Charles University in Prague Faculty of Mathematics and Physics BACHELOR THESIS

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1 Charles University in Prague Faculty of Mathematics and Physics BACHELOR THESIS Martin Slezák The determination of energy of the 9.4 kev gamma ray transition in 83 Rb decay with a precision at level of 1 electronvolt Nuclear Physics Institute Academy of Sciences of the Czech Republic Supervisor: Mgr. Drahoslav Vénos, CSc. Study programme: Physics, General physics 2008

2 Acknowledgements I would like to express my sincere gratitude to Drahoslav Vénos for his professional unremitting support, encouragement, patience and valuable ideas and comments during writing of this bachelor thesis. I also greatly appreciate the support, stimulating conversations and thoughts from Otokar Dragoun. I wish to thank Jaroslav Frána for lending the computer fitting software. I truly appreciate the willingness of the entire electron spectroscopy group at NPI and people involved in Mainz to present and explain to me the fundamentals and depths of the KATRIN experiment. Above all, I am indepted to my family for their everlasting ability to support and encourage me under all possible circumstances. Prohlašuji, že jsem svou bakalářskou práci napsal samostatně a výhradně s použitím citovaných pramenů. Souhlasím se zapůjčováním práce. I declare that I wrote my bachelor thesis independently and exclusively using the quoted references. I agree with lending the work. Prague, 22 November, 2008 Martin Slezák 2

3 Contents Preface 5 1 Introduction to problem Work procedure Experimental setup Rb production method Detector apparatus and geometry Basic fitting software Radioisotope x-ray fluorescence analysis Measurements results Shapes of spectral lines Developed description Asymmetry suppression Measurements and analysis Simulations of possible systematic errors Manganese and krypton calibration lines Copper and arsenic calibration lines Nickel and arsenic calibration lines, gain setups kev line energy for fixed step and slope Verification of applied procedure for energy determination Conclusions and outlook 41 Bibliography 42 3

4 Název práce: Stanovení energie přechodu záření gama 9.4 kev v rozpadu 83 Rb s přesností na úrovni jednoho elektronvoltu Autor: Martin Slezák Katedra (ústav): Ústav jaderné fyziky v.v.i., Akademie věd České republiky Vedoucí bakalářské práce: Mgr. Drahoslav Vénos, CSc., Oddělení jaderné spektroskopie vedoucího: venos@ujf.cas.cz Abstrakt: Námět bakalářské práce úzce souvisí s mezinárodním projektem KATRIN, na kterém se podílí skupina elektronové spektroskopie ÚJF. Projekt KATRIN (KArlsruhe TRItium Neutrino experiment) představuje vybudování unikátního elektronového spektrometru, který umožní stanovit hmotnost elektronového antineutrina s citlivostí 0.2 ev, tj. o řád vyšší než je tomu dosud. Jednou z hlavních činností skupiny je vývoj zdroje konverzních elektronů z rozpadu 83 Rb. Elektrony vnitřní konverze přechodu gama 9.4 kev představují jeden z nástrojů pro studium vlastností budovaného spektrometru. Energie přechodu gama, od níž se odvíjejí hodnoty energie příslušných konverzních elektronů, byla stanovena v několika pracích, ale s rozptylem až 10 ev. V předkládané práci byla metodou gama spektroskopie energie tohoto přechodu stanovena na (4) ev. Klíčová slova: KATRIN, gama spektroskopie, energie přechodu, krypton, rubidium. Title: The determination of energy of the 9.4 kev gamma ray transition in 83 Rb decay with a precision at level of 1 electronvolt Author: Martin Slezák Department: Nuclear Physics Institute, Academy of Sciences of the Czech Republic Supervisor: Mgr. Drahoslav Vénos, CSc., Department of nuclear spectroscopy Supervisor s address: venos@ujf.cas.cz Abstract: The bachelor work is connected with the international project KATRIN in which the group of electron spectroscopy at NPI takes part. The KATRIN project (KArlsruhe TRItium Neutrino experiment) represents a build up of an unique electron spectrometer the aim of which is to measure neutrino mass with sensitivity of 0.2 ev, i.e. by one order of magnitude higher than the current one. Main activity of the group lies in development of conversion electron source based on 83 Rb. Conversion electrons of the 9.4 kev gamma transition act as one of the tools for properties studies of the KATRIN spectrometer. The energy of the gamma transition, from which the energy of related conversion electrons is deduced, was established in several works but with deviation of up to 10 ev. In the present work the energy of this transition was determined by means of gamma spectroscopy to be (4) ev. Keywords: KATRIN, gamma spectroscopy, transition energy, krypton, rubidium. 4

