energy resolution versus X-ray energy of the NaI(Tl) crystal detector.

The energy resolution in fig.3.14 is measured using the radioactive sources 55F e, 137Cs and 241Am as 137 well as the X-ray fluorescence Kα line (using Cs as source) from the lead shielding brick measurements in fig.3.13. The fit of the energy resolution is performed using the same fit function as in case of the XR-100CR detector, namely:

∆E p0 = √ (3.7) E FWHM E + p1 At the cost of a little energy resolution, the rate capabilities of the detector could be improved by using a TFA (see fig.3.11). A comparison using an 55F e source with/without the TFA is shown in fig.3.15 right and left respectively. The signals have similar rise-times of ≈ 400 ns however, the fall-time of 20 µs is significantly reduced to ≈ 115 ns by using the TFA and substantially reducing any pile-up problems.

26 Figure 3.15: Screen shot of the digital oscilloscope showing the NaI(Tl) output signal (55F e source). The picture on the right shows the NaI(Tl) signal, processed with a TFA (Timing Filter Ampliﬁer). Using a TFA the fall time can be shortened signiﬁcantly (note: in case of the picture on the right, rise and fall time are in reversed order since the signals are negative).

For high X-ray rates some pileup problems with the NaI(Tl) detector (pre-amplifier) are solved by using a TFA. In fig.3.15 (left) pileup pulses are visible which do not occur using the Timing Filter Amplifier.

3.4 Avalanche Photo Diode and Surface Barrier Detector

Suitability tests on two further X-ray detectors namely an Avalanche Photo Diode (130 µm thick Si-layer) and a Silicon Surface Barrier Detector with a large depletion layer (1 mm thick Si-layer) were performed. For both detectors, the signal-to-noise ratio is not suﬃcient to distinguish the low-energy 55F e X-ray line at 5.9 keV from noise. Fig.3.16 shows the X-ray spectrum for an 241Am source (left) and a 109Cd source (right) measured with the APD detector:

Figure 3.16: Left: Spectrum of 241Am calibrated with the pedestal and the 60 keV 241Am X-ray line. The mean value of 21.8 keV does not agree well with the energy of 17.74 keV for the 241Am X-ray line. Right: Spectrum of 109Cd calibrated with the 60 keV 241Am X-ray line from the spectrum on the left (same experimental conditions). The peak at 22.5 keV agrees with the theoretical value (22.98 keV for Kα1 and 23.17 keV for Kβ , see interactive periodic table of the Brookhaven National Laboratory [12]) for the 109Cd X-ray line.

27 In case of the 241Am spectrum in ﬁg.3.16 the 13.95 keV X-rays are probably rejected by the high trigger level and the ﬁrst peak is due to the 17.74 keV 241Am X-rays only.

Besides the low signal-to-noise ratio there was a disturbing noise signal (see ﬁg.3.17) of unknown origin arising randomly from time to time. Therefore the trigger level has be set higher than usual for high statistics measurements (long exposure time).

Figure 3.17: The graph on the left shows the X-ray spectrum for a 109Cd source (active spectrum in the front) and an 241Am source (passive spectrum in the back, measured earlier and reloaded). The graph on the right shows the same X-ray spectrum less than two minutes later, when a disturbing noise signal appears.

Fig.3.17 (left) shows the X-ray spectrum for a 109Cd source measured with the APD detector (at 18:40:19). The analogue signal does not have much noise. The graph on the right shows the same spectrum less than two minutes later (at 18:42:08). The analogue signal shows a large superimposed disturbing noise signal. Even with a high trigger level some of the disturbing signals cause triggers. Because of this problem and the fact that low energetic X-rays (below ≈ 15 keV) can not be separated from the noise, the APD detector in its present form is not suitable for X-ray measurements in the energy range of ≈ 5 − 25 keV (characteristic X-ray energy for possible target foils). Improvements to the signal-to-noise ratio would require cooling the detector.

Before using the SBD detector it had to be made light tight. This was achieved using 20 µm Alu- minum foil mounted on the detector. The transmission through the Al foil (close to 100%) is included in the eﬃciency plot in the appendix (see ﬁg.1), but since the signal-to-noise ratio of the SBD is also low, only X-rays with an energy & 20 keV can be measured. For these X-rays the transmission probability in the detector varies between 40% to 96% up to 100 keV. Fig.3.18 shows the 109Cd spectrum measured with the SBD, the peak at lower energy in the spectrum 109 is very likely due to the Cd Kα1 and Kα2 X-rays (at 22.98 keV and 23.17 keV). Together with the pedestal, an energy calibration was performed and the second peak at 73.2 ± 0.2 keV is probably due to the K- and L-shell electrons at 62.5 keV and 84.2 keV (with probability 41.7% and 44%, see homepage of the Brookhaven National Laboratory) [12]. Taking only the K- and L-shell X-rays into account and using the probabilities mentioned above, the mean value hEi for the second peak is given by:

0.417 · 62.5 keV + 0.44 · 84.2 keV hEi = = 73.6 keV (3.8) 0.417 + 0.44 The prediction agrees with the measurement of 73.2 ± 0.2 keV, assuming that the peak at lower energy 109 is due to Cd Kα X-rays.

28 Figure 3.18: Screen shot of the digital oscilloscope showing the 109Cd spectrum and the analogue signal (note that the energy decreases from the left to the right). The spectrum (on the right) is calibrated with the pedestal and the ﬁrst peak 109 which is attributed to the Cd Kα X-ray line at 23.1 keV.

Since low-energy X-rays such as Copper K-shell or Tantalum L-shell X-rays can not be measured using the APD or the SBD, these two detectors are not used for further X-ray measurements. The NaI(Tl) detector is suitable for our X-ray fluorescence measurements as long as it is not placed in magnetic fields (see discussion in section3.3). Therefore the NaI(Tl) detector is only used for the C-W (Cockcroft-Walton) proton induced X-ray measurements, whereas all muon induced X-ray fluorescence measurements were performed with XR-100CR detector.

29 Chapter 4

Calculation of the X-ray emission rate

In order to find an optimal solution to monitoring the muon beam-rate in the experiment, a suitable radiator-foil material and geometry as well as detector combination must be found. Where as there was virtually no literature found on X-ray fluorescence production by muons, there is a wealth of such material for protons and heavier ions. An attempt was made to calculate the production cross-sections using computer code written for protons and heavier ions, under the assumption that muons are equivalent to light hydrogen ions. An assumption that works well for calculating the energy-loss and range of muons [13] (comparison of calculations from GEANT and SRIM). As a reliability check and a test of the method, the same foil materials chosen to be tested with the muon beam (see chapter 6) were also studied both theoretically and experimentally using protons. The latter using the MEG Cockcroft-Walton proton accelerator (see chapter 5). The calculation of the X-ray rate consists of several steps. First of all the number of X-rays produced within the target material has to be calculated. On one hand this requires knowledge of the energy dependent X-ray emission cross-section σ(E), i.e. the probability for a primary particle to ionize the target atom such that it de-excites to the ground state under emission of the specified X-ray. On the dE dE other hand the total energy loss dx el. + dx nucl. of the incident particles in the target material has to be known. This information enters the X-ray production rate as follows:

N Z Ei σ(E) Γ = Γ ρ A dE (4.1) X i Cu M dE Cu Ef dx tot. (E) where ΓX and Γi denote the X-ray rate and the rate of incoming particles causing the X-ray ﬂuorescence

(muons or protons) respectively and ρCu, MCu are the density and molar mass of the target material (here Copper). Since the X-rays are produced within the target, reabsorption has to be considered. The probability of being reabsorbed depends not only on the depth at which the X-rays are produced but also on the target material. The attenuation due to reabsorption in the target is described by the material speciﬁc, energy dependent mass attenuation coeﬃcient. Since the target can emit multiple

lines of monoenergetic X-rays (in the case of Copper, Kα and Kβ X-rays with an energy of 8.05 keV and 8.9 keV respectively are produced) and the mass attenuation coeﬃcient is energy dependent, the relative X-ray emission rates must be known. Since no theoretical predictions for these were available (ISICS06 calculates the total K-shell X-ray emission cross section), the relative emission rates were determined from experimental data (interactive chart of the Berkeley LAB [11]). The X-ray emission cross-section for the diﬀerent elements (and projectiles) are evaluated with ISICS06 (Inner Shell Ionization Cross Section [14]), a C++ program, which calculates K, L and M sub-shell ionization and X-ray production cross-sections from the PWBA (Plane Wave Born Approximation [15]) and ECPSSR (PWBA with corrections [16]) theories for incident ions. The X-ray emission cross-section for muons is calculated by substituting the hydrogen ion mass with the muon mass. Ionization and emission

30 cross-section calculations using ISICS06, as well as comparisons to experimental data are presented in section4.1. dE The energy dependent energy loss dx (E) for protons and muons in the target material is computed with SRIM 2008 (The Stopping and Range of Ions in Matter [17]). As in case of ISICS06 the program is designed to calculate the energy loss for incident ions so that the energy loss for muons is evaluated by assuming the muon to be a light ion and replacing the hydrogen mass with that of the muon. Simulation results and discussions of the energy loss for protons and muons in matter calculated with SRIM 2008 are presented in section4.2. The mass attenuation coeﬃcients are tabulated on the NIST web page [18] (National Institute of Stan- dards and Technology). The consequences of including attenuation in the target material for the X-ray rate estimation are quite diﬀerent for incident protons and muons as discussed in section4.3.

4.1 Ionization and emission cross-section results using ISICS06

In order to evaluate candidate foils for the particle induced X-ray ﬂuorescence measurements the behavior of the emission cross-section for K- and L-shells as a function of the atomic number Z has to be investigated. The corresponding graphs are shown in Fig.4.1, calculated with ISICS06.

Figure 4.1: Ionization and emission cross-section for 500 keV protons (left) and 3657 keV (≈ 28 MeV/c) muons (right) as a function of the atomic number, calculated with ISICS06

There are however some restrictions on the X-ray energy. In order to have a good signal-to-noise ratio, X-rays should have an energy greater or equal to that of 55F e X-rays. In case of K-shell X-rays this requires an atomic number larger than (Mn) 25 (55F e actually decays into Mn via beta decay and the exited Mn state then de-excites to the ground state by emitting the 5.9 keV and 6.5 keV X-rays) whereas the atomic number has to be larger than 64 (which corresponds to the element Gd) in case L-shell X- rays. M-shell X-rays are of very low energy and are therefore not considered in this work. Note that the X-ray emission cross-section calculations with ISICS06 for M-shell X-rays are not as precise as for K- and L-shell X-rays. The K-shell emission cross-section in Mn for 3657 keV muons is roughly 200 times larger than for 500 keV protons. The proportions are also similar for the L-shell X-ray emission cross-section in Gd. Since the K- and L-shell X-ray energy increases for increasing atomic number, the lower bound for the atomic number of possible target elements due to the X-ray energy restriction is given by 25Mn (K-shell X-rays) and

64Gd (L-shell X-rays). Examining the X-ray emission cross-sections one sees the general trend for both protons and muons that for Z & 40 the K-shell ionization and emission cross-section are comparable, whereas below this limit radiationless transitions dominate, especially at low-Z. In case of L-shell transitions, radiationless

31 transitions dominate for all Z, though again greatest at low-Z. For protons and muons the emission cross-sections generally decrease rapidly with Z, whereas the L- shell emission probability peaks around Z ≈ 21 for protons and reaches a broad above Z ≈ 28 (Ni) for muons. Therefore considering the energy constraints and the form of the emission cross-sections for protons and muons candidate foils for K-shell production should be close to Z = 25 (Mn) whereas for L-shell production a material with Z > 64 (Gd) is needed. Based on practical considerations the following material were examined in detail as target materials: Copper (Z = 29), Molybdenum (Z = 42), Silver (Z = 47) and Tantalum (Z = 73). Fig.4.2 shows the X-ray emission cross-section for incident protons (left) and muons (right) as a function of the projectile energy evaluated with ISICS06:

Figure 4.2: X-ray emission cross section versus energy for incident protons (left) and muons (right) for all target materials used in this work.

σ(E) The X-ray production rate is determined by the fraction dE in the integral of eqn.4.1. On the ( dx )(E) one hand the X-ray emission cross-section σ(E) below ≈ 100 keV rapidly decreases as function of the projectile energy (see fig.4.2) while on the other hand the projectile’s differential range (reciprocal if energy-loss in the integral) also decreases as a function of the projectile energy. Hence the X-ray emis- σ(E) sion cross section, given by the fraction dE quickly falls to zero. The number of X-rays produced ( dx )(E) while the projectile slows down from 100 keV kinetic energy to zero is negligible for all presented X-ray fluorescence measurements (even for the proton induced X-ray fluorescence measurements at 250 keV the production rate below 100 keV kinetic energy compared to the total X-ray production rate is at the level of 1%). A qualitative understanding of X-ray production yields can be obtained by examining fig.4.3, which shows the X-ray emission cross-sections for protons and muons versus the particle velocity β. Also marked are the respective β’s for the proton and muon beams studied here. The ratio between the ionization and emission cross-sections increases dramatically when progressing from K- to L- and to M-shell transitions (in Cu ≈ 2 : 102 : 106). This shows that at least in Copper significant portion of the ionization of the K-shell leads to X-ray emission, rather than the predominance of radiationless transitions from the higher shells.

32 Proton and muon emission cross-section vs beta (K,L and M-shell) Muon emission and ionization cross-section vs beta (K,L and M-shell) 1.E+04 1.E+08 proton M-shell K-shell emission muon M-shell 1.E+07 K-shell ionization proton L-shell 1.E+03 L-shell emission muon L-shell 1.E+06 L-shell ionization proton K-shell M-shell emission muon K-shell 1.E+05 M-shell ionization 1.E+02 1.E+04

1.E+01 1.E+03

1.E+02 1.E+00 1.E+01

Emission cross-section [barn] Emission 1.E+00 1.E-01

Emission / Ionization cross-section [barn] 1.E-01

1.E-02 1.E-02 1.E-03 1.E-02 1.E-01 1.E+00 1.E-02 1.E-01 1.E+00 beta (v/c) beta (v/c)

Figure 4.3: Left: Muon and proton induced X-ray emission cross-section for Copper as a function of beta. Note that the muon induced cross sections are evaluated by substituting the proton mass with that for the muon. Right: Muon induced X-ray emission and ionization cross-sections versus beta.

Since the total X-ray yield is proportional to the integral of ﬁg.4.3, over the respective β-ranges, until the particle is stopped (β = 0), one can clearly understand the expected larger yield for 3657 keV muons

(0 < βµ < 0.256) rather than from 1 MeV protons (0 < βp < 0.046). However, the higher abundance of X-rays in Copper come from the L-shell (87%) for both muons and protons.

In order to check the accuracy of ISICS06 calculations, a comparison of the particle induced X-ray ionization and emission cross-section with experimental data of several papers including diﬀerent projectiles such as protons, 3He-ions and α-particles was performed.

Figure 4.4: Comparison of the calculated proton induced Ni K-shell X-ray ionization cross section using ISICS06 (ECPSSR algorithm) with experimental data (J.Phys.B: At.Mol.Opt.Phys. [19])

Fig.4.4 shows the proton induced K-shell ionization and emission cross-section for Nickel calculated with ISICS06 compared to experimental results published in J.Phys.B: At.Mol.Opt.Phys., Vol.9, No.3 (Proton induced x-ray production in Titanium, Nickel, Copper, Molybdenum and Silver).