5 Preface One objective of modern physics is to establish the mass of a neutrino as it is of great interest to particle physics, astrophysics and cosmology. Before time the particle was known an inexplainable phenomenon could have been seen in β-decays of radioactive isotopes. In this process of nucleus disintegration, an electron (or positron - dependent on the type of decay) is emitted and can be registered. Observations show that energy spectrum, i.e. dependency of number of detected particles on their energy, of emitted electrons is continuous and not discrete as was expected. In order to explain the effect a very light particle was postulated by W. Pauli in this one was later named neutrino. Existence of neutrinos was then confirmed experimentally in 1956 by F. Reines and C. Cowan. It has been long thought neutrinos do not possess any mass at all and they propagate at speed of light. However, this property is needed to be measured experimentally as theory does not predict what the mass should be. Many attempts were performed to solve the question but only recent experiments (since 1998) revealed that neutrinos actually do carry some small mass. Namely, it was found out neutrinos may have one of three possible lepton flavors and they undergo a process called neutrino oscillations (flavor transformations of neutrinos); according to quantum mechanics a non-zero mass is required for this process. However, from oscillation experiments only differences of neutrino squared masses can be determined. Currently upper limit on the absolute neutrino mass was established 2 ev/c 2 [1]. Nowadays, an effort is made to build up experimental facilities that will be used for determination of the neutrino mass or setting a lower limit for its value. One way to carry out a precise measurement is to inspect the end part of hydrogen isotope tritium β-spectrum, as its shape depends on the mass of the neutrino [2]. However, only a very small fraction of decays fall into this region of energy, therefore a long-term measurement with great preciseness and stability is of both importance and demand. An experimental setup using the principle of a MAC-E filter type spectrometer [3,4] and tritium as a radioactive source is just being prepared at Karlsruhe, Germany; therefore the project was denominated KATRIN (KArlsruhe TRItium Neutrino Experiment). This project will allow measuring the desired (specifically electron antineutrino) mass with a sensitivity of 0.2 ev/c 2, which is a ten times better result compared with the current value. Indeed, it requires much attention to any systematic errors during the experiment as well as precise calibration and long-term stability of all vital systems. Especially, the long term stability of the 18 kv spectrometer retarding voltage at ppm 5

6 PREFACE level represents a problem. As stated in more detail in [2], two primary methods will be applied for energy calibration and spectrometer energy scale monitoring. One of them will use a monitoring spectrometer principially of the same type as KATRIN main spectrometer - upgraded Mainz neutrino mass spectrometer MAC-E filter [3]. Retarding voltage of both the monitoring and main spectrometers will be common (from the same power supply). The monitoring spectrometer will be equipped with a source of mono-energetic electrons the energy of which will be stable and close to the tritium endpoint energy. Measurement of the spectrum will be provided by means of scanning low voltage power supply attached to the source itself. Any change of the energy of mono-energetic electrons measured on the monitoring spectrometer will indicate a possible change of the common retarding voltage. The conversion electrons of the isomeric state of 83m Kr proved to be useful for the calibration and systematic studies in previous tritium neutrino experiments. These electrons are emitted by a process when the nucleus de-excites to a lower energy state, the released energy is however not carried out by a photon but it is rather transformed to an electron located in an atomic shell. After then the electron is emitted. Energies of conversion electrons are therefore given by difference of the transition energy and the binding energy of those from the related atomic subshell. The most important conversion spectral line in this case is formed by K-shell electrons corresponding to 32 kev gamma transition as it has its energy signature very closely spaced to the end point of the tritium spectrum. Precise value of the 32 kev transition energy was determined by various authors, see [5 8], the most recent one using gamma spectroscopy to my knowledge has been reported in [9]. Nevertheless, other conversion lines from 83m Kr decay may and should also be used for either stability check, calibration or comparison with existing results, namely, the conversion electrons corresponding to a gamma ray transition of 9.4 kev. This gamma line shall be designated L-9.4. The energy of L-9.4, however, was measured using gamma spectroscopy with a standard deviation of about 10 ev and more (see [10 12]) only. Another results [7, 8, 13, 14] were obtained using conversion electrons spectroscopy, where the most precise values (with standard deviations of 0.8 ev and 0.35 ev [7,8]) were determined by using theoretically corrected binding energies. Standard deviation of about tens of ev is not sufficient for the planned KATRIN precision. As to have confidential direct value, as precise as possible and for comparison with existing results, the aim of this thesis is to report a new measurement, which has been done using gamma spectroscopy, and its results on the 9.4 kev gamma line energy value. The 83m Kr decays via cascade of 32 kev and 9.4 kev gamma ray transitions to its ground state with a half-life of only 1.83 hours [15]. Fortunately, this isotope is continuously generated by electron capture decay of 83 Rb with a sufficiently long halflife of 86.2 days [15]. That is a reason for which a radioactive sample of 83 Rb produced at Řež cyclotron has been used as the main source of 83m Kr. 6