33 For low kinetic energies the prediction of the proton induced K-shell ionization cross-section for Ni agrees well with the experimental data presented in [19], whereas the relative deviation ∆σ, given by:

|Exp. − ISICS| ∆σ = (4.2) Exp. increases with kinetic energy and reaches 9.5% for a proton energy of 3 MeV. The values for the measured cross-section, the predicted cross-section and the relative deviation for the Ni target as well as for the other targets (T i, Cu, Mo and Ag) discussed in the paper are listed in tab.7 in the appendix. The calculations with ISICS06 are compared to three additional papers [20][21][22] where α-particle induced K-shell ionization, 3He-ion and proton induced K-shell emission cross-section measurements are presented (see tab.7 and tab.7 in the appendix). An overview of all ISICS06 calculation comparisons to measurements is presented in the following graph:

Comparison of ISICS06 calculations with measurements 18.0 3He Phys.Journ. Vol.25 Nr.7 proton, Phys.Journ. Vol.9 Nr.3 16.0 alpha, Phys.Journ. Vol.14 3153 proton, NIMB 14.0

12.0

10.0

8.0

6.0 Relative deviation %

4.0

2.0

0.0 0 102030405060708090 Atomic number Z

Figure 4.5: Comparison of ISICS06 calculations to experimental data from three diﬀerent |Exp.−ISICS| papers [20][21][19]. The graph shows the relative deviation ∆σ = Exp. as a function of the atomic number.

The relative deviation in ﬁg.4.5 is calculated by taking the average of the individual relative deviations for a whole measuring series (X-ray ionization / emission for one element and diﬀerent projectile energies, see tab.7, tab.7 and tab.7). The total uncertainty ∆ISICS for ISICS06 calculations is estimated from the standard deviation of relative deviations, calculated using eqn.4.3. This approach is rather pessimistic as it assumes no systematic shift of the relative deviations, i.e. the expectation value hISICSi for the deviation of ISICS06 calculations is assumed to be 0%.

s P (∆σ − hISICSi)2 ∆ = i = 6.6% (4.3) ISICS N Since the prediction is significantly worse in case of the K-shell emission cross-section for elements with high atomic number and since such target foils are not used in this work, the comparison with paper [21] (green points in fig.4.5) is not considered in the calculation above (the experimental situation, namely the use of α-particles at high energies at 9 − 155 MeV is also quite different). For all proton and muon induced X-ray rate predictions the uncertainty for the X-ray emission cross- section evaluated with ISICS06 is taken to be 6.6% as calculated in eqn.4.3. Note that for the proton induced K-shell X-ray fluorescence in Sm the last point in the measuring series at 2.5 MeV (tab.8) is not included in the above calculation 1 therefore in conclusion ISICS06 seems to reproduce the experimental

1Sm data point at 2.5 MeV excluded from calculation since the proton energy far exceeds that used in these measurements, as well as deviation attributed to high-energy deviation behaviour which is not well understood

34 results quite well for low proton energy.

Summary of ISICS06 calculation:

• Calculations agree with experimental data to within ≈7%

• The 3657 keV muon induced emission cross-section is roughly 200 times higher than the one for 500 keV protons, so that the total cross-section (integral) will be several orders of magnitude higher.

• The velocity dependence of the emission cross-sections show the qualitative expected X-ray yield for a given material. The cross-sections are totally dependent on particle speed but almost independent of particle type.

4.2 Energy loss calculations with SRIM 2008

Besides the X-ray emission cross-section calculated with ISICS06, the energy loss in the target material for the incident particles (protons or muons) has to be known in order to evaluate the X-ray production rate using eqn.4.1. The energy loss in matter is computed with SRIM 2008 [17], a program designed to calculate the stopping range of ions in matter. Fig.4.6 shows the energy loss of protons (left) and muons (right) in Copper:

Figure 4.6: Energy loss of protons (left) and muons (right) in Copper calculated with SRIM 2008

Since the X-ray production cross-section increases significantly with increasing projectile energy (in the low energy regime, see fig.4.2) only very few X-rays are produced when the projectile slows down below ≈ 100 keV (see discussion in sec.4.1). Therefore a first hint how the projectile’s energy loss in matter influences the X-ray production rate is given by comparing the energy loss of protons and muons at their initial energy. Comparing for example the energy loss of a 1 MeV proton in Copper to that of a muon at ≈ 3500 keV kinetic energy, shows that keV keV the energy loss for muons (≈ 10 µm ) is roughly 15 times lower than that of protons (≈ 150 µm ). Since dE the energy loss dx tot arises in the denominator in the expression for the X-ray production rate (see eqn4.1) the smaller energy loss in the case of incident muons causes a higher X-ray rate compared to protons. For the plot in fig.4.6 a muon momentum of 28 MeV/c was assumed, which corresponds to a kinetic energy of 3657 keV. For the X-ray fluorescence measurements the muon momentum was remeasured to be 27.75 ± 0.26 MeV/c which corresponds to 3583 keV kinetic energy. This small deviation however does not change the ionization and emission cross sections significantly. On the SRIM homepage [17] there are comparisons of SRIM 2006 calculations with experimental data available. It is assumed that the mean error (deviation from experiment) of SRIM 2008 calculations

35 is smaller or equal to that of SRIM 2006 calculations (as there are only comparisons for SRIM 2006 available). The following table shows the mean deviations for SRIM 2006 of the used target elements.

Table 4.1: Comparison of SRIM 2006 calculations with experimental data for the diﬀerent target foil elements Cu, Mo, Ag and T a.

Element Relative error in % Cu 4.0 Mo 3.2 Ag 3.8 Ta 3.7

The error propagation in sec.4.5 considers the uncertainties listed in tab.4.1 for SRIM 2008 calculations.

4.3 Rate calculation including attenuation in the target

In order to evaluate the X-ray production rate, the integral in eqn.4.1 is approximated by a sum, where the integral is split into equal intervals of 1 keV (energy loss of the projectile in the target material). Before summing these partial rates, which correspond to X-rays produced within a certain depth inside the target, attenuation due to reabsorption has to be considered. Assuming that an incident proton hits a target and at the depth l it produces n X-rays while loosing 1 keV kinetic energy and that the number of X-rays propagating in the direction of the detector (placed on the target entry side) is given by nΩ, where Ω is the solid angle. Then since the dimensions of the target are small compared to the distance to the X-ray detector these nΩ X-rays produced at a depth l inside the target have to penetrate the same distance within the target material until they reach the surface and hit the detector (i.e. in this approximation, the nΩ X-rays propagate parallel to each other).

The number nS of X-rays that reach the surface and hit the detector is then given by:

−αlρ nS = nΩ 1 − e (4.4) where α is the mass attenuation coeﬃcient [cm2/g], which is a material constant for a given X-ray energy and ρ is the density [g/cm3]. Mass attenuation coeﬃcients can be accessed on the NIST web page [18].

The attenuation coefficients for all target materials (for the energy of the material specific Kα and Kβ or Lα and Lβ X-rays) used for X-ray rate measurements in this work are also listed in tab.2 in the appendix. Fig.4.7 shows the X-ray production rate for 500 keV protons at a beam rate of 6.25 · 1012 Hz (1 µA) hitting a thick Copper target. The two pictures on the top show the production rate as a function of the residual proton energy (left) and as a function of the residual penetration depth in the Copper target (right). Furthermore, the two plots on the bottom of fig.4.7 show the rate of X-rays reaching the surface (i.e. the number of X-rays that are not reabsorbed). Since the solid angle is later calculated using a separate program it is still set to 4π for these calculations. In other words, the X-ray rate shown in the graphs including attenuation, when multiplied by the real solid angle (in the order of 10−5) give the correct X-ray rate hitting the detector.

36 Figure 4.7: Proton (500 keV, 6 · 1012 Hz) induced K-shell Copper X-ray production rate as a function of the projectile energy (left) and penetration depth (right), with (bottom) and without (top) attenuation in the target.

As previously mentioned, the solid angle is introduced later for the X-ray rate calculation, however an important parameter that is included from the beginning is a factor f, fixing the ratio of the projectile’s current penetration depth and the distance a produced X-ray would have to propagate within the target material in order to reach the surface and hit the X-ray detector (f is a constant for a given measuring setup). For all proton induced X-ray fluorescence measurements with the C-W proton accelerator, a very simple geometry was chosen (see setup in fig.5.3) where the target was mounted at both 45 degrees with respect to the beam axis and the detector window. Using this setup the factor f simply reduces to 1. More generally, the factor f always reduces to 1 if the angle of incidence (proton on the target) equals the angle of reflection (X-ray propagating along the connecting line between the center of the target and the center of the detector active area). A comparison of the X-ray production rate with and without attenuation in fig.4.7, does not show any difference. This is due to the fact, that the stopping range of 500 keV protons in Copper (≈ 3 µm) is very short and therefore nearly all X-rays escape the target material (still assuming all produced X-rays to propagate in direction of the detector). Fig.4.8 shows a similar calculation for a 3583 keV muon beam at a rate of 108 Hz hitting a Copper target (this corresponds to the kinetic energy of muons used in the MEG experiment, whereas the 108 Hz corresponds to the MEG high rate mode). Comparing the X-ray rates in this case, with and without attenuation shows clearly the major role of attenuation within the target. The attenuation in case of muons is important since their energy loss in Copper is smaller (the range of 3583 keV muons in Copper is ≈ 200 µm) which allows them to penetrate deeper inside the target and therefore the produced X-rays have to propagate further until they reach the surface. Thus the muon induced X-ray rate is reduced significantly by attenuation in the case of thick targets.

37 Figure 4.8: Muon (3583 keV, 108 Hz) induced K-shell Copper X-ray production rate as a function of the projectile energy (left) and the penetration depth (right), with (bottom) and without (top) attenuation in the target.

An overview of the output parameters for the proton and muon induced X-ray fluorescence calculations presented in fig.4.7 and fig.4.8 is given in the following table:

12 Table 4.2: Comparison of 500 keV proton (at 6.25 · 10 Hz) induced Copper Kα X-rays to 8 3583 keV muon (at 10 Hz) induced Copper Kα X-rays

range in X-ray rate without X-ray rate with % transmitted beam rate Copper [µm] attenuation [Hz] attenuation [Hz] X-rays proton 6.25 · 1012 Hz 3.1 2.54 · 107 2.48 · 108 93.4% muon 108 Hz 203 6.4 · 107 7.0 · 106 11.0%

Surprisingly the muon induced X-ray production rate is larger than the proton induced X-ray production rate (see tab.4.2) although the proton rate is a factor 6.25 · 104 higher than the muon rate. A rough approximation yields a correct order of magnitude estimation. The particle induced X-ray rate, given by eqn4.1, is approximated by replacing the integral:

Z Ei σ(E) σ(E) dE dE −→ dE ∆E (4.5) Ef dx tot. (E) dx tot. (E) In case of 500 keV very few X-rays are produced once the proton energy falls below 200 keV. The X-

ray emission cross-section for protons, whose energy lies within the interval 200 keV ≤ Ep ≤ 500 keV, hitting a Copper target is of the order of 0.3 barn, see ﬁg.4.2, whereas their energy loss is approximately 170 keV/µm as shown in ﬁg.4.6. Similar considerations for 3500 keV incident muons yield an X-ray emission cross-section of ≈ 500 barn and an energy loss of ≈ 30 keV/µm, where X-rays produced while the muon energy falls below 500 keV are not considered.

38 The muon- to proton induced X-ray rate ratio for equal beam rates is then given by:

σµ(E) ∆E 500barn dE µ keV · 3000keV Γ ( dx ) 30 X,µ ≈ µ ≈ µm = 9.4 · 104 (4.6) σ (E) 0.3barn ΓX,p p · 300keV dE ∆Ep keV 170 µm ( dx )p The normalized muon- to proton induced X-ray rate using the values stated in tab.4.2 yields

7 8 ΓX,µ/Γµ 6.4 · 10 Hz/10 Hz 5 = 7 12 = 1.6 · 10 (4.7) ΓX,p/Γp 2.54 · 10 Hz/6.25 · 10 Hz which agrees with the approximated value stated in eqn.4.6 within an order of magnitude.

Although the conditions are actually better for muon induced X-ray fluorescence compared to protons (higher X-ray emission cross-section and lower energy loss in matter) it is still very challenging to produce a setup with sufficient X-ray yield produced from one of the world’s most intense surface muon beams. The influence of attenuation in the target is given in the last column of tab.4.2, where the percentage of X-rays escaping the entrance face of the target material with respect to X-ray production rate is listed (only 11% of the muon induced X-rays escape the target whereas 93% manage to escape in case of proton induced X-rays).

For the calculations involved in fig.4.7 and fig.4.8 it is assumed that all Copper K-shell X-rays are emitted as Kα X-rays (which is obviously not the case, see for example fig.3.1) having an energy of 8.05 keV. In order to predict the final X-ray rate, this calculation was also made assuming all K-shell

X-rays to be emitted as Kβ X-rays and ﬁnally a weighted sum for the two X-ray rates, according to their relative abundance (see ﬁg.3 in the appendix), was performed in order to evaluate the true X-ray rate. All proton and muon induced X-ray rate predictions in chapter 5 and chapter 6 are calculated according to this method. This model could be further improved by considering the division of Kα into Kα1 and

Kα2 etc.

4.4 Calculation of the solid angle

In order to determine the X-ray rate, the solid angle has to be known. The solid angle depends on the distance d from the target foil to the detector, the angle α between the planes spanned by the target foil and the active area A of the detector. Using this information the solid angle can easily be calculated analytically if the beam profile is point like. However the beam spot profile on the target foils shows an extended gaussian profile distribution with different σy and σz sizes (where y (z) is the horizontal (vertical) direction on the target foil and the x-direction is parallel to the beam axis), the solid angle was computed using a small Monte Carlo simulation. Fig.4.9 shows the output of the simulation for

σy = σz = 10 mm and a distance d = 20 mm from the detector to the foil, where the X-rays are produced. The simulation is shown for 10’000 incident beam particles hitting the foil and producing an X-ray.

39 Figure 4.9: Output of a simulation in order to estimate the solid angle

The distribution at x = 0 shows the gaussian beam profile on the target foil. For the measurements with the C-W proton accelerator 2 mm thick Copper and Tantalum targets of 5 cm diameter were used. The incident protons were completely stopped in this case (the X-rays produced within the target can only escape the target on the same side as the incident protons). For each of the incident particles hitting the Copper target, a random vector, uniformly distributed on a unit sphere is generated. If the random vector intersects the detector (blue circle) the X-ray is counted as being detected and shown as a red point in fig.4.9. In order to calculate the solid angle it is assumed that all X-rays hitting the detector are absorbed, i.e. the detector’s efficiency is introduced later. The solid angle is simply given by the number of counts on the detector and the number of incident protons (muons):

Ω n = hits (4.8) 4π nincident Since the calculation deals with uncorrelated, randomly distributed events, the statistical error ∆Ω of the solid angle due to the simulation is given by: √ ∆Ω n = hits (4.9) 4π nincident

The error in the solid angle calculation can therefore be reduced by increasing the number of incident particles. For realistic calculations ≈ 108 incident particles were used (such a calculation already takes about 5 hours, therefore the choice of the number of incident X-rays is restricted by the performance of the laptop) yielding a statistical error below 1%. The error of the solid angle also depends on additional uncertainties, originating from the parameters σx, σy, d, α and A.

In order to run the Monte Carlo program, σy and σz of the gaussian distributed beam profile have to be known. The beam profile is measured by placing a quartz crystal at the centre of the beam (see fig.5.3), using a pneumatic system which is controlled online. The light produced in the crystal is then monitored by using a webcam and the intensity of the beam is directly proportional to the intensity of the light produced by the crystal. Fig.4.10 shows a snapshot of the beam spot using a webcam:

40 Figure 4.10: left: Snapshot of the beam spot using a webcam, right: the same picture where the intensity is used as z-coordinate (in order to perform a two dimensional gaussian ﬁt

The picture is then loaded with Matlab and the corresponding matrix is stored as an ascii-file which is then processed with ROOT [23] afterwards in order to analyze the beam spot. The σy and σz of the beam spot are evaluated by performing a two dimensional gaussian fit, with a grouping of four neighboring pixels being averaged, before hand, in order to eliminate noise fluctuations.

The beam spot size given as σy and σz in units of pixels must be transformed into units of mm. This calibration is done with the crystal itself (which has a diameter of 46 mm). By setting the gain of the webcam to a very large value, the complete crystal becomes visible (see ﬁg.4.11), but the pixels in the centre of the beam spot are then saturated. Therefore two snapshots under the same conditions have to be done, one for the gaussian ﬁt and one for the calibration.

Figure 4.11: Snapshot of the webcam with large gain, showing the quartz crystal of 46 mm diameter

Since the quartz crystal in fig.4.11 is viewed under an angle of 45◦ it appears as an ellipse. As already mentioned, this picture can only be used for the calibration, since the pixels in the centre of the beam spot are saturated and therefore the gaussian profile shows a plateau which makes it very difficult to perform the gaussian fit. Since the position of the crystal and the webcam do not change during the measurements, the calibration measurement needs only to be done once, whereas a snapshot of the beam spot at low gain must be taken for every measurement as several factors such as the proton energy influence the focus and therefore the beam spot size.

Combining all calculation steps of chapter 4 the measured particle induced X-ray ﬂuorescence rate follows:

Γ = ΓX,A · Ω · TMylar · Edet. (4.10)

Γ denotes the measured X-ray rate, ΓX,A is the X-ray production rate as given in eqn.4.1 but including

41 attenuation as discussed in sec.4.3. The target is mounted inside the evacuated beam line (for proton induced X-ray measurements), which has a 175 µm thick Mylar window (≈ 5 cm diameter, see ﬁg.5.3) allowing the X-rays to escape from the beam-pipe. Some of the X-rays can be absorbed by the Mylar

window which is considered by the Mylar transmission coeﬃcient TMylar given by

−ρMylar ·α·175µm TMylar = e (4.11)

where ρMylar is the density of the Mylar foil and α is the mass attenuation coeﬃcient for the Mylar foil

at a given X-ray energy. Finally Edet. in eqn.4.10 denotes the the detector’s efficiency for a given X-ray energy, which is the product of transmission probability through the entrance window and absorption probability in the active layer of the detector. In case of the muon induced X-ray fluorescence measurements the target is not mounted inside the evacuated beam line and therefore the transmission through Mylar window does not have to be considered. More details on the rate calculation for specific situations are given in the particular chapters (chapter 5 in case of proton induced X-rays and chapter 6 in case of muon induced X-ray fluorescence measurements).

4.5 Error calculation

The main error in the rate prediction originates from the uncertainties of the calculations with ISICS06 σ(E) and SRIM 2008, which means that the error of the expression f = dE has to be evaluated (see eqn.4.1). ( dx ) In order to do so, it is assumed that the uncertainty for ISICS06 and SRIM 2008 is just some fraction cσ(E) (see eqn.4.3) and c dE respectively (see tab.4.1) of the calculated value: ( dx ) σ (E ) dE f = i Set a = σ (E) , ∆a = c · a , b = , ∆b = c · b (4.12) dE a dx b dx s q ∆a2 a · ∆b2 ⇒ ∆f = (∂ f · ∆a)2 + (∂ f · ∆b)2 = + (4.13) a b b b2 Together with eqn.4.12, the error of f in eqn.4.13 becomes:

aq σE q ∆f = c2 + c2 ⇒ ∆f = c2 + c2 (4.14) a b dE σE dE b ( dx ) dx Since the total error of f is simply some percentage of f, the error for the X-ray production rate in eqn.4.1 can be taken out of the integral and written as:

Z Ei q NA σ(E) q ∆Γ = c2 + c2 · Γ ρ dE = c2 + c2 · Γ (4.15) X σE dE i Cu dE σE dE X ( dx ) M ( dx ) Cu Ef dx tot. As explained in sec.4.3 the integral in eqn.4.1 is approximated by a sum, where for all partial rates (individual summands) different attenuations (due to different depth in the target material where the X-rays are being produced) are considered. None the less the error ∆Γ for the measured X-ray rate Γ is given by the fixed percentage

q ∆Γ = c2 + c2 · Γ (4.16) σE dE ( dx ) of the rate. Other parameters such as the density, molar mass and the rate of incident particles occurring in eqn.4.1 as well as the attenuation coefficient for the rate calculation including attenuation and also the Mylar transmission, the detector’s efficiency and the solid angle for the final prediction of the measured rate are subjected to errors. Since the errors for these parameters are small compared to the uncertainties for ISCIS06 (6.9%, see sec.4.1) and SRIM 2008 (see tab.4.1), these errors are neglected for the calculation of the rate prediction (even the statistical error for the solid angle simulation is below 1%).

42 The error for the X-ray rate measurements is given by the statistical error, which is the square root of the number of measured X-rays. In case of the proton induced X-ray measurements with C-W proton accelerator also a systematic error, evaluated via the reproducibility of the 500 keV proton induced K- shell Copper X-ray measurements, is included (see chapter 5). In order to compare measurements and prediction, the measured X-ray rate is plotted as percentage of the prediction (see ﬁg.4.5). The error ∆comp. for the fraction

Γ comp. = 100% · mes. (4.17) Γpred. is evaluated using gaussian error propagation, which yields: v u 2 !2 u ∆Γmes. Γmes. · ∆Γpred. ∆comp. = 100%t + 2 (4.18) Γpred. Γpred.

All errors for the proton and muon induced X-ray ﬂuorescence measurements are calculated following the steps presented in this section.

43 Chapter 5

Measurements with a proton beam

First particle induced X-ray ﬂuorescence measurements were performed with the Cockcroft-Walton proton accelerator to check the reliability of the predictions, which form the basis for predicting the X-ray yield for muon induced X-ray ﬂuorescence. A brief discussion of the C-W is given in the following section:

5.1 Cockcroft-Walton proton accelerator

The C-W accelerator is mainly used to calibrate the MEG liquid Xenon calorimeter. In order to do so, protons of 550 keV are shot onto a Lithium target in form of a LiF crystal. The main reaction used for the calibration is the resonant (p, γ) reaction in Lithium at 440 keV:

7 8 3Li + p −→ 4Be + γ (5.1)

Two gamma lines, a main line at 17.6 MeV used to monitor the energy scale and resolution of the liquid xenon calorimeter, and a broader gamma line at 14.7 MeV are produced. A series of three further γ-lines between 6 − 7 MeV are also formed from the 19F (p, αγ)16O reaction. Fig.5.1 shows a picture of the Cockcroft-Walton proton accelerator:

Figure 5.1: Picture of the Cockcroft-Walton proton accelerator

44 The accelerator is composed of three main parts, the vacuum tank with two internal semi-cylindrical dynode plates connected to a radio frequency (RF ) resonator coil and driver, the high voltage dome and RF ion-source and finally the accelerator columns and voltage multiplier diode-stack with corona rings and resistor chain. The proton source is a glass volume filled with a small amount of hydrogen gas, which is ionized separate via a RF -oscillator which is capacitatively coupled to the glass vessel and hence becomes a plasma, when the source is switched on. The amount of hydrogen is regulated with a thermo-leak system, the RF gas inlet. The RF probe voltage, a potential applied to a metal pin inside the source glass volume, determines the amount of protons injected in the accelerator tube hence it controls the proton current. In order to accelerate protons within the accelerating tube, a high potential, called terminal voltage, is applied between a terminal and the ground. The terminal voltage, applied to a plate close to the source, is stepped down through a resistive chain along the accelerator column in order to achieve a constant field along the proton trajectory. The amount of the first step, called RF extraction voltage, is regulated independently and used to control the beamspot focus.

Figure 5.2: The pictures show the accelerator column surrounded by the so called corona rings. For the picture on the right, some of the corona rings were removed, allowing a view of the ion source. The pink glow is due to ionized hydrogen gas (plasma).

Fig.5.2 shows the accelerator column, surrounded by the corona rings which are linked to resistors and diodes, equivalent to a classical C-W "voltage-doubling stack". The terminal voltage of max. 1 MV is generated via a solid state RF -driver, an oscillator circuit and a parallel fed C-W type multiplier stack. The RF -driver feeds power to the oscillator circuit, which acts as an ampliﬁer. The RF voltage on the dynode plates is capacitatively coupled to the multiplier diode stack via the corona rings, mounted on both sides of the accelerator tube. These diodes act as rectiﬁers to produce the DC terminal voltage.

The accelerating tube and the source are placed inside a tank ﬁlled with SF6 gas at a pressure of 6 bar in order to reduce the risk of discharges.

+ + The extracted proton beam consists of approximately 73% protons, 25% H2 -ions and 2% H3 -ions (see: Field-test of the MEG C-W Accelerator at HV Engineering in Amersfoort [24]). Since ISICS06 and SRIM 2008 are designed to calculate the inner shell ionization cross-section and stopping range in matter for incident ions respectively, these calculations are probably more precise for protons than for muons where the cross-section and stopping range are calculated for a hydrogen ion having the mass of a muon. Fig.5.3 shows the experimental setup for the proton induced X-ray ﬂuorescence measurements:

45 Legend: 1. XR100-CR Detector 2. Mylar window (175µm thickness) 3. Target (Cu/Ta) / Faraday cup 4. Faraday cup 5. Quartz crystal 6. Vacuum connection 7. Beam shutter

Figure 5.3: Experimental setup for the Cockcroft-Walton (C-W) proton induced X-ray measurements

A schematic drawing of the experimental setup for the Cockcroft-Walton (C-W) measurements is given in the appendix, fig.4. The Quartz crystal used to measure the beam profile (see sec.4.4) is moved into the beam via a pneumatic motor. The Faraday cup (see fig.5.3), which is also moved via a pneumatic motor, could be used as an independent current measurement. However, the target / Faraday cup was used to measure the integrated charge on the target and together with the exposure time the proton rate follows (or more precisely the rate of charged particles, since the beam does not only consist of protons [24]). More precisely, the target holding pipe was used as a Faraday cup and the charge from the whole target-piece, which was insulated to act as a charge collection device, was integrated. The Faraday cup works in the following way: + Since the target is irradiated with protons and H2 ions, it becomes positively charged. Eventually protons may knock out electrons via secondary emission, that manage to escape the target. Electrical fields ensure that such electrons are captured by the Faraday cup (an ideal Faraday cup would be infinitely long), otherwise this single proton would cause twice the elementary charge on the target (since minus one elementary charge is carried away by the electron) and lead to a wrong current estimate. An independent method of measuring the proton rate is to use the beam shutter itself, which is also electrically insulated from the rest of the beamline as is the Faraday cup and target, to determine the proton current and hence the number of stopped protons. A rate is determined before and after each measurement. For the prediction of the particle induced X-ray rate, the beam rate estimated with the integrated charge is used whereas the one measured with the beam shutter provides a check.

5.2 X-ray rate calculation / measurement

Fig.5.4 shows a proton induced X-ray spectrum of Copper (left) and Tantalum (right) for 500 keV incident protons. In order to calibrate the X-ray spectra, calibration spectra of the radioactive 55F e source with known X-ray lines at 5.9 keV and 6.5 keV are also recorded for each measurement.

46 Figure 5.4: Proton (500 keV) induced X-ray spectra for 2 mm thick Copper (left) and Tan- talum (right) targets using the XR-100CR detector.

The measured X-ray energies in this case do not so agree well with the tabulated values (≈ 1 − 2% in case of Cu). The agreement is better for spectra recorded with the Multi Channel Analyzer, see for example comparison of proton and muon induced X-ray fluorescence spectra for a thick Copper target show in fig.6.8 in chapter 6. The relative abundance for K-shell X-ray lines is quite different to that for L-shell X-ray lines, see fig.5.4 and compare with the relative abundances given in tab.7 in the appendix. As mentioned, X-ray spectra were also recorded using the NaI(Tl) detector. Because of the low energy resolution of the NaI(Tl) detector (at low X-ray energy), the 55F e and the Copper K-alpha lines almost completely overlap (see fig.5.5), which makes is difficult to calibrate the spectrum.

Figure 5.5: Combined Copper and 55F e spectrum. The energy calibrations is performed with the "zero" of the spectrum and the 55F e K-alpha lines.

However, the Copper and the 55F e spectra were also measured separately under the same experimental conditions allowing to calibrate the Copper spectrum with the independently measured 55F e spectrum. Fig.5.6 shows the Copper spectrum, measured with the NaI(Tl) detector and calibrated with an independently measured 55F e spectrum.

47 Figure 5.6: Copper spectrum, measured with the NaI(Tl) detector. The energy calibration is performed with the "zero" and the 55F e K-alpha lines of the separately measured 55F e (same experimental conditions).

Since the K-shell X-ray lines of 55F e, measured with the NaI(Tl) detector, completely overlap, the expected mean for the K-shell X-ray line is evaluated using a weighted sum. Tab.5.1 shows the X-ray energies and emission probabilities for the 55F e K-shell X-rays:

Table 5.1: 55F e X-ray lines and emission probabilities, see homepage of the Brookhaven National Laboratory) [12].

X-ray line X-ray energy [keV] Emission probability Kα2 5.888 16.2% Kα1 5.899 8.2% Kβ3 6.49 1.89% Kβ1 6.49 0.96%

55 Using the values stated in tab.5.1, the expected mean hE55F ei for the F e K-shell X-rays is given by:

5.888keV · 16.2% + 5.899keV · 8.2% + 6.49keV · 1.89% + 6.49keV · 0.96% hE55 i = = 5.95keV (5.2) F e 16.2% + 8.2% + 1.89% + 0.96%

Since the Copper K-shell X-rays, measured with the NaI(Tl) detector also overlap, a similar calculation for the expected mean hECui is needed, which yields 8.19 keV, where the relative abundance of Copper

Kα and Kβ X-rays is given in tab.7 in the appendix. The measured value of 8.23 ± 0.03 keV agrees very well with the prediction of 8.19 keV.

Fig.5.7 shows a proton induced Copper X-ray spectrum measured for 1 MeV protons at 3.3 · 1012 Hz, which gives an X-ray rate of ≈ 7 kHz.

The two large signal peaks in ﬁg.5.7 are due to the Copper Kα and Kβ X-rays, whereas the third small peak at ≈ 6.4 keV are probably Iron Kα X-rays, induced by Copper X-rays. The large X-ray rate of ≈ 7 kHz causes pileup as shown in the screen shot of the digital oscilloscope (focus on the analogue signal in persistence mode in ﬁg.5.7).

48 Figure 5.7: Screen shot of the digital oscilloscope (left) showing the proton induced Cop- per X-ray spectrum measured with the XR-100CR detector (1 MeV protons at 3.312 Hz ⇒ ≈ 7 kHz X-ray rate).

In order to determine the amount of Copper X-rays, the noise in ﬁg.5.7 (especially occurring at high

X-ray energy) must be subtracted. The number of measured proton induced Copper K-shell X-rays nCu

is determined from the number of measured X-rays i.e. measured counts in the spectrum nmes. by:

nCu = cK · nmes. (5.3)

where cK denotes the proportion of measured K-shell Copper X-rays with respect to the total number of measured X-rays, determined by the spectrum in ﬁg.5.7.

In the case that the rate measurements were taken with the digital oscilloscope the true rate RT is

given by the observed RO rate (number of measured proton induced Copper X-rays nCu divided by the exposure time) and the dead time τ of the detector as in eqn.3.4, whereas for measurements using the

MCA, the true rate RT is determined by nCu and the Live-time:

n R = Cu (5.4) T Live-time

In both cases, the statistical error follows by replacing the number of measured Copper X-rays nCu by √ nCu (see sec.4.5). Moreover, a systematic error was determined from the reproducibility of the 500 keV measurements on 13.05.08. The last 500 keV proton induced X-ray ﬂuorescence measurement performed during the measurement series where the projectile energy was varied (second-to-last measurement performed on 13.05.08, see tab.9) is taken as the central value. The error is given by the standard deviation σ of all 500 keV measurements, divided by the square root of the number N of measurements:

s P 2 P σ (x − xi) xi ∆xcentral = √ , σ = , x = N N − 1 N

where xi denotes the percentage of prediction (see ﬁg.5.8) for an individual measurement at 500 keV proton energy and x denotes the mean value of all 500 keV proton induced X-ray measurements performed on 13.05.08. The systematic error calculated this way is 1.8% and was taken as the systematic uncertainty for all proton induced X-ray ﬂuorescence measurements (not only for the measurements at 500 keV kinetic energy and not only for the XR-100CR detector).