7 1 Introduction to problem Method used in this work to establish a precise energy value of the desired gamma ray transition line is based on measuring it by means of a semiconductor detector together with characteristic x-ray lines of suitable elements whose energies are well-known from results of previous effort of other authors. These x-rays, which correspond uniquely to specific elements, were chosen in a way that both the energy of L-9.4 is located inside an interval specified by the energies of those x-ray lines and the interval itself is as suitable in its size as possible (i.e. neither very large nor small). X-ray line intensities, required adequately comparable to both one another and the L-9.4 intensity, are considered as well. The precise energy value for L-9.4 can not be established my means of γ- lines as such closely spaced and precise energy γ-lines do not exist. As positions of the peaks in spectra are obtained in channels, where a channel is technically a small interval of energies, using known energy values one receives a single linear relation between energy and channel. Thereby, having its position in channels likewise, the energy of the unknown line can be interpolated. Interpolation procedure for energy determination in gamma ray spectrometry relying on the linearity of the spectrometric chain is successfully used and well described, see [16]. In case of 83m Kr/ 83 Rb and L-9.4 we have an advantage as strong x-ray K α and K β radiations observed in the decay cause fluorescence in nearby material, which means also from intentionally embedded elements. It is therefore possible to measure the x-ray lines together with L-9.4 simultaneously and analyze them in equal experimental conditions. Stability of these conditions, in addition, may also be observed using comparison of spectra measured sequentially. The most important is, however, the determination of reliable spectral line positions. This problem represents the main part of the entire process for energy obtaining. 1.1 Work procedure This thesis is organized in chapters in which all of the analysis problems are one after another carefully examined using measurements or simulations. Conclusions are then made and recommendations to further stages are stated. First of all, experimental setup, rubidium production method and basic computer software is described in Chapter 2. Next, x-ray purity of applied equipment had to be proven. This means that its material would not contain a significant amount of unwanted element(s) which would 7

8 CHAPTER 1. INTRODUCTION TO PROBLEM otherwise radiate parasitic x-ray lines with energies possibly within the region of interest. Any peak present in spectra not having its origin in atoms of desired elements adds an extra feature to fit, therefore making the spectra more difficult to analyze and inducing possible undeterminable and unneeded systematic errors. If parasitic elements in a remarkable quantity (i.e. produced x-rays are intensive enough) are found in the components, exchange of these is to be carried out whenever possible. However, in case they are present in vital parts of the experimental setup, e.g. in the detector itself, it is impossible to suppress them. They have to be identified according to tabled energy values and considered in preparing any further setup. Chapter 3 - Radioisotope x-ray fluorescence analysis reports on this problem. The next no less important stage is to select a proper collimator of γ-rays. The primary task of a collimator is to deflect incoming radiation to the best and most suitable parts of the detector and restrain the background coming from local environment. It was found out that this also leads to lowering of the exponential-like tail on the lower side of spectral peaks, a problem which is widely seen on Si(Li) detectors. However, an immediate effect of a partially shielded detector space is that much less radiation in final arrives at that space. Less events detected cause lower statistics and therefore higher uncertainities, which can only be suppressed by longer exposition times. Consequently a compromise has to be made. Spectral lines characteristics are described and the asymmetry suppression task is solved in Chapter 4 - Shapes of spectral lines. Chapter 5 - Measurements and analysis then leads throughout various analyses which were done in order to obtain confidential L-9.4 energy value. Simulations were performed to be aware of possible systematic shifts. Experience from various combinations of elements and gain setup was earned and used for the most suitable choice of final configuration. An analysis of the final measurement of L-9.4 and characteristic x-ray lines from elements nickel and arsenic is carried out and the energy of L-9.4 is determined. An attempt of verification of the applied procedure is made as well. Eventually, the systematic error of L-9.4 energy is established from known issues. Finally, Chapter 6 - Conclusions and outlook gives a brief characterization of what has been done in this work for L-9.4 energy value determination, comments on comparison with existing results and states future desirable work to be carried out. 8