49 As mentioned in sec.4.5 the total measurement error is composed of the statistic and the systematic error: q 2 2 ∆tot = ∆syst. + ∆stat. (5.5) The X-ray production rate due to protons is given by:

ΓX,p = cp (Γp,αcαTM,αEα + Γp,βcβTM,βEβ)Ω (5.6)

+ whereas the one for H2 -Ions is similarly given by: Γ + = c + Γ + cαTM,αEα + Γ + cβTM,βEβ Ω (5.7) X,H2 H2 H2 ,α H2 ,β

+ where cp = 0.745 (c + = 0.255) is the fraction of protons (H -ions) in the proton beam (see: Field-test H2 2 + of the MEG C-W Accelerator at HV Engineering in Amersfoort [24]. Note, the 2% H3 -ion contamination is not considered), cα (cβ) is the amount of α (β) X-rays (for example in case of copper, cα is the yield

of Kα X-rays compared to the total yield of K-shell X-rays), Tα (Tβ) is the transmission probability

through the 175 µm thick Mylar window (see C-W setup in fig.5.3) for the different X-rays, Eα (Eβ) is the detector efficiency (stopping probability, which depends on the X-ray energy as well as the detector material and thickness) and finally Ω is the solid angle.

Γp,α denotes the proton induced Kα (or Lα in the case of Tantalum) X-ray rate, assuming a pure proton

beam and also that all proton induced K-shell X-rays are emitted as Kα X-rays. Similar calculations + are performed for the proton induced Kβ X-ray rate Γp,β and for the H2 ion induced Kα and Kβ X-ray rate (Γ + and Γ + ) respectively. The total amount of induced X-rays is evaluated by a weighted H2 ,α H2 ,β sum according to eqn.5.6 and eqn.5.7. Since the main error contribution is due to ISICS06 and SRIM 2008 computations, these are the only ones considered in order to determine the uncertainty for the X-ray rate prediction. The error ∆Γtot of the expected X-ray rate Γtot = ΓX,p + Γ + is calculated according to the error propagation presented X,H2 in sec.4.5:

q ∆Γ = c2 + c2 · Γ (5.8) tot σE dE tot ( dx ) where 100% · cσE is the percentage error of ISICS06 calculations (see sec.4.1) and 100% · c dE is the one ( dx ) for SRIM 2008 computations (see sec.4.2).

50 5.3 Rate comparison to predictions

Fig.5.8 shows an overview of all proton induced X-ray ﬂuorescence measurements compared to theoretical predictions:

Figure 5.8: Overview of all proton induced X-ray ﬂuorescence measurements. The percentage of the measured rate with respect to the prediction is plotted as a function of the projectile energy. The same overview divided into two plots but including error bars is shown in ﬁg.5 (Appendix).

The Copper X-ray ﬂuorescence measurements on 13.05.08 as well as the Tantalum measurements (with the XR-100CR and the NaI(Tl) detector) agree with the theoretical prediction within the uncertainties. The measured X-ray rate is slightly higher than the prediction. This behavior is also predicted by the X-ray production cross-section measurements of K.L. Streib et al. (Nucl. Instr. and Meth. in Phys. Res. B 249 (2006) 92-94 [25]):

"One can see from the spectral data that the ISICS model can be quite close to experimental cross section data. In the cases where it is not very close, it is within 60% of the experimental value and a conservative estimate, yielding values that are lower than the experimental cross section. Therefore, in the focused ion beam, spectral intensities would be expected to exceed any values predicted by ISICS."

The two data points taken on 13.05.08 at 250 keV and 1 MeV proton energy are somewhat below 100% most likely due to pileup problems in case of incident protons at 1 MeV kinetic energy (see tab.9) and low statistics in case of the 250 keV measurement, which is close to the "threshold" for proton induced X-ray fluorescence in Copper (below 250 keV kinetic energy, the X-ray emission cross section rapidly decreases, (see fig.4.2)). An anomaly in the Copper measurements is seen after the first series of measurements on 13.05.08. This was confirmed by two different detector systems, the XR-100CR and the NaI(Tl) detector as well as being a reproducible effect 1 month later during the measurement series between 10.06.08-12.06.08. Other systematic checks show the reliability of the beam current measurements, thus pointing to the target itself as a possible cause.

51 As shown in fig.5.8 the proton induced X-ray rate for the Copper target is approximately a factor three lower than the prediction for all measurements after this date. Since the proton rate (more precisely the + rate of charged particles since there is a H2 contamination of approximately ≈ 25%), determined via the integrated charge on the target, is checked with the independent current measurement from the beam shutter, the rate measurement is believed to be correct. Furthermore the X-ray rate is also measured with the NaI(Tl) detector in order to check the performance of the XR-100CR Si detector. These two X-ray rate measurements are consistent hence the XR-100CR is believed to operate correctly. Since everything except the target itself is changed for these independent measurements, the disagreement could originate from the target. As shown in fig,.5.8 the low X-ray rate for the Copper target (on 14.05.08) is consistent with measurements perfomed one month later (on 10.06.08, 11.06.08 and 12.06.08). Therefore it is likely that something happened to the Copper target during the first irradiation. Fig.5.9 shows the Copper target, where the dark spot is due to radiation damage / beam interaction:

Figure 5.9: The copper target showing the radiation damage / beam interaction (dark spot)

It is not known what exactly causes the radiation damage shown in fig.5.9. Three possible effects that could change the properties of the target material are listed below: • Chemical reactions: Since the Copper target does not consist of highly purified Copper, contam- inations by other metals remain. Furthermore the pressure in the beamline is ≈ 10−6 bar, which means that there is still some air (nitrogen and oxygen) left which could react with Copper or its contaminants.

• Vacancies. Due to the irradiation with protons vacancies are produced (lattice defects caused by dislocation of atoms), as shown in ﬁg.5.10. The inﬂuence of vacancies on the X-ray production rate and also whether the vacancies could cause such a dark spot on the Copper target, is not known.

• Nuclear reactions: In principle, nuclear reactions in the target material can be induced by proton bombardment. However the proton energy does not exceed 1 MeV which is to small for nuclear reactions to be induced, it is unlikely that the radiation damage shown in ﬁg.5.9 is due to proton induced nuclear reactions. A damage simulation (number of produced vacancies per angstrom and proton) for incident protons at 500 keV (1 MeV) hitting a Copper target were performed with SRIM 2008 and are presented in ﬁg.5.10. Note that damage simulations with SRIM 2008 do not consider vacancies produced by earlier protons, i.e. the damage calculations assume the same conditions for every incident proton, therefore it is not possible to check with SRIM 2008 whether vacancies produced in Copper change the energy loss for protons. The number of produced vacancies increases with increasing penetration depth and reaches a maximum at the so called Bragg peak where the protons stop (the mean value for the depth of the Bragg peak determines the proton range). The position (depth) of the Bragg peak or equivalently the proton range is energy dependent and increases with increasing kinetic energy.

52 Figure 5.10: Radiation damage simulation with SRIM 2008. The pictures show the number of vacancies created in Copper per angstrom and proton as a function of the penetration depth for 500 keV protons (left) and 1 MeV protons (right). The simulation is generated using 99999 incident protons.

Irradiating a Copper target with 500 keV protons produces vacancies within a thin surface layer of ≈ 3 µm. Further protons at 500 keV kinetic energy only penetrate damaged material whereas protons at 1 MeV kinetic energy, once they penetrate beyond the range of 500 keV protons, lose their energy within undamaged Copper. Therefore, assuming the radiation damage to reduce the induced X-ray rate, higher X-ray rates (compared to predictions) are expected for higher proton energies in a given series, as performed (since the fraction of penetrated undamaged Copper increases). Such a behavior is observed (see fig.5.8) for the proton induced Copper X-ray measurements on 13.05.08 and 14.05.08. In order to check the influence of radiation damage, a comparison of measurement and prediction as a function of the integrated charge on the Copper target (which is equivalent to the exposure time) at a fixed proton energy of 500 keV is performed. In case of radiation damage, the measured X-ray rate in terms of the prediction is expected to decrease as a function of the integrated charge. The corresponding graph is shown in fig.5.11:

Figure 5.11: Measured proton induced Copper X-ray rate in terms of the predicted rate as a function of the integrated charge for a ﬁxed proton energy of 500 keV

After performing a ﬁrst X-ray rate measurement using 500 keV incident protons, the Copper target was

53 irradiated with the proton beam for approximately 10 minutes after which another X-ray spectrum was taken. The irradiation time between following X-ray rate measurements was gradually increased. As shown in fig.5.11 the percentage of the predicted X-ray rate increases as function of the integrated charge, whereas in case of radiation damage, the opposite behavior is expected. The observed behavior however could be due to annealing effects (recovering) which take place at high temperatures [26]. Since the Copper target is continuously irradiated in order to produce the measuring series presented in fig.5.11, the target is expected to heat up which could lead to annealing. For all other X-ray measurements, the situation is different. There the beam shutter is closed after each measurement and therefore the target is expected to cool down between measurements and therefore such an annealing effect is not expected, at least not to this extent. Although the effect of radiation damage does not appear in the measuring series in fig.5.11 the decrease in the proton induced Copper X-ray rate (after 13.05.08) is believed to originate from some change of the material properties produced by the first irradiation on 13.05.08. The Tantalum target also shows radiation damage but not to the same extent as the Copper target. None of the targets used for the muon induced X-ray fluorescence show any optical sign of radiation damage which is probably due to the fact that the muon mass is smaller than the proton mass. + As mentioned in sec.5.2 a contamination of ≈ 25% H2 ions in the proton beam is considered in order to compute the theoretical X-ray rate. The X-ray emission cross-section, as well as the energy loss in + + the target material, is calculated for incident H2 ions, i.e. it is assumed that the H2 ions do not break + up in the target material, which is not obvious. In case the 500 keV H2 -ions do break up in the target material, they should be replaced by two independent protons of 250 keV kinetic energy (the low energy + electron is negligible) in order to calculate the H2 ion induced X-ray rate. Tab.5.2 shows the measured X-ray rate as percentage of the prediction assuming a pure proton beam (last column) and assuming a + contamination of H2 ions (second-to-last column) for some chosen measurements.

Table 5.2: Comparison of the proton induced X-ray production rate measurements with + predictions. In the second-to-last column the prediction includes a H2 contamination of 25.5% whereas in the last column a pure proton beam is assumed.

Detector Proton energy Percentage of prediction Percentage of prediction + Target type Date [keV] including H2 ions assuming a pure p-beam Cu XR100CR 13.05.2008 1000 96.5 ± 8.0 73.9 ± 6.0 Cu XR100CR 13.05.2008 900 114.8 ± 9.5 87.8 ± 7.1 Cu XR100CR 13.05.2008 800 114.0 ± 9.4 87.1 ± 7.1 Cu XR100CR 13.05.2008 700 113.4 ± 9.4 86.5 ± 7.0 Cu XR100CR 13.05.2008 600 111.4 ± 9.2 85.0 ± 6.9 Cu XR100CR 13.05.2008 500 108.0 ± 9.0 82.3 ± 6.7 Cu XR100CR 13.05.2008 250 94.5 ± 9.1 71.7 ± 6.4 Cu XR100CR 14.05.2008 700 38.4 ± 3.1 29.3 ± 2.3 Cu NaI(Tl) 14.05.2008 700 29.0 ± 2.3 22.2 ± 1.8 Ta XR100CR 15.05.2008 700 110.7 ± 9.0 85.0 ± 6.8 Ta NaI(Tl) 15.05.2008 700 107.1 ± 8.7 82.2 ± 6.6

+ Since the H2 -ion induced X-ray rate is signiﬁcantly smaller than the proton induced X-ray rate, including + H2 -ions gives an X-ray rate close to the one for a pure proton beam having only 75% intensity (i.e. the + amount of H2 ion induced X-rays is negligible with respect to the proton induced X-ray rate). In conclusion, apart from the anomalous thick Copper target behaviour post 13.05.08, the measurements are in general agreement with predictions, using two very diﬀerent detector systems. The reproducibility of results was also demonstrated as were the reliability of various sources of systematic uncertainty. Hence the predictions can be used as a basis for the muon X-ray yield measurements.

54 Chapter 6

Measurements with a muon beam

6.1 Pion production

Muons are produced by an extremely intense proton beam (. 2 mA, 590 MeV [27]) hitting a rotating graphite target (radiation cooling). The incident protons interact with target nucleons to predominantly form delta resonances, which decay into pions and subsequently the charged pions decay into muons. A resonance structure seen in the inelastic πN- and NN-scattering is associated with the ∆(1232) resonance production at 1232 MeV centre-of-mass energy. The ∆(1232) resonance occurs in a multiplet of 4 states. Using the notation |I,Mi, where I denotes the total and M denotes the third component of the isospin which is an addiditive quantity, the ∆ states are given by:

++ 3 3 + 3 1 0 3 1 − 3 3 ∆ = , ∆ = , ∆ = , − ∆ = , − (6.1) 2 2 2 2 2 2 2 2

Above a threshold energy of ≈ 300 MeV, single pion production dominates. The cross-sections show a

broad maximum at a proton kinetic energy of Tp ≈ 1 GeV, hence meson factories operate in the energy range of 0.5 − 0.8 GeV (PSI: 590 MeV, LAMPF: 800 MeV, TRUIMF: 500 MeV). Above the proton threshold energy of ≈ 600 MeV, 2-pion production can occur, however, the cross-sections are smaller than for single pion production within the energy range of 0.5 − 0.8 MeV. The following 2- and 3-body ﬁnal state reactions are open to incident protons to produce pions. The three body ﬁnal states are typically peaked around 200 MeV for incident proton energies of 600 MeV, whereas the 2-body reaction produces monenergetic π+ of 300 MeV in the forward direction:

Table 6.1: Incident protons interact with target nucleons to form delta resonances. Due to conservation of charge only three out of the four delta states can be produced.

pp −→ ∆+p pp −→ ∆++n pn −→ ∆+n pn −→ ∆0p pp −→ dπ+

Considering the pp- and pn-interactions mentioned above, one expects approximately a 4:1 ratio for π+ to π−.

55 Table 6.2: Decay channels for the delta resonances.

∆++ −→ pπ+ ∆+ −→ pπ0 nπ+ ∆0 −→ pπ− nπ0

6.2 Pion-decay / Muon production

Two main types of muons are produced from the pions in pp- and pn-interactions, namely "surface" / "sub-surface" muons and "cloud" muons, depending on whether the muons originate from pion-decay at rest or from pion-decay in ﬂight.

6.2.1 "Surface" / "Sub-surface" muons

As the name suggests "surface" muons are produced at the surface of the target while "sub-surface" muons are produced further below the surface. Both types originate from stopped pion-decay, hence the muon momentum Pµ and kinetic energy Tµ are well deﬁned since one has a 2-body decay at rest:

+ + π −→ µ + νµ where Pµ = 29.79MeV/c and Tµ = 4.12MeV (6.2)

Since the stop-density of pions is highest on the entrance face of the target, this is also the most intense source of "surface" and "sub-surface" muons. The momenta for these two muon types are as follows:

• Surface muons: Pµ = (27.79 − ∆P ) MeV/c, where ∆P is the momentum-byte of the channel. In

case of the standard rate settings for MEG, the muon momentum (±3σ) is Pµ = (27.8±0.9) MeV/c.

• Sub-surface muons: The muon momentum is in the range of 10 MeV/c ≤ Pµ ≤ 28 MeV/c.