9 2 Experimental setup Rb production method The production of 83 Rb radioactive source was carried out at the U-120M cyclotron of NPI in Řež with a proton beam via the reaction nat Kr(p, xn) 83 Rb using a water cooled krypton target. Basic features of its design and construction were published in [17]. Pressurized krypton gas (absolute pressure of 7.5 bar at room temperature in volume of 22 cm 3 ) was exposed to external 6 µa proton beam for 12 hours (total beam charge of 250 mc). Primary energy of the proton beam was set to 27.0 MeV, due to energy degradation in the cyclotron output aluminimum window, target titanium input window and the krypton gas itself a beam of about MeV arrived at the gas. This range is optimal for 83 Rb production rate and minimizing amount of 84 Rb. The irradiated target was left for a week to let short lived activities of rubidium to decay. After then the mixture of rubidium isotopes deposited on the target walls was two times washed out by 25 cm 3 of distilled water. Complete produced activity was about 100 MBq [18]. The gamma source was then prepared by passing the rubidium water solution through a cation exchange paper (diameter of 8 mm), drying it in open air and placing it in a safety polyethylen foil. Activity of such source of about 3.9 MBq was obtained. 2.2 Detector apparatus and geometry For all performed measurements a commercial apparatus has been used. This one is represented by a silicon lithium detector of 80 mm 2 5 mm with build-in preamplifier and spectroscopy amplifier (models SL80175 and 2026 from Canberra). The detector is equipped with beryllium window of thickness of 0.05 mm. The resolution of the detector amounts to 180 ev at 5.9 kev energy. Computer-based ADC card TRUMP from EG&G Ortec digitizes the amplifier output signals into 8192 channels which then can be seen in PC computer software. In Fig. 2.1 a view on the gamma spectrometry apparatus is shown. Throughout all measurements various geometry setups were used. The base configuration has been schematically plot in Fig In the figure all dimension values are presented in mm. The detector itself is highlighted by grey filling. The detector is closed in circular stainless steel endcup with the beryllium window. Pure aluminium 9

10 CHAPTER 2. EXPERIMENTAL SETUP Figure 2.1 Canberra Si(Li) gamma spectrometer apparatus. construction (hatched in the figure) supports aluminium collimator and plastic interchangeable cylinder with a lid. The cylinder with suitable height G allows to establish the desired geometry of radioactive source and the detector. The value coll denotes the inner diameter of the collimator construction which will be discussed in Sec The radioactive source itself is situated on the of the lid in the 24 mm diameter hollow. In the text a notation such as G = 48.9 has been used appears. This means that the corresponding measurement geometry was established according to the schematics in Fig. 2.2 with applied support collimator of height G = 48.9 mm. A different geometric configuration was set for the x-ray fluorescence analysis, this one is shown later in Fig Basic fitting software For elementary spectra analysis a fitting software called Deimos, which was kindly lent by its author Mgr. Jaroslav Frána, CSc. from the Department of Nuclear Spectroscopy at NPI Řež, was used. This software fits a Gaussian shape to a spectral peak on a linear or quadratic background in selected region of interest minimizing the chisquare function. Multiple peaks may also be added into the same region. Lorentzian widths of the spectral lines as well as their any asymmetric shaping are not taken into account. Obtained results from the fit are various peak parameters such as its position in channels, full width at half maximum, area, corresponding errors and the background coefficients. With this software multiplets such as from K α or K β x-ray 10