Theory assumes the muon rate dependence to drop-oﬀ with P −3.5 below the kinematic edge at 29.79 MeV/c. Fig.6.1 shows the measured momentum spectrum for the MEG beam including a ﬁt to the theoretical prediction (red line):

Figure 6.1: MEG beam momentum spectrum. Points are measured rate with the whole beam line tuned to that momentum. The red line is a ﬁt to the data. Theory assumes a P −3.5 dependence below the kinematic edge plus a constant "cloud" muon contribution (see subsec.6.2.2), folded with a Gaussian resolution function for the momentum-byte.

56 6.2.2 "Cloud" Muons

The so-called "cloud" muons originate from a diffuse source around the production target due to pion decay-in-flight. "Cloud" muons are less intense than "surface" muons (see rate drop below the kinematic edge in fig.6.1), but show a broad energy spectrum due to the broad energy spectrum of the parent pions and the kinematics of decay-in-flight. Some of the cloud muons fall within the acceptance of the muon channel, which is set to transmit muons of momentum P0 − ∆P/2 to P0 + ∆P/2, where P0 and ∆P are the central momentum and the full momentum byte of the channel respectively. "Cloud" muons that are transmitted along the channel stem from pions with two distinct energies namely forward and backward going muons in the rest frame of the pion. The pion decay is a weak two body decay and therefore parity violating. The neutrino helicity is negative i.e. spin and momentum are antiparallel and the pion has zero spin. Therefore in order to conserve both momentum and angular momentum the muon must also have it’s spin antiparallel to it’s momentum vector, hence the muon is 100% spin polarized at production, whereas "forward" ("backward") decays have their spin antiparallel (parallel) to the momentum. Unlike "surface" muons, "cloud" muons can have either charge-sign, since their parent pions are not captured before decaying.

6.3 MEG muon beam line

The initial beam components, "surface / sub-surface" muons, "cloud" muons as well as positrons originating from π0 decay into two photons within the target and subsequent electron-positron production, are selected, according to their momenta, ﬁrst. The selection is made by the bending magnet AHSW 41, which is located in the proton beam close to target E, see ﬁg.6.2.

Figure 6.2: Schematic drawing of the secondary beam lines available at PSI and a zoom of the πE5 beamline showing the "Z"- and "U"-branch, bending (dipole) magnets (blue), focusing quadrupole magnets (red) and higher order correction sextupole magnets (yellow). Beam deﬁning slits are shown in green.

57 The MEG experiment is situated at the πE5 beam line which is a low energy (10 − 120 MeV/c) pion and muon beam line viewing the 4 cm thick rotating graphite target E (truncated-cone shaped) at 165◦ (backward channel) with respect to the primary proton beam. Fig.6.2 shows the secondary beam lines available at PSI as well as the πE5 channel. Tab.6.3 shows the characteristic properties of the πE5 beam line:

Table 6.3: Characteristic properties of the πE5 beam line

Length 10.4 m Solid angle 150 msr Momentum acceptance (FWHM) 10% Momentum resolution (FWHM) 2% Spot size 15 mm horizontal 20 mm vertical Angular divergence (FWHM) 450 mrd horizontal 120 mrd vertical e+/µ+ ratio at 28 MeV/c ≈ 6.75

The MEG part of the beam line couples to the "Z"-channel magnet ASC41 with a quadrupole triplet magnet combination QSK41-43. In addition to the πE5 magnets, 10 normal conducting magnets and a superconducting beam transport solenoid (BTS) allow for optimal transmission. Fig.6.3 shows the MEG beamline.

Figure 6.3: Schematic drawing of the MEG muon beam line showing the triplet magnets, the separator, collimator system, the superconducting beam transport solenoid BTS with degrader system and the COBRA spectrometer with the polyethylene target where the muons are stopped also shown is the insertion system, allows to connect the C-W proton beamline to connect to COBRA in order to undertake calibrations.

Triplet I, consisting of 3 quadrupole magnets, acts as an extraction device and allows for optimal transmission through the crossed-field separator (WIEN-filter), which has a vertical electric field generated by a potential difference of ≈ 200 kV over a gap of 19 cm. Muons and positrons are deflected by the electric

field where the deflection power is inversely proportional to the particle velocity and since βµ ≈ 0.26 and βe . 1, muons are deflected more.

58 A magnetic field at 90o to the electric field produces an inverse deflection such that muons pass the

separator unperturbated whereas positrons are dumped into a 11X0 thick Pb-collimator. Triplett II in fig.6.3 focuses the separated positron and muon beams at the collimator system into two beam spots spatially separated by ≈ 12 cm (close to 8σ separation), see fig.6.4. The separator is also efficient in removing Michel positrons due to muon decay-in-flight along the beamline.

Figure 6.4: Separation quality of positrons and muons at the collimator. At constant HV the magnetic ﬁeld is varied allowing to scan the beam across a "pill" scintillator. The peak on the left shows the positrons and that on the right the muons.

It is also possible to change the settings of the separator in a way that instead of a muon beam, a pure positron beam results. This allows one to check whether positron induced X-rays have to be considered for the prediction of the muon induced X-ray rate (in thick target foils muons are stopped and decay into positrons). After the collimator system, the clean muon beam is focused at the centre of a superconducting beam transport solenoid magnet BTS. With a degrader system at this position, the momentum is reduced to match the range-straggling of the beam to the 200 µm thick polyethylene target placed under an angle of 20o to the incoming beam, at the centre of the superconducting COBRA spectrometer magnet. Fig.6.3 also shows the insertion system connecting the C-W proton accelerator beamline to COBRA. As mentioned in chapter 5 the C-W accelerator is predominantly used to calibrate the liquid Xenon calorimeter. The special gradient magnetic field of COBRA yields a final round beam-spot of size σ ≈ 10 mm with a maximum muon rate of ≈ 1.36 · 108 Hz reaching the polyethylene target for a proton current of 2 mA. By the time, the muons reach the target, some of them have already decayed and produced a diffuse source of Michel positrons. The survival probability (SP ) over the 22.1 m from the target station to the centre of COBRA for a 27.8 MeV/c muon is given by the relativistic relationship:

N − ∆L SP = = e βγL0 (6.3) N0

where ∆L is the ﬂight distance and L0 = cτ0 denotes the decay length at rest, which is 658.654 m for muons. Using eqn.6.3, a survival probability of 88% results, i.e. 12% of surface muons decay over the whole length of the channel.

6.4 Muon induced X-ray rate measurements

The experimental setup for the muon induced X-ray fluorescence measurements is shown in fig.6.5. The target foils are placed right in front of the superconducting beam transport solenoid (BTS), see fig.6.3. In the case of protons only thick Copper and Tantalum targets, mounted at 45 degrees with respect to the beamline were used, whereas for muon induced X-ray fluorescence rate measurements also thin foils of Copper, Tantalum, Silver and Molybdenum, mounted perpendicular to the beamline (see fig.6.5), were

59 used. This allows a beam transmission type of setup to be studied, a prerequisite for the implementation of such a beam monitoring system. Also, with thin foils (thickness much less than the particle range) the relative influence of fluorescent X-ray production from positrons can be studied. Since Michel decay positrons are predominantly produced from muons stopping in thick targets (thickness greater than particle range) where as only decay-in-flight positrons form a diffuse source inside the vacuum system can produce fluorescent X-rays.

Figure 6.5: Experimental setup for the measurements using the muon beam. Incident muons from the left hit the target foil (here: 5 cm · 5 cm copper foil of thickness 25 µm) and induce ﬂuorescence X-rays.

In order to determine the beam spot size, the beam at the position of the target foil (in front of BTS) is scanned. A rough scan is performed in order to determine the centre of the beamspot (close to the beam axis). This allows a precise scan in the horizontal and vertical direction to be made in order to evaluate the sigmas. Fig.6.6 shows a horizontal and vertical scan of the muon beam at the positron for muon induced X-ray ﬂuorescence measurements:

Figure 6.6: Horizontal and vertical scan of the muon beam at the position for muon induced X-ray ﬂuorescence measurements

60 The beam spot size has to be known for two reasons. First of all in order to determine the solid angle and secondly because some of the targets are smaller than the beam spot size. Therefore, using the measured beam spot size, the number of muons hitting the target foil can be evaluated.

The muon induced X-ray rate calculation is similar to the one for proton induced X-rays. The measured X-ray rate must be corrected for pileup and noise, similar to the calculations presented in chapter 5. One major diﬀerence is the noise, which is signiﬁcantly higher in case of incident muons (this could be due to Bremsstrahlung originating from positrons which are dumped in a Pb collimator or from positrons interacting in the surrounding material as well as the target). Fig.6.7 shows the muon induced X-ray spectrum for a thick Silver target:

Muon induced X-ray fluorescence spectrum for a Ag target Muon induced X-ray fluorescence spectrum for a Ag target 1.E+05 55Fe 400 muon induced Ag Lα,β 2.21keV 1.E+04

300

1.E+03

200 Counts Counts Ag Kα 22.4keV 1.E+02

100 Fe Kα 6.36keV 1.E+01 Ni Kα 7.49keV Ag Kβ 25.3keV

0 1.E+00 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 X-ray energy [keV] X-ray energy [keV]

Figure 6.7: Muon induced X-ray spectrum for a 2 mm thick Silver target, calibrated with the K-shell X-ray lines of the radioactive 55F e source. The picture on the right shows the full rage of the spectrum where is a large overﬂow (due to Bremsstrahlung), orders of magnitude larger than the signal peaks, is observed.

The energy calibration for the Silver spectrum presented in ﬁg.6.7 is performed using the calibration spectrum of the radioactive 55F e source. The ﬁrst, large peak is most probably due to Ag L-shell X-rays although the energy does not agree well with the theoretical value of 2.98 keV for Lα and 3.15 keV for

Lβ X-rays (see X-ray lookup chart in ﬁg.2). The second and third peak are probably Fe Kα and Ni Kα

X-rays respectively. The measured X-ray energies of 22.4 keV for the Ag Kα and 25.3 keV for the Ag

Kβ X-rays agree with the tabulated values of 22.16 keV and 24.94 keV respectively. Besides the large overflow the whole spectrum shows a continuous level of "noise" which is not observed for the proton induced X-ray fluorescence measurements. The percentage of signal X-rays with respect to "noise" is above 70% for all proton induced X-ray measurements and approximately 98% for the Copper target (measured with the XR-100CR detector). For the muon induced X-ray fluorescence measurements the percentage of signal X-rays is only in the order of 3% (this could cause problems because even for a small signal rate, the total amount of measured X-rays is large which leads to pileup). A direct comparison of proton- and muon induced X-ray fluorescence spectra for a thick Copper target is given in fig.6.8. Although the proton induced Cu K-shell X-ray rate in fig.6.8 ≈ 130 Hz is larger than the muon induced X-ray rate of ≈ 50 Hz, the latter shows significantly more noise and additionally a large overflow is observed. An overview of muon induced X-ray fluorescence spectra for thin foils is given in fig.6 in the appendix.

61 Comparison of p- and µ−induced X-ray spectrum for a thick copper target 1.E+05 Proton induced muon induced 55Fe Kα 55Fe calibration 1.E+04

55Fe Kβ Cu Kα 1.E+03

Counts Cu Kβ 1.E+02

1.E+01

1.E+00 0 5 10 15 20 25 X-ray energy [keV]

Figure 6.8: Proton- and muon induced X-ray fluorescence spectra for a 2 mm thick Copper target, calibrated with the 55F e K-shell X-ray lines. The muon induced X-ray spectrum shows significantly more noise than the proton induced spectrum and also a large overflow is observed. The rate of K-shell X-rays compared to the total X-ray rate is 99.3% in case of the proton induced and 5.2% in case of the muon induced X-ray fluorescence spectrum.

In order to study the influence of positrons, a positron induced X-ray fluorescence spectrum for all targets was also taken, using a pure positron beam (by changing the settings of the separator such that positrons pass and muons are dumped). The positron induced X-ray spectra typically show less noise (approximately a factor of two). In the case of the X-ray fluorescence spectra for a 50 µm thick Molybdenum foil, shown in fig.6.9, the signal X-ray rate (Mo K-shell X-rays) compared to the total X-ray rate is roughly a factor 10 higher in case of incident positrons.

Comparison of µ+- and e+−induced X-ray spectrum for a 50µm thick Mo foil 1.E+05 positron induced muon induced 55Fe Kα 55Fe calibration 1.E+04

55Fe Kβ

1.E+03 Mo Kα

Counts Mo Kβ 1.E+02

1.E+01

1.E+00 0 5 10 15 20 25 X-ray energy [keV]

Figure 6.9: Muon- and positron induced X-ray fluorescence spectra for a 50 µm thick Molyb- denum foil, calibrated with the 55F e K-shell X-ray lines. The positron induced X-ray spectrum shows significantly less noise than that for muons. The rate of K-shell X-rays compared to the total X-ray rate is 16% in case of the positron induced and 1.4% in case of the muon induced X-ray fluorescence spectrum.

62 Also no visible diﬀerence in X-ray spectra produced from thick or thin targets of the same material was seen, apart from the absolute rate. The statistical error for the measured X-ray rate is also calculated in a similar fashion to the case of incident protons (see sec.5.2). Since no reproducibility measurements were performed for incident muons, a systematic error is not included. The prediction for the muon induced X-ray rate is again similar to the prediction in eqn.5.6 for incident protons, except that there is no Mylar window in case of the muon measurements. Another diﬀerence is

the beam spot size. When it comes to muons, the beam spot (σhoriz. = 20.5 mm, σvert. = 14.4 mm) is larger than some of the targets hence the fact, that only part of the muon beam hits the target, has to be considered. For example the round (diam.= 49.5 mm), 2 mm thick Tantalum target, used for proton induced as well as for muon induced X-ray fluorescence measurements, is hit by 52% of the muon beam if it is mounted at the centre of the beam and at 45 degrees with respect to the beam axis. Since the proton beam is well focused all protons will hit the target, see for example the radiation damage shown in fig.5.9, which completely fits on the target area. Note that the target is mounted at 45 degrees with respect to the beam axis therefore a circular beam profile would be seen as an ellipse. Tab.6.4 shows the measured X-ray rate in terms of the predicted rate, considering only muon induced X-rays:

Table 6.4: Comparison of the measured muon induced X-ray rate with theoretical predictions

Target Target Percentage of prediction element thickn. considering only muons Cu 2 mm 256.2 ± 20.8 Cu 2 mm 255.9 ± 20.8 Ta 2 mm 192.5 ± 15.5 Ta 2 mm 163.4 ± 13.4 Ag 1 mm 226.5 ± 18.3 Cu 0.1 mm 137.6 ± 11.1 Cu 25 µm 92.9 ± 7.5 Ta 4 µm 126.4 ± 10.2 Mo 50 µm 67.6 ± 5.3

As shown in tab.6.4 the measured X-ray rate far exceeds the predicted rate, especially for thick targets. Three possible effects that could change the predicted X-ray rate are examined, namely: • Momentum window: In case of the proton induced X-ray fluorescence, the protons are accelerated in a potential difference of 106 V (for 1 MeV protons), yielding a monoenergetic proton beam, which is not the case for the muon beam having a momentum window (3σ) of 27.75 ± 0.9 MeV/c.

• As explained in sec.4.5 it is assumed, that the variable f, ﬁxing the ratio of penetrated distance of the projectile within the target until an X-ray is produced and the distance the X-ray has to propagate within the target in order to reach the surface, is a constant. This is only true for small target dimensions compared to the distance to the detector. Therefore this approximation might not be good for the large Copper foil.

• Muons are stopped in thick targets and decay into positrons. For all target foils an additional spectrum, using a positron beam, was taken. This allows a correction factor to be applied to account for X-rays produced from decay positrons originating from stopped muon decay in the target (note that the beam positrons are removed by the separator). The three possible inﬂuences on the X-ray rate estimation mentioned above are discussed in the following sections.