11 CHAPTER 2. EXPERIMENTAL SETUP Figure 2.2 Sketch of the experimental source-detector geometry. The dimensions are given in mm. For further description see the text. line series with the resolution of the detector of about 230 ev in the region of energy interest are indistinguishable from each other. This means only one peak can be fitted for a given multiplet. For more detailed analysis a more advanced programme, which uses the code of the MINUIT package [19], has been applied and the parameters, which are included in the fit with this software, are described in Chapter 4. 11

12 3 Radioisotope x-ray fluorescence analysis When starting a new measurement, experimental conditions and origin of possible background or systematic effects should be known to the furthest possible extent as their knowledge represents useful aid for experimental outcome analysis. The ionizing radiation in 83 Rb decay affects any material nearby including the detector. In particular, electrons mainly from inner shells are being thrown out of atoms of the material. Another electron from a higher shell then fills the created vacancy and energy difference may be emitted in form of a characteristic photon. For photon spectroscopy this results in a significant effect: not only the desired radiation is detected but we acquire such characteristic x-ray photons as well. Nevertheless, we may use this phenomenon on our behalf if we intentionally radiate the required material with strong enough radioactive isotope with well-known spectrum. The detector then registers this spectrum superimposed with various characteristic x-ray lines which are the main concern to us. This method is known as x-ray fluorescence analysis and is widely used just for this objective - to determine the elemental composition of an unknown material [20]. For this purpose we applied a cilcular emitter of a commonly used radioactive isotope 241 Am with a half-life of years [21] and activity of about 3.55 GBq in a ceramic enamel sealed in a frame from stainless steel. The pure spectrum of americium was obtained for example in [22] and energy values of its spectral lines are well-known. Therefore we are able to compare our measurement with this existing one and determine the origin of new peaks. The specific geometry used for this task has been sketched in Fig A dural support construction was placed on top of the detector endcup. Into this support component lead collimator (hatched in the figure) with the 241 Am source (highlighted by black filling) was placed. Shielding by additional lead ring and cadmium cover was used on the top. A typical fluorescence spectrum is plot in Fig The sample used for this exemplary measurement was a disc of 40 mm diameter and 15 mm thickness of leaded bronze with certified concentration of various elements. The corresponding x-ray lines of these elements can be seen in the spectrum, specifically the most intensive lines are from copper which makes about 75 % part of the material. The K α peaks of Fe and Ni (present in the sample by weight of 0.2 % and 1.9 %) demonstate power as for the elemental analysis of the fluorescence method. Beside that parasitic lines of Compton and Rayleigh scattering of the radiation originating in the 241 Am source, titanium and lead are visible as well. 12

13 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS Figure 3.1 Sketch of the fluorescence geometry setup. All dimension values are again presented in mm Cu K α Counts Ti K α Fe K α Ni K α Pb L α Pb L β Scattering Pb L γ Scattering Channel number Figure 3.2 A typical fluorescence spectrum of the certified leaded bronze disc. For explanation of spectral lines see the text. 13

14 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS line type channel energy [ev] Mn K α Np L α Table 3.1 Energy scale calibration values for x-ray peak analysis. Standard deviations are not taken into account for this rough approximation. Energy values are taken from [23]. K α1 and K α2 of Mn are indistinguishable with the Deimos fitting programme, K α line in general is used instead. The energy of this line is calculated as a weighted mean of both K α1 and K α2 energies with their relative intensities according to [24] used as the weights. 3.1 Measurements results For the actual fluorescence analysis three configurations were set up. Firstly, the spectrum without a sample was taken. Secondly, a double-sided polyethylen (PET) casing with one side thickness of 0.23 mm and diameter of about 10 mm was placed in the measured place and thirdly, also a piece of cation-exchange paper of diameter of 8 mm was added. Reason for that is the 83 Rb source itself has been created by passing solution of Rb isotopes through such paper and placed in a PET foil as described earlier so x-ray purity of these components had to be checked as well. The spectra are shown in Fig. 3.3a, 3.3b and 3.3c. The vertical axis scale has been set to logarithmic in all graphs in order to obtain a better insight of lower statistics parts of the spectra, which are of main interest. Exposition live time for all measurements was set to 6 hours each and dead time did not exceed 10 % of real time. First of all, spectral lines originating at the 241 Am source are well visible in all of the three graphs together with peaks from Compton and Rayleigh scattering processes (the two most significant triplets). There are, however, another aspects that need to be pointed out and checked. An effect of the PET foil presence may take place as noticeable from Fig. 3.3b; the foil may be responsible for stronger scattering of some of the radiation from 241 Am to nearby surroundings and to the detector sensitive volume as well. This has also resulted in higher background rate, especially in region of lower energies. Particularly interesting are peaks which do not originally come from the 241 Am source. In order to inspect them more precisely at least rough linear calibration of the channel to energy scale is necessary as pure visual examination is insufficient. Peak analysis has been done using the fitting programme Deimos. A spectrum was recorded using radioactive sources of 241 Am and 55 Fe (Fe was of EFX and Am of EG3 etalon type). In Table 3.1 the used peaks, their locations and energies for the calibration are listed. From these values we find out that coefficients k and q in the calibration equation where E is the energy in ev and c channel number, are E = kc + q, (3.1) k = ev, q = 0.69 ev. (3.2) 14

15 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS Counts Counts Channel number Channel number (a) Background only (b) PET foil Counts Channel number (c) PET foil with a cation-exchange paper Figure 3.3 X-ray analysis spectra. 241 Am peaks are visible, there are, however, more spectral lines not originating in americium (more specifically in its daughter product Np) present as well. Note the 0 line in the spectra with PET foil which is described in more detail in the text. 15

16 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS Energy Energy Peak no. tab [kev] [kev] Lines Ti K α Fe K α Cu K α Au L α Pb L α Au L β Pb L β & Comp Comp Np L α1 & Rayl Pb L γ Comp Comp Comp Np L β1 & Rayl ? unkown Table 3.2 X-ray analysis results. Found values do not correspond exactly to tabled ones, which are taken from [23], as a rough calibration of the energy scale over relatively wide interval is used. In case of a multiplet tabled energy is given for the most intensive line. Single peaks in close multiplets are with this fitting programme undistinguishable with this detector resolution. With these coefficients we are able to determine energies of the unkown lines, compare them with tabulated values published in [23] and specify elements at which corresponding x-ray photons emerge. It is also possible to estimate probable position of the L-9.4. If we take its energy value of ev, as obtained in [7], we determine from Eq. (3.1) a channel number of about 940. From this it is obvious the depicted part of the x-ray analysis spectrum covers well the surroundings of this expected location. In graphs in Fig. 3.3a, 3.3b and 3.3c every recognized line has been marked with an unique number and analysed with the same fitting procedure as the reference lines during the calibration. Results are presented in Tab In the same table experimental values from [23] are shown that best correspond to our measured values both numericaly and physically. This means, since the most probable x-ray transitions in this energy region belong to the K α and K β series and for heavier elements the L series, matching values have been chosen to satisfy these conditions as well. In additon, corresponding element had to be meaningful in a sense that presence of, for example, sulphur in the apparatus or nearby is highly improbable despite the energies would otherwise fit together. Name of the corresponding element is then given likewise. As we can clearly see from Tab. 3.2 and shown spectra (Fig. 3.3b, 3.3a and 3.3c) the main interest should be fixed on a few metallic elements. Titanium, iron and lead spectral lines come mainly from the components used for the measurement geometry. 16