63 6.5 Consideration of the momentum window

The muon beam is not monoenergetic but shows a momentum distribution of 27.75 ± 0.9 MeV/c (±3σ width). On one hand higher energy muons produce more X-rays since the emission cross-section increases as a function of the projectile energy (see fig.4.2) and the energy loss decreases with increasing muon energy (see fig.4.6) while on the other hand the muon range increases as a function of the kinetic energy and therefore attenuation becomes more important. In order to study the influence of the momentum window, the gaussian distributed beam profile (as a function of the muon momentum) is approximated by three monoenergetic muon beams α, β and γ:

• Beam α: all muons having a momentum in the interval [0 , (27.75−0.26) MeV/c], which corresponds to 15.85%.

• Beam β: all muons having a momentum in the interval [(27.75−0.26) MeV/c , (27.75+0.26) MeV/c], which corresponds to 68.3%.

• Beam γ: all muons having a momentum in the interval [27.75 MeV/c , ∞], which corresponds to 15.85%.

Since the muon beam is approximated by three monoenergetic muon beams, the expectation value hpi of the momentum has to be computed for the three intervals mentioned above. In case of the beam β the expectation value is simply given by the central value of 27.75 MeV/c. In case of beam γ the expectation value hpγ i is given by:

Z ∞ 2 1 − (p−mean) hpγ i = √ p · e σ2 dp (6.4) σ π mean+σ where mean = 27.75 MeV/c and σ = 0.26 MeV/c. A similar calculation is performed for beam α (the lower limit of the integral in eqn.6.4 can be replaced by minus inﬁnity since the gaussian peak is narrow). Using the expectation value for the momentum and the relativistic energy-momentum equation the three monoenergetic beams are given by:

• Beam α: 3483 keV muons, 15.85% of the beam

• Beam β: 3583 keV muons, 68.3% of the beam

• Beam γ: 3685 keV muons, 15.85% of the beam

The predicted muon induced X-ray rate is recalculated for the Tantalum target where the muon beam is approximated by the weighted sum of three individual monoenergetic beams (α, β and γ). Since the inﬂuence on the muon induced X-ray rate is well below 1%, the muon beam is assumed to be monoenergetic for further analysis.

6.6 Rate prediction for the large Copper foil

For the rate calculation it is assumed, that X-rays produced withing the same depth of the target material have to penetrate the same distance within the target in order to reach the surface and ﬁnally hit the detector. This is a good approximation for small targets, where the target dimensions are small compared to the distance between the centre of target and the X-ray detector. Fig.6.10 shows a simulation of the beam proﬁle on the large Copper foil (290 · 300 · 0.1) mm3, as used for some of the measurements.

64 Figure 6.10: Left: Beam proﬁle on the copper foil (290 mm · 300 mm), right: zoom of the foil. The X-ray production rate is calculated separately for each rectangle and summed afterwards.

The farthest points on the Copper foil shown in the experimental setup in fig.6.5 to the XR-100CR detector are the two corners on the left (left upper and left lower corner). Imagine, the large Copper foil (schematic drawing with the gaussian beam profile in fig.6.10) to be mounted at same position, then the two rectangles on the left (upper left and lower left rectangle) are the farthest with respect to the X-ray detector. For the simulation the target foil is subdivided into 9 equal segments as shown, with the rectangles labeled in the following way:

Table 6.5: Labeling of the divisions on the large Copper foil.

LU MU RU LM MM RM LL ML RL

For geometrical reasons X-rays produced in "LU" and "LL" have to penetrate the largest distance within the target in order to reach the surface and hit the detector compared to X-rays produced at the same depth in any other division of the Copper foil. Therefore attenuation plays the most important role for these two segments. For symmetry reasons (assuming the target foil to be mounted exactly horizontally and at the centre of the beam with the detector centered on the horizontal beam plane), attenuation has the same effect on the two rectangles "LU","LL" and on "MU","ML" and on "RU","RL" (also the solid angle is equal for the two rectangles of such a pair). In order to take the differing attenuation into account, the X-ray rate is predicted for each of these 9 rectangles independently and a weighted sum according to the percentage of the muons that hit each rectangle (determined by the simulation presented in fig.6.10), is performed. For geometrical reasons, the percentage of muons hitting the corner rectangles "LU", "RU", "RL" and "LL" is equal, as well as the percentage hitting "LM", "MU", "RM" and "ML". The width of such a rectangle is equal to σhoriz. whereas the height is given by σvert.. Therefore these rectangles enclose a ±3σ region of the beam. It is assumed for this approximation, that all muons hit the target within one of these 9 rectangles (i.e. the gaussian distributed beam profile is restricted to the 9 rectangles).

65 Similar to the calculations in sec.6.5 the expectation value of the impact coordinates (muon on the foil) is computed for each rectangle in order to evaluate the constant factor f (penetrated distance of the X-ray in the target until it reaches the surface in the direction of the detector divided by the distance the muon propagated within the target until the X-ray is produced) for the individual rectangles. The prediction of the X-ray rate, calculated individually for the 9 rectangular divisions and added up according to fraction of muons that hit the rectangle, only changes by ≈ 1% compared to prediction using the simpliﬁed model where f is assumed to be constant for the whole target area, therefore the parameter f is taken to be constant for further analysis.

6.7 Rate prediction including positrons

Finally the inﬂuence of positrons on the predicted X-ray rate is examined. As shown previously the separation of muons and positrons is very good and therefore it is a good approximation to assume a pure muon beam. The range of muons (≈ 200 µm for 3583 keV muons in Copper) is less than the thickness of some targets, hence in these foils they will be stopped and decay according to:

+ + µ −→ e + νµ + νe (6.5) which is the Michel decay. For every stopped muon, a decay positron is produced, which, while escaping the target can produce positron induced X-rays. Since the decay positrons are relativistic and their mass substantially smaller, it is not possible to perform positron induced X-ray emission calculations with ISICS06, or energy loss computations with SRIM 2008. Therefore the positron induced X-ray rate is determined from experimental data. After every muon induced X-ray fluorescence measurement, the parameters of the separator were changed such that a positron beam results and an X-ray spectrum under the same experimental conditions as for the muon measurement was recorded. For the positron measurements, the hypothetical muon rate (muon rate, if the separator where on muons) is known and together with the "muon to positron rate conversion factor" of 6.75 (which means that the positron rate is 6.75 times higher than the muon rate if the separator is switched off) the positron rate follows. The positron rate and the "Live-time", during which a spectrum is taken, determine the amount of X-rays that are produced on average for a single incident positron. Since all muons stop in the thick targets and decay into a positron and two neutrinos, the rate of positrons (due to stopped muons) "produced" within the target is equal to the muon rate of the incident beam. Also the positron rate and the average number of X-rays produced for a single positron are known (determined by the positron spectrum), it is therefore then possible to estimate the positron induced X-ray rate. A comparison of the measured X-ray rate as a percentage of the prediction with and without inclusion of positron induced X-rays is given in tab.6.6. Since muons are only stopped in thick targets, the inclusion of positrons only changes the values for those targets that are thicker than the range of muons in the specified material (which is the case for the 2 mm thick Copper and Tantalum targets, as well as for the 1 mm thick Silver target).

66 Table 6.6: Comparison of the muon induced X-ray production rate measurements with predictions. In the second-to-last column the prediction includes positron induced X-ray production due to decay positrons from stopped muons (only for thick targets), whereas they are neglected in the last column.

Target Target Percentage of prediction Percentage of prediction element thickn. including positrons considering only muons Cu 2 mm 152.3 ± 8.4 256.15 ± 20.79 Cu 2 mm 152.1 ± 8.4 255.86 ± 20.77 Ta 2 mm 101.8 ± 5.2 192.52 ± 15.45 Ta 2 mm 86.2 ± 4.7 163.40 ± 13.43 Ag 1 mm 112.2 ± 5.5 226.48 ± 18.26 Cu 0.1 mm 137.6 ± 11.4 137.64 ± 11.08 Cu 25 µm 92.9 ± 7.7 92.89 ± 7.52 Ta 4 µm 126.4 ± 10.5 126.43 ± 10.22 Mo 50 µm 67.6 ± 5.4 67.59 ± 5.25

As shown in tab.6.6 the influence of positron induced X-rays on the true muon X-ray rate is not negligible for thick targets. For the final setup where a thin foil, allowing the muons to pass with little influence on their trajectory, will be used, these positrons will not have to be considered. A comparison of the number of muon induced X-rays to the number of positron induced X-rays is presented in tab.7 in the appendix. Fig.6.11 shows a graphical comparison of the muon induced X-ray fluorescence measurements to theoretical predictions including positron induced X-rays:

Figure 6.11: Muon measurement results

The predictions for the muon induced X-ray rate reproduce the experimental data (although the measured rate still exceeds the prediction for thick Copper targets). The uncertainty for ISISC06 and SRIM 2008 calculations is assumed to be the same for incident muons and protons (the uncertainty is probably larger in case of incident muons). Since no theoretical prediction for positron induced X-rays was available, the X-ray rate due to positrons is evaluated by experimental data, where only a statistical error is considered (since the spectra are recorded with high statistics, the statistical error is small). The

67 two situations, namely irradiating the target with positrons or to "produce" positrons within the target by decaying muons, are however not equivalent and only an approximation. The uncertainty for the positron induced X-ray rate should therefore be larger than just the statistical error. For these reasons, the error bars in ﬁg.6.11 are too small.

6.8 Comments on the positron induced X-ray rate

The prediction of the positron induced X-ray rate due to stopped muons by experimental data from a positron beam hitting a target is only an approximation for the following reasons: • Geometrical arrangement: When beam positrons were used they penetrate the target (since the positrons are relativistic, their range is large) from the left to the right in ﬁg.6.5, whereas positrons originating from stopped muons are produced within the target and then propagate in any direction. This geometrical diﬀerence for the two situations could be included in the calculation and would necessitate a more sophisticated model.

• Another effect that influences the rate prediction is the muon spin. The pion decay into muons is a two body decay, which takes place due to weak interaction, which only couples to left handed particles and therefore the muon spin points opposite to the direction of propagation (antiparallel), i.e. the muons are spin polarized. The decay of spin polarized muons is not isotropic (see fig.6.12), which should also be considered for the prediction of the X-ray rate, however this depends totally on the choice of target material used. Fig.6.12 shows the asymmetric muon decay in case of spin polarized muons.

Figure 6.12: The ﬁgure shows the probability of the positron resulting from a muon decay emerging at diﬀerent directions with respect to the muon-spin direction (which is shown by the large horizontal arrow) [28].

Including the points mentioned above for the positron induced X-ray rate could further improve the theoretical predictions in case of thick targets.

6.9 Summary of the muon measurements

First X-ray ﬂuorescent measurements were undertaken with a surface muon beam, showing a clear signature for their production. The motivation being a new non-destructive method to monitor the beam intensity of very high-rate charged particle or photon beams, such as the MEG surface muon beam. Theoretical simulation tools available for such a purpose are not directly applicable and need to be checked since they are more clearly associated with heavier ions. A variety of target material and thick- nesses were measured and various systematic inﬂuences such as target thickness and X-ray production mechanism (stopped muon decay, positron induced X-ray emission) were studied. Comparison to predictions based on the assumption of a muon seen as a light hydrogen-ion show reasonable agreement and allow this approach to be used to further study and optimize a muon beam intensity monitor.

68 Chapter 7

Conclusion

The aim of this work was to study the feasibility of implementing a detector system based on a method of non-destructive, beam-intensity monitoring for one of the world’s highest intensity surface muon beams. The non-destructive monitoring in a high magnetic field environment for such an intense low-momentum secondary beam is non-trivial and does not readily allow conventional means to be used, as in the case of high-energy or more intense primary beams. The method of X-ray fluorescence induced by protons (PIXE) is a well established technique for trace element analysis. The idea of using muons to produce X-ray fluorescence photons while traversing an ultra-thin foil and measuring their yield as a means of determining the muon beam intensity, seems a logical consequence, however, it is not reflected in literature. Hence the idea was pursued by firstly studying a variety of possible detectors for X-rays, using the fluorescence technique with radioactive sources. Then testing known simulation tools based on heavy charged ions by initially predicting the X-ray yield for a given setup using protons and comparing these to actual measurements with the MEG Cockcroft-Walton proton accelerator. In a second step these tools were used in a modified way, treating a muon as a light hydrogen-ion, to predict the X-ray yield from various targets placed in the MEG muon beam. These predictions were then finally compared to measurements in the beam. Four different X-ray detectors were tested for their suitability to perform X-rays measurements within the energy region of 5 − 25 keV. In case of the APD (Avalanche Photo Diode) and the SBD (Surface Barrier Detector), the signal-to-noise ratio is not sufficient to distinguish these low energetic X-rays from noise without further improving the detectors (e.g. cooling etc.), whereas in case of the APD, additionally a disturbing signal causes problems. The XR-100CR and the NaI(Tl) are both suitable for X-ray measurements within the mentioned energy region. On the one hand, the energy resolution for the XR-100CR detector is much better than that of the NaI(Tl) detector, though on the other hand, the active area of the NaI(Tl) detector is significantly larger than that of the XR-100CR detector and hence the probability for an X-ray to hit the detector is larger, which leads to an increased X-ray rate. Also the NaI(Tl) detector is thicker than the XR-100CR detector, leading to a higher efficiency, which is especially important for "high energy" X-rays. The main disadvantage with the NaI(Tl) detector is that according to the manufacturer it is not to be placed in magnetic fields. However, by suitable exchange of the photomultiplier the problem could be solved and with its large active area, which has an effect on the solid angle, measurements at higher X-ray rates are possible. The low energy resolution of the NaI(Tl) detector (although finally only a rate measurement without any energy information is needed), could be limiting if the noise is wrongly identified as signal X-rays. This only has an effect if the background is not linear within the region of the peak, since linearly distributed noise is simply subtracted afterwards. However, since muon induced X-ray spectra show a lot of (non linearly distributed) noise, see fig.6.7, this effect has to be studied.

69 The predictions for the proton induced X-ray fluorescence measurements agree well with experimental data, considering the uncertainties for ISICS06 and SRIM 2008 calculations. The measured X-ray rates are slightly higher than the prediction, which is expected since the particle induced X-ray emission cross-sections calculated with ISICS06 are slightly higher than the predictions too. Also there seems to be some change of the material properties in Copper, causing a lower X-ray rate than predicted. It is still not fully understood what happens to the Copper target under irradiation with protons therefore + + further investigations are also needed. The influence of H2 -ions (the proton beam consists of ≈ 25% H2 ions) is not negligible and is therefore considered for the theroretical predictions, where it is assumed + that the H2 -ions do not break up when hitting the target. In case of incident muons, it was possible to record a clear muon induced X-ray fluorescence spectrum. Furthermore, a theoretical prediction (by treating the muons as lightweight protons) considering also positron induced X-rays due to muons stopped in thick targets, yields a correct order of magnitude estimation of the X-ray rate (deviations to measurements are smaller than a factor of 1.5). Since no theoretical prediction for positron induced X-ray fluorescence is available, the X-ray rate is estimated by experimental data using a pure positron beam, although the experimental situation is not quite the same as for positrons produced within the target (see sec.6.8). Since muons are only stopped in thick targets then the rate predictions in this particular case must take into account positron induced X-rays. The goal for the final setup to continuously monitor the muon beam by means of induced X-rays, is a rate of at least 100Hz. This would allow one to measure an X-ray spectrum for 100 s with a statistic uncertainty of the measured rate of 1% (recording a spectrum for 100 s at a rate of 100 Hz yields 10’000 X-ray counts, where the uncertainty, given by the square root is 100 counts or equivalently 1%). Typical measured X-ray rates ranged from 2.6 Hz for the 50 µm thick Molybdenum foil to 46 Hz for the 2 mm thick Copper target using the 13 mm2 XR-100CR detector. Since a thin foil has to be used as a target material in order to minimize the influence on the muon trajectory (which will be stopped in a polyethylene target inside COBRA after passing the target foil), the muon induced X-ray rate must be increased by roughly a factor of 20 in order to reach the desired 100 Hz X-ray rate. On the one hand the rate can be increased by placing the detector closer to the target (probably a factor of two is possible, yielding a factor of 4 for both the solid angle and the X-ray rate), and on the other hand, by replacing the photomultiplier type of the NaI(Tl) detector, this detector could be used, which would increase the X-ray rate by roughly a factor of 90 (from the detector active area). In conclusion therefore, with some minor changes to the experimental setup, the concept of muon induced X-ray fluorescence can provide a muon rate measurement within a reasonable time and precision, which influences the low-energy muons minimally in terms of energy loss and beam divergence induced by multiple scattering, provided the target foil is placed at a suitable location along the beam line - namely at a focus.