17 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS Copper, gold (and perhaps also iron) on the other hand appear to be part of the material of the detector itself. Other lines seem to have their origin in the 241 Am source itself, therefore they are of no concern as soon as the source is put away. A comparison between the two spectra in addition shows that specific peaks have gained much in intensity, more than other peaks and the background, as the PET foil was added due to the Compton and Rayleigh scattering. We might expect a similar effect when measuring the L-9.4 from 83 Rb/ 83m Kr source placed in the same foil. A difference can also be found in the spectrum measured with cation-exchange paper, Fig. 3.3c; a small increase of Cu lines is apparent. Though the evaluated elements may be very well taken into account as the corresponding energies rest relatively far below the expected energy of L-9.4, this does not hold true for L α series of gold. Despite the fact these are almost not visible in the presented spectra at all, during later measurements with Rb source they become significant. Unfortunately, energies of the most intense lines of these series, L α1 and L α2, are approximately 200 to 300 ev above the energy of L-9.4 [23] and therefore affect the shape of L-9.4 peak. Description of these Au spectral lines is therefore needed to be included in given fitting. Although an attempt had been made to check another Si(Li) detector in the department, no improvement was found. A note should be added to the 10.2 kev energy peak marked with number 0 in the spectra. We were unable to assign its energy to any tabled one either of x- or γ-ray type. This peak has arisen when the PET foil was placed in the measured place so this effect might be a consequence of some process that takes place in the foil. However, later measurements of L-9.4 energy value were performed with much weaker 83 Rb isotope than for the x-ray fluorescence used GBq americium and no peak of 10.2 kev energy has been observed. This anomaly perhaps represents a very low probability phenomenon which is only visible with high activity source in use. Thus from this point now on no other attempts to seek the origin of this effect or to describe it in more detail will be made. One phenomenon has not, however, been pointed out yet. If a measurement with 83 Rb/ 83m Kr is to be performed intense x-ray K α lines of Kr are going to appear in the spectra. We may expect a corresponding so-called escape peak to show up in the spectrum as well. In a case when silicon characteristic photon escapes from sensitive volume of the detector after a photoelectric event, caused by incident x-ray photon, takes place, a lower energy is registered. As the highest probability stands for the K shell electrons of silicon to be emitted by the photoeffect, the K α characteristic photons, being the most probable events similarly, are to appear when the vacancy is filled by another electron from a higher shell. When such a photon escapes from the detector sensitive volume it can not be further registered. Measured energy of the primary incident photon is thus then given by its original value substracted by the energy of the silicon K α characteristic photon. Finally, despite the analysed spectral lines and corresponding elements, undiscovered ones in trace amounts may still be present in the surroundings. The material may consist also of zinc which has its accordant K α lines approximately 800 ev below and 17

18 CHAPTER 3. RADIOISOTOPE X-RAY FLUORESCENCE ANALYSIS K β lines 170 ev under the L-9.4 energy [23]. Attention is therefore required to this lower region; if any peak of such characteristics is to arise, its presence needs to be acknowledged. 18

19 4 Shapes of spectral lines An appropriate description, which should be as precise as possible, of the peaks in spectra is essential to obtain their proper positions on the channel scale. A numerical fitting programme containing this description is thus required. Such programme, which is based on the MINUIT code [19], was developed in the Department of Nuclear Spectroscopy at NPI earlier and has already been used in spectra analysis [9]. In addition, a spectrum simulation programme was developed simultaneously and represents a valuable tool for systematic studies. The fitting is based on minimizing the chi-square function of the free variables that are included in the description of the measured spectrum. Initial parameters are set in the beginning of the fit and changed by the computer performed calculations. In case no problem is encountered and the number of free variables is reasonably not high the fit converges to the chi-square global minimum. The free parameters, which now best characterize the spectrum with the used description, are then returned. This is the primary way in which the positions of the peaks, essential to this measurement, are obtained. Energy E 0 of x-ray or gamma ray transition is in general not an entirely discrete value but it undergoes a widening. Intensity I for a given energy E is described by a profile called Lorentzian distribution I L (E) = I L0 Γ 2 /4 (E E 0 ) 2 + Γ 2 /4, (4.1) where I L0 is the amplitude of the peak (i.e. value of I L for E = E 0 ) and Γ is the so-called Lorentzian width and is physically the full width at half maximum (FWHM) value for the distribution. On the other hand, the spectrometer response function is of Gaussian type, which can be expressed in the term of intensity as I G (E) = I G0 exp ( (E E 0) 2 2σ 2 ), (4.2) where I G0 is the amplitude of the peak. The σ value corresponds to the corresponding full width at half maximum by the relation FWHM = 2σ 2 ln 2. (4.3) 19

20 CHAPTER 4. SHAPES OF SPECTRAL LINES On the whole, an ideal detector for a given radiation registers the intensity distribution which is a convolution of the above mentioned ones and is called the Voigt profile I(E) = + I G (E )I L (E E ) de. (4.4) Therefore if a totally correct description is to be used to fit the spectral lines the Voigt profile has to be utilized. However, in the particular case of a Si(Li) detector the FWHM in the energy region of interest is about 230 ev, but the Lorentzian widths for the x-ray lines are in the order of maximum of several ev. The Lorentzian width for the L-9.4 is even a number of orders of magnitude smaller. Simulations may be performed to show that neglect of the Lorentzian profile with these Γ values causes minimal (less than a tenth of ev) shift to the peak position and is well under the expected precision of L-9.4 energy results. Nevertheless, as real detectors are not ideal, the peaks registered by the apparatus experience various degenerations and asymmetric behaviour. A common effect, which is widely seen with the Si(Li) detectors, is an exponential-like tail on the lower side of energies for a given peak. This results mainly from the Auger radiative effect and incomplete charge collection process, especially at the detector edges. For the time being it was decided to include such behaviour in the peak description in an empirical way. 4.1 Developed description With the mentioned computer fitting programme we are able to perform a fit to a peak or multiple peaks in some arbitrary channel region of interest with the Gaussian or the Voigt profile. In the second case the Lorentzian width has to be entered as stationary. Moreover, the background can be fitted as well up to the second order polynomial degree. Parameters of the peaks, which are fitted and finally returned, are the positions, amplitudes and FWHMs. If the last value from the three is fitted to each peak separately the procedure converges very slowly. Thus a linear dependence of the FWHM on channel number is assumed. This is not an unphysical fact as the linearity of this value may be very well seen in the spectra, especially in small channel intervals such as used in this measurement. A Gaussian and a Voigt profile have been simulated with typical detector resolution and are shown in Fig. 4.1a and 4.1b. The Γ value for the Lorentzian part of the Voigt distribution was intentionally chosen to be unphysically high - about 100 ev - in order to see the shape difference from the Gaussian profile. The asymmetry behaviour of the peaks was chosen to be described by simple, but noticeably accurate, convolution of a delta function and an adjoined rectangular distribution with the Gaussian or Voigt profile. This approach was adopted for example in [5]. The corresponding parameters were called step and slope. For a better explanation a simulated Gaussian peak with an intentionally large step value has been plot in Fig. 4.1c and the same peak with large slope value in Fig. 4.1d. A Poisson 20

21 CHAPTER 4. SHAPES OF SPECTRAL LINES Counts Counts Channel number Channel number (a) Simulated Gaussian profile with the typical detector resolution on a constant background. Note the difference in shape from the Voigt profile visible especially on the low intensity sides of the peaks. (b) Simulated Voigt profile with the same detector resolution and the Lorentzian width Γ = 15 channels on the same constant background Counts Counts Channel number Channel number (c) Simulated Gaussian profile on a constant background with intentionally large step value, which is denoted by the double-headed arrow in the spectrum. (d) Simulated Gaussian profile on a constant background with intentionally large slope value, which is characterised by the angle between the leg and the horizontal dotted line of the triangle, again marked with a doubleheaded arrow. Figure

22 CHAPTER 4. SHAPES OF SPECTRAL LINES distribution type statistics is possible to apply to simulated counts as noticeable from the figures. The step value is basically a difference in background value of the left from the right side of the peak. It is measured in relative units of the delta function amplitude. The real difference size (in counts) seen in the spectrum is therefore not exactly the inserted step value due to the convolution process. The step can be altered during the fitting procedure. The slope value is defined as the difference in background values of the two neighbouring channels taken on the left side of the peaks. Similar as was for the step, after convolution the real observed value is different. The slope can be fitted as well. When this description is put together and placed on a linear or quadratic background a complex structure of the peak is obtained and real measurements can be well described. There are however some disadvantages of such description. Mainly, as the step and slope are completely empirical parameters they can be obtained only experimentally and no theoretical comparison is generally available. Secondly, these parameters describe similar properties of the spectrum as the background, especially linear, and minimization of the chi-square can lead to unphysical results. It is therefore necessary to check these results in every fit and take actions when unphysicalities are encountered. During measurements of L-9.4 energy it is necessary to obtain precise positions of the characteristic x-ray peaks. These peaks consist in first approximation of two separate lines, these are however indistinguishable visually with the detector resolution. An approach, which was finally adopted to overcome this problem, is to fit these doublets with description by two Gaussian peaks with fixed distance and amplitude ratio. This showed to be the most stable fitting procedure compared to a fit with only one Gaussian peak and two Gaussian peaks with free distance and amplitude