70 Acknowledgment

I gratefully acknowledge Prof. Urs Langenegger for oﬀering me the chance to participate in the MEG experiment at PSI and Peter-Raymond Kettle for assisting in the practical work and the valuable discussions and inputs. Thanks also to Prof. Carlo Bemporad and Dr. G.Signorelli for the assistance with the C-W accelerator, to Angela Papa for her help with the C-W beamspot analysis and Dr. Dimitri Grigoriev for helping with the measurements. Thanks to the whole MEG / Pisa group and my family for their support.

71 Appendix

Eﬃciency of the diﬀerent X-ray detectors:

Figure 1: Efficiency plot for the different detectors. The efficiency is given by the product of transmission factor for the entrance window and absorption probability of the detector’s active area.

Table 1: Properties of the different X-ray detectors. The efficiency plot in fig.1 is calculated using the entrance window material and thickness in tab.1 for the transmission and the layer material and thickness for the absorption probability. The efficiency is then given by the product of the transmission and absorption probability. In case of unknown entrance window material and / or thickness, the transmission factor is set to 1.

Detector entrance window active layer Type window thickness layer thickness XR-100CR Be 254 µm Si 500 µm NaI(Tl) Be ? NaI(Tl) 1 mm APD Al 20 µm Si 130 µm SBD Al 20 µm Si 1 mm

Table 2: Detector efficiency for all X-ray lines used in the experiment. The efficiency for the XR-100CR detector is given by the product TBe · AXR100CR of transmission probability TBe through the Beryllium window and absorption probability AXR100CR in the active layer. In the last column but one the proportion of the specified X-ray line is listed (for example in case of the copper Kα line this is the amount of Kα X-rays with respect to the total amount of K-shell X-rays). The relative abundance is determined by measurements (comparison of the peak areas), since ISICS06 does not make any theoretical predictions.

X-ray energy Efficiency Efficiency Relative Attenuation cm2 X-ray Line [keV] XR100CR NaI(Tl) abundance coefficient [ g ] Cu, Kα 8.05 95.4 % 100.0 % 81.5 % 51.7 Cu, Kβ 8.9 96.1 % 100.0 % 18.5 % 39.2 Mo, Kα 17.48 51.7 % 100.0 % 75 % 18.7 Mo, Kβ 19.61 40.4 % 100.0 % 25 % 13.8 Ag, Kα 22.16 30.8 % 99.2 % 66 % 13.9 Ag, Kβ 24.94 22.9 % 98.3 % 34 % 10.1 Ta, Lα 8.15 95.5 % 100.0 % 47.5 % 156 Ta, Lβ 9.34 96.1 % 100.0 % 52.5 % 111

72 Lookup chart for K and L-shell X-rays 2 Ar 54 86 Kr 36 10 18 Xe He Ne Rn VIIIA 0.851 98) 89-103 2.96 3.19 1.59 1.64 4.11 4.42 83.80 94.88 12.65 14.11 29.80 33.64 11.72 14.32 Actinides at NTP) 3 I 9 F Lr Cl At 17 Br 35 53 71 85 Lu 103 0.677 2.62 2.82 1.48 1.53 3.94 4.22 7.65 8.71 11.92 13.29 28.61 32.29 54.06 61.28 11.42 13.87 81.53 92.32 (density in g/cm Yttrium - Y 39 (3.8) Zinc - Zn 30 (7.1) Amptek Inc. 14 DeAngelo Drive www.amptek.com Bedford, MA 01730 USA 8 S O e-mail: [email protected] 34 52 84 70 16 Te Se Po Yb No 102 0.526 2.31 2.46 1.38 1.42 3.77 4.03 7.41 8.40 11.22 12.50 27.47 30.99 52.36 59.35 11.13 13.44 79.30 89.81 ) Tele: +1 781-275-2242 Fax: 781-275-3470 7 P N Bi 83 69 15 51 33 As Sb Md Tm 101 0.392 2.02 2.14 1.28 1.32 3.61 3.84 7.18 8.10 77.10 87.34 10.54 11.73 26.36 29.72 50.73 57.58 10.84 13.02 6 C Si Er 14 32 50 82 68 Sn Pb Ge Fm 100 0.282 1.74 1.83 1.19 1.21 3.44 3.66 6.95 7.81 9.89 10.98 74.96 84.92 25.27 28.48 49.10 55.69 10.55 12.61 16.38 21.79 120.60 136.08 5 B In Tl Al IIIA IVA VA VIA VIIA 13 31 67 49 81 99 Es Ga Ho 0.185 1.49 1.55 1.10 1.12 3.29 3.49 6.72 7.53 9.25 10.26 72.86 82.56 24.21 27.27 47.53 53.93 10.27 12.21 16.02 21.17 117.65 132.78 Rubidium - Rb 37 (1.53) Tellurium - Te 52 (6.25) Silver - Ag 47 (10.49) Cf 48 80 98 30 66 Zn Dy Cd Hg 1.01 1.03 3.13 3.32 6.50 7.25 8.64 9.57 9.99 11.82 70.82 80.26 23.17 26.09 45.99 52.18 15.66 20.56 114.75 129.54 29 47 79 97 65 Tb Au Bk Cu Ag 8.05 8.90 0.93 0.95 2.98 3.15 6.28 6.98 9.71 11.44 68.79 77.97 44.47 50.39 15.31 19.97 22.16 24.94 111.90 126.36 Oxygen - O 8 (0.001429) Xenon - Xe 54 (0.00585) Phosphorus - P 15 (1.83-Y 2.20-R) Ni Pt 28 78 64 46 96 Pd Gd R Cm 7.48 8.26 0.85 0.87 2.84 2.99 6.06 6.71 9.44 11.07 66.82 75.74 21.18 23.82 42.98 48.72 14.96 19.39 109.10 123.24 Ir VIII 95 27 45 63 77 Eu Co Rh Am Group 6.93 7.65 0.78 0.79 2.70 2.83 5.85 6.46 9.19 10.71 64.89 73.55 20.21 22.72 41.53 47.03 14.62 18.83 106.35 120.16 Molybdenum - Mo 42 (10.22) Platinum - Pt 78 (21.45)Neodymium - Nd 60 (6.96) Plutonium - Pu 94 (19.8) Ruthenium - Ru 44 (12.1) Samarium - Sm 62 (7.75) Terbium - Tb 65 (8.229) Thallium - Tl 81 (11.86) Zirconium - Zr 40 (6.4) Niobium - Nb 41 (8.57)Nitrogen - N 7 (0.001251) Promethium - Pm 61 Protactinium - Pa 91 (15.4) Sodium - Na 11 (0.97) Tungsten - W 74 (19.3) Titanium - Ti 22 (4.5) Mendelevium - Md 101Mercury - Hg 80 (13.55) Palladium - Pd 46 (12.16) Rhodium - Rh 45 (12.44) Technetium - Tc 43 (11.5) Ytterbium - Yb 70 (6.965) Lutetium - Lu 71 (9.84) Nobelium - No 102 Radium - Ra 88 (5.0) Strontium - Sr 38 (2.56) Uranium - U 92 (18.7) X-123 26 62 44 76 94 Fe Pu Ru Os Sm AMP TEK 6.40 7.06 0.70 0.72 2.56 2.68 5.64 6.21 8.91 10.35 62.99 71.40 19.28 21.66 40.12 45.40 14.28 18.28 103.65 117.15 43 93 61 75 25 Tc Re Np Mn Pm 5.90 6.49 0.64 0.65 2.42 2.54 5.43 5.96 8.65 10.01 18.41 19.61 61.13 69.30 38.65 43.96 13.95 17.74 101.00 114.18 Krypton - Kr 36 (0.00368)Lanthanum - La 57 (6.15)Lawrencium - Lr 103 Neptunium - Np 93 (20.4) Potassium - K 19 (0.86) Selenium - Se 34 (4.82) Thulium - Tm 69 (9.321) Polonium - Po 84 (9.27) Scandium - Sc 21 (3.02) Praseodymium - Pr 59 (6.48) Thorium - Th 90 (11.3) Hydrogen - H 1 (0.0000899) Manganese - Mn 25 (7.41) Rhenium - Re 75 (21.0) Tantalum - Ta 73 (16.6) Holmium - Ho 67 (8.795) Magnesium - Mg 12 (1.74) Osmium - Os 76 (22.5) Radon - Rn 86 (4.4) Sulphur - S 16 (1.92) Vanadium - V 23 (5. X-Ray and Gamma Ray Detectors U W 92 60 74 Cr 24 42 Nd Mo 5.41 5.95 0.57 0.58 2.29 2.40 8.40 9.67 5.23 5.72 17.48 19.61 59.31 67.23 37.36 42.27 13.61 17.22 98.43 111.29 XR-100CR / XR-100T-CdTe GAMMA-8000 Amptek K and L Emission Line Lookup Chart V Pr 73 41 23 59 91 Ta Pa Nb 4.95 5.43 0.51 0.52 2.17 2.26 8.15 9.34 5.03 5.49 16.61 18.62 57.52 65.21 36.02 40.75 13.29 19.70 95.85 108.41 1 1 β β K L Ti Zr Hf 40 79 22 58 72 90 Th Ce Au 1 1 α α in keV Key to 0.45 0.46 2.04 2.12 7.90 9.02 4.84 5.26 4.51 4.93 L K 15.77 17.67 34.72 39.26 55.76 63.21 12.97 16.20 93.33 105.59 Energy Values Y IIIB IVB VB VIB VIIB IB IIB 21 57 89 39 La Sc Ac 0.40 1.92 2.00 4.65 5.04 4.09 4.46 57 - 71 14.96 16.74 12.65 15.71 33.44 37.80 90.89 102.85 4 IIA Sr 88 20 56 12 38 Ca Ba Be Ra 0.34 Mg 0.110 1.25 1.30 3.69 4.01 1.81 1.87 4.47 4.83 14.16 15.83 32.19 36.38 12.34 15.23 88.46 100.14 57-71 1 3 IA K H Li Fr 87 37 19 11 55 Na Cs Rb 0.052 Group Lanthanides 1.04 1.07 3.31 3.59 1.69 1.75 4.29 4.62 86.12 97.48 12.03 14.77 13.39 14.96 30.97 34.98 Bismuth - Bi 83 (9.78)Boron - B 5 (2.53) Copper - Cu 29 (8.96) Curium - Cm 96 Gold - Au 79 (19.32) Lead - Pb 82 (11.34) Hafnium - Hf 72 (13.3) Lithium - Li 3 (0.534) Actinium - Ac 89 (10.07)Aluminum - Al 13 (2.70)Americium - Am 95 (11.87) Bromine - Br 35 (0.007139)Antimony - Sb 51 (6.62) Calcium - Ca 20 (1.55) Cadmium - Cd 48 (8.65)Argon - Ar 18 (0.001783) Dysprosium - Dy 66 (8.55)Arsenic - As 33 (5.73) Californium - Cf 98Astatine - At 85 Helium - He 2 (0.0001785) Carbon - C 6 (2.25-G; 3.51-D) Einsteinium - Es 99 Erbium - Er 68 (9.066) Barium - Ba 56 (3.5) Fermium - Fm 100Berkelium - Bk 97 Cerium - Ce 58 (6.90)Beryllium - Be 4 (1.85) Europium - Eu 63 (5.234) Chlorine - Cl 17 (0.003220) Iodine - I 53 (4.94) Cesium - Cs 55 (1.87) Fluorine - F 9 (0.00169) Cobalt - Co 27 (8.71) Gadolinium - Gd 64 (7.90) Indium - In 49 (7.28) Chromium - Cr 24 (7.14) Iridium - Ir 77 (22.42) Francium - Fr 87 Gallium - Ga 31 (5.93) Germanium - Ge 32 (5.46) Iron - Fe 26 (7.88) Neon - Ne 10 (0.000900) Nickel - Ni 28 (8.88) Silicon - Si 14 (2.42) Tin - Sn 50 (7.3

Figure 2: Amptek K- and L-emission line lookup chart [29]

73 Relative abundance of K- and L-shell X-rays:

Figure 3: Plot showing the percentage of Kα X-rays with respect to all K-shell X-rays. The graph on the right shows the analogue data for L-shell X-rays. The precise numbers are listed in tab.7. The relative abundance is determined by comparison of the peak height of the Kα and Kβ line using the interactive chart of the Berkeley LAB.

Table 3: Percentage of Kα (Kβ ) X-rays with respect to the sum of Kα and Kβ X-rays Atomic percent. of percent. of Table 4: Percentage of Lα (Lβ ) X-rays with respect to the sum of L and L Element number K X-rays K X-rays α β α β X-rays Fe 26 83.3 % 16.7 % Atomic percent. of percent. of Cu 29 83.3 % 16.7 % Element number L X-rays L X-rays Ge 32 85.7 % 14.3 % α β Gd 64 44.7 % 55.3 % Br 35 82.4 % 17.6 % Ho 67 49.6 % 50.4 % Sr 38 82.2 % 17.8 % Yb 70 43.6 % 56.4 % Mo 42 81.8 % 18.2 % Ta 73 47.8 % 52.2 % Rh 45 81.2 % 18.8 % Os 76 36.8 % 63.2 % In 49 79.7 % 20.3 % Au 79 55.2 % 44.8 % Sb 51 78.9 % 21.1 % Pb 82 58 % 42 % Te 52 78.6 % 21.4 % Th 90 58.2 % 41.8 % Cs 55 77.7 % 22.3 % Ce 58 76.6 % 23.4 % Gd 64 76.3 % 23.7 %

74 Comparison of ISICS06 calculations with experimental data:

Table 5: Comparison of ISICS06 calculations for the 3He induced K-shell emission cross- section with experimental data. J.Phys.B: At.Mol.Phys. Vol.25, Nr.7, 3He ion-induced K x-ray emission cross- section of elements between Mn and Zn [20].

Energy Mn rel.err. F e rel.err. Ni rel.err. [MeV] Exp ISICS % Exp ISICS % Exp ISICS % 1.5 7.35 7.44 1.2 5.49 5.35 2.6 2.82 2.83 0.4 3 71.1 70.4 1.0 55.6 52.6 5.4 29.8 29.7 0.3 4.5 225 207 8.0 185 159 14.1 99.1 95.2 3.9 6 400 391 2.3 349 310 11.2 202 194 4.0

Energy Cu rel.err. Zn rel.err. [MeV] Exp ISICS % Exp ISICS % 1.5 2.36 2.09 11.4 1.51 1.54 2.0 3 25.3 22.5 11.1 16.7 17.1 2.4 4.5 86.4 73.9 14.5 55.4 57.3 3.4 6 180 154 14.4 116 122 5.2

Table 6: Comparison of ISICS06 calculations for the proton induced K-shell ionization cross- section with experimental data. J.Phys.B: At.Mol.Phys. Vol.9, Nr.3, Proton induced X-ray production in titanium, nickel, copper, molybdenum and silver [19]

Energy T i rel.err. Ni rel.err. Ag rel.err. [MeV] Exp ISICS % Exp ISICS % Exp ISICS % 1 249 242 2.6 24.2 23.5 2.7 0.085 0.0827 2.7 1.1 312 303 3.0 30.9 30.9 0.1 0.119 0.1181 0.8 1.2 382 367 4.0 38.7 39.2 1.2 0.162 0.1620 0.0 1.3 465 434 6.6 47.7 48.4 1.6 0.215 0.2152 0.1 1.4 537 504 6.1 57.6 58.6 1.7 0.279 0.2783 0.2 1.5 621 576 7.2 68.7 69.6 1.3 0.357 0.3520 1.4 1.6 706 650 8.0 80.9 81.3 0.5 0.446 0.4367 2.1 1.7 793 723 8.8 94.2 93.7 0.5 0.551 0.5329 3.3 1.8 879 797 9.3 108 106.7 1.2 0.667 0.6409 3.9 1.9 951 871 8.4 123 120.2 2.3 0.799 0.7611 4.7 2 1050 945 10.0 138 134.2 2.7 0.942 0.8937 5.1 2.1 1140 1018 10.7 153 148.7 2.8 1.1 1.0390 5.5 2.2 1220 1089 10.7 169 163.4 3.3 1.26 1.1970 5.0 2.3 1300 1160 10.8 184 178.5 3.0 1.44 1.3680 5.0 2.4 1370 1229 10.3 199 193.7 2.6 1.61 1.5518 3.6 2.5 1450 1297 10.5 213 209.2 1.8 1.79 1.7487 2.3 2.6 1510 1364 9.7 226 224.8 0.5 1.96 1.9583 0.1 2.7 1580 1428 9.6 237 240.6 1.5 2.13 2.1809 2.4 2.8 1640 1492 9.1 248 256.4 3.4 2.28 2.4164 6.0 2.9 1700 1553 8.6 256 272.2 6.3 2.42 2.6646 10.1 3 1760 1613 8.4 263 288.0 9.5 2.53 2.9254 15.6

75 Energy Cu rel.err. Mo rel.err. [MeV] Exp ISICS % Exp ISICS % 1 16.1 16.5 2.6 0.308 0.295 4.1 1.2 27.1 27.8 2.7 0.551 0.560 1.6 1.4 42.2 42.1 0.2 0.91 0.938 3.0 1.5 51 50.2 1.5 1.14 1.172 2.8 1.6 60.4 59.0 2.3 1.41 1.439 2.1 1.8 81.4 78.1 4.0 2.07 2.071 0.0 2 104 99.1 4.7 2.88 2.837 1.5 2.2 126 121.5 3.5 3.82 3.737 2.2 2.4 146 145.1 0.6 4.82 4.769 1.1 2.5 156 157.2 0.8 5.32 5.334 0.3 2.6 164 169.5 3.4 5.79 5.931 2.4 2.8 179 194.4 8.6 6.63 7.216 8.8 3 189 219.7 16.2 7.22 8.618 19.4

Table 7: Comparison of ISICS06 calculations for the α-particle induced K-shell ionization cross-section with experimental data. J.Phys.B. At.Mol.Phys. Vol.14, pages 3153-3161, K-shell ionization cross-sections and relative x-ray emission rates of Sn, Ho, Au, Pb and Bi bombarded with 9- 155MeV alpha particles [21]

Energy Sn rel.err. Ho rel.err. T m rel.err. [MeV] Exp ISICS % Exp ISICS % Exp ISICS % 9 3.12 2.45 21.3 0.181 0.141 22.2 0.138 0.108 22.0 15.5 13.5 11.71 13.3 0.851 0.725 14.8 0.615 0.553 10.1 16.5 15.9 13.80 13.2 1.01 0.867 14.1 0.727 0.661 9.1 17.5 18.5 16.06 13.2 1.22 1.024 16.0 0.817 0.781 4.4 18 20 17.24 13.8 18.5 20.9 18.47 11.6 1.38 1.196 13.3 0.993 0.913 8.1 19 23 19.73 14.2 19.5 24.3 21.04 13.4 1.62 1.384 14.6 1.18 1.056 10.5 20.5 28.2 23.74 15.8 1.9 1.586 16.5 1.36 1.211 11.0 21.5 30.8 26.58 13.7 2.1 1.804 14.1 1.62 1.378 14.9 22.5 33.8 29.55 12.6 2.38 2.037 14.4 1.77 1.557 12.0

Energy Au rel.err. P b rel.err. [MeV] Exp ISICS % Exp ISICS % 9 0.0387 0.0333 14.0 0.0258 0.0246 4.6 16.5 0.244 0.1974 19.1 17.5 0.28 0.2327 16.9 0.193 0.1692 12.3 18 0.303 0.2517 16.9 18.5 0.304 0.2715 10.7 0.213 0.1972 7.4 19.5 0.388 0.3138 19.1 0.252 0.2276 9.7 20.5 0.419 0.3597 14.2 0.298 0.2607 12.5 21.5 0.528 0.4092 22.5 0.327 0.2963 9.4 22.5 0.56 0.4624 17.4 0.361 0.3346 7.3

76 Table 8: Comparison of ISICS06 calculations for the proton induced total L-shell emission cross-section in Sm and Y b with experimental data. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Proton induced L and L-sub shell X-ray cross-sections in Sm and Yb at 1 − 2.5 MeV [22]

Energy Sm rel.err. Y b rel.err. [MeV] Exp ISICS % Exp ISICS % 1 37.4 35.518 5.0 13.4 13.775 2.8 1.5 77.1 89.169 15.7 36.8 37.42 1.7 1.8 123.1 129.41 5.1 57.4 56.432 1.7 2 142.8 158.41 10.9 71.07 70.788 0.4 2.2 155.5 188.54 21.2 83.7 86.271 3.1 2.4 90.7 102.69 13.2 2.5 116.5 234.49 101.3 108.6 111.2 2.4

Schematic drawing of the C-W X-ray measurement setup:

Figure 4: Schematic drawing of the Cockcroft-Walton setup for the proton induced X-ray ﬂuorescence measurements with the XR-100CR detector in June 2008. The setup for the NaI(Tl) detector and for the measurements with the XR-100CR detector in May 2008 were very similar. In case of the NaI(Tl) detector the solid angle is more than an order of magnitude higher because of the large active area compared to the XR-100CR detector (see tab.9). The numbers for "σ on target" refer to the beam spot size on the target. In case of σvert. this is the same as for the beam, whereas σhoriz. equals the horizontal sigma of the beam multiplied by square root of two, since the target is mounted at 45 degrees with respect to the beam line.

77 Comparison of C-W X-ray rate measurement and prediction:

Figure 5: Graphical comparison of C-W measurements with predictions. The measurements include statistical and systematic errors calculated according to sec.4.5. Note, for reasons of clarity the proton energy for the Tantalum measurements is increased by 10 keV for the plot (the measurements are at 500 keV and 700 keV).

78 Table 9: Cockcroft-Walton measurements. The proton rate is given by the proton current, measured as integrated charge on the target. For some measurements only the rate was counted without taking a spectra. These measurements are obviously not corrected for noise as indicated in the last but one column. The error of the percentage of prediction includes a statistical error calculated via the standard deviation of the number of measured X-rays (measuring period of 100s) and a systematic error. The reproducibility (standard deviation) of the copper X-ray measurements for 500 keV protons with the XR-100CR detector is taken as systematic error for all data points (individually for the copper measurements on May 5th and the ones later on).

Iproton Ekin,p percentage noise solid angle Ω Date Target Detector [µA] [ keV] X-ray rate of prediction correction 4·π 13.05.2008 Cu XR100CR 1.07 500 396.7 100.8 ± 8.3 yes 2.03E-05 13.05.2008 Cu XR100CR 0.32 500 126.0 106.3 ± 8.8 yes 2.03E-05 13.05.2008 Cu XR100CR 0.55 500 216.1 106.8 ± 8.8 yes 2.03E-05 13.05.2008 Cu XR100CR 0.82 500 296.5 98.9 ± 8.1 yes 2.03E-05 13.05.2008 Cu XR100CR 0.54 1000 5638.3 96.5 ± 7.9 yes 2.03E-05 13.05.2008 Cu XR100CR 0.51 900 3871.3 114.8 ± 9.4 no 2.03E-05 13.05.2008 Cu XR100CR 0.52 800 2270.9 114.0 ± 9.3 no 2.03E-05 13.05.2008 Cu XR100CR 0.52 700 1175.3 113.4 ± 9.3 no 2.03E-05 13.05.2008 Cu XR100CR 0.51 600 525.1 111.4 ± 9.1 no 2.03E-05 13.05.2008 Cu XR100CR 0.52 500 205.3 108.0 ± 8.9 no 2.03E-05 13.05.2008 Cu XR100CR 0.52 250 3.7 94.5 ± 9.0 no 2.03E-05 14.05.2008 Cu XR100CR 0.50 250 1.5 41.0 ± 3.6 no 2.03E-05 14.05.2008 Cu XR100CR 0.50 400 17.5 31.1 ± 2.5 yes 2.03E-05 14.05.2008 Cu XR100CR 0.50 500 64.2 34.9 ± 2.8 no 2.03E-05 14.05.2008 Cu XR100CR 0.50 600 170.6 36.9 ± 3.0 no 2.03E-05 14.05.2008 Cu XR100CR 0.49 700 380.0 38.4 ± 3.1 no 2.03E-05 14.05.2008 Cu XR100CR 0.50 800 751.5 39.6 ± 3.2 no 2.03E-05 14.05.2008 Cu XR100CR 0.50 900 1333.5 40.4 ± 3.2 no 2.03E-05 14.05.2008 Cu XR100CR 0.49 1000 2224.2 42.0 ± 3.4 no 2.03E-05 14.05.2008 Cu NaI(Tl) 0.48 500 1754.4 25.8 ± 2.1 yes 7.44E-04 14.05.2008 Cu NaI(Tl) 0.48 700 10665.5 29.0 ± 2.3 yes 7.44E-04 15.05.2008 Ta XR100CR 0.39 500 136.4 111.9 ± 9.1 yes 2.03E-05 15.05.2008 Ta XR100CR 0.39 700 729.2 110.7 ± 8.9 yes 2.03E-05 15.05.2008 Ta NaI(Tl) 0.38 500 5490.3 118.5 ± 9.5 yes 7.44E-04 15.05.2008 Ta NaI(Tl) 0.38 700 26457.2 107.1 ± 8.6 yes 7.44E-04 15.05.2008 Ta NaI(Tl) 0.38 300 225.6 116.0 ± 9.4 yes 7.44E-04 15.05.2008 Ta NaI(Tl) 0.39 500 5512.0 118.2 ± 9.5 yes 7.44E-04 10.06.2008 Cu XR100CR 0.52 500 115.9 31.2 ± 2.5 yes 3.95E-05 10.06.2008 Cu XR100CR 0.52 1000 3730.0 34.3 ± 2.7 yes 3.95E-05 10.06.2008 Cu XR100CR 0.50 900 2330.9 36.2 ± 2.9 yes 3.95E-05 10.06.2008 Cu XR100CR 0.51 800 1321.9 34.9 ± 2.8 yes 3.95E-05 10.06.2008 Cu XR100CR 0.50 700 703.7 36.4 ± 2.9 yes 3.95E-05 10.06.2008 Cu XR100CR 0.50 600 321.1 35.4 ± 2.8 yes 3.95E-05 10.06.2008 Cu XR100CR 0.50 500 124.7 34.8 ± 2.8 yes 3.95E-05 10.06.2008 Cu XR100CR 0.51 400 37.4 34.1 ± 2.7 yes 3.95E-05 10.06.2008 Cu XR100CR 0.50 250 2.8 38.7 ± 3.2 yes 3.95E-05 10.06.2008 Cu XR100CR 0.48 500 116.8 34.4 ± 2.8 yes 3.95E-05 10.06.2008 Cu XR100CR 0.48 500 123.0 36.3 ± 2.9 yes 3.95E-05 10.06.2008 Cu XR100CR 0.48 500 123.0 36.1 ± 2.9 yes 3.95E-05 10.06.2008 Cu XR100CR 0.47 500 124.2 37.0 ± 3.0 yes 3.95E-05 10.06.2008 Cu XR100CR 0.47 500 127.1 37.8 ± 3.0 yes 3.95E-05 11.06.2008 Cu XR100CR 0.49 500 109.2 31.4 ± 2.5 yes 3.95E-05 12.06.2008 Cu XR100CR 0.48 500 129.4 37.5 ± 3.0 yes 3.95E-05 12.06.2008 Cu XR100CR 0.48 500 128.9 37.6 ± 3.0 yes 3.95E-05

79 Comparison of muon induced X-ray rate measurement and prediction:

Table 10: Comparison of muon induced X-ray fluorescence rate measurements with predictions (the muon rate in the upper table is measured after the X-ray measurement. At present it cannot be determined while performing measurements with muons. Performing continuous muon rate measurements with minimal influence on the muons is precisely the goal of this diploma thesis). As shown in the upper table, the influence of positron induced X-rays for thick targets (positrons originating from stopped muons decaying in the target) is not negligible.

Target Target Target Solid angle Measured X-ray Ω element dimension thickness Muon rate 4π rate [Hz] Cu 18.8 cm · 18.8 cm 2 mm 4.78E+07 1.101E-05 46.1 Cu 18.8 cm · 18.8 cm 2 mm 4.78E+07 1.101E-05 46.0 Ta diam.= 49.5 mm 2 mm 3.64E+07 9.013E-06 5.4 Ta diam.= 49.5 mm 2 mm 4.65E+07 9.013E-06 5.9 Ag diam.= 49.4 mm 1 mm 4.86E+07 9.013E-06 4.5 Cu 29cm · 30cm 0.1 mm 4.96E+07 1.101E-05 25.7 Cu 50mm · 50mm 25 µm 5.02E+07 1.089E-05 11.0 Ta 50mm · 50mm 4 µm 4.99E+07 1.089E-05 3.2 Mo 50mm · 50mm 50 µm 4.99E+07 1.089E-05 2.6

Target Target Target Prediction of the Prediction of the Percentage element dimension thickn. total rate [Hz] e+ induce X-ray rate of prediction Cu 18.8 cm · 18.8 cm 2 mm 30.3 12.3 152.3 ± 8.4 Cu 18.8 cm · 18.8 cm 2 mm 30.3 12.3 152.1 ± 8.4 Ta diam.= 49.5 mm 2 mm 5.3 2.5 101.8 ± 5.2 Ta diam.= 49.5 mm 2 mm 6.8 3.2 86.2 ± 4.7 Ag diam.= 49.4 mm 1 mm 4.0 2.0 112.2 ± 5.5 Cu 29cm · 30cm 0.1 mm 18.7 0 137.6 ± 11.4 Cu 50mm · 50mm 25 µm 11.8 0 92.9 ± 7.7 Ta 50mm · 50mm 4 µm 2.5 0 126.4 ± 10.5 Mo 50mm · 50mm 50 µm 3.9 0 67.6 ± 5.4

80 Overview of muon induced X-ray ﬂuorescence measurements using thin foils:

Muon induced X-ray spectra, calibrated with 55Fe 1.E+04 55Fe 55Fe, K α Cu, 25micron thick Ta, 4micron thick 55 Fe, Kβ Mo, 50micron thick

1.E+03 Ta, Kα

Ta, K β Mo, Kα

Cu, Kα 1.E+02 Mo, Kβ Counts

Cu, Kβ

1.E+01

1.E+00 0 5 10 15 20 25 X-ray energy [keV] Figure 6: Muon induced X-ray spectra for a thin Copper (25 µm), Tantalum (4 µm) and Molybdenum (50 µm) foil. The energy calibrations is performed with the known K-shell X-ray lines of the radioactive 55F e source at 5.9 keV and 6.5 keV respectively.

The measured as well as the tabulated X-ray energies for the muon induced X-ray ﬂuorescence spectra shown in ﬁg.6 are presented in tab.11.

Table 11: Measured and tabulated [29] X-ray energies for the muon induced X-ray spectra shown in ﬁg.6.

X-ray line Measured X-ray energy [keV] Tabulated X-ray energy [keV] Cu Kα 8.07 8.05 Cu Kβ 8.97 8.9 Ta Lα 8.23 8.15 Ta Lβ 9.44 9.34 Mo Kα 17.72 17.48 Mo Kβ 19.95 19.81

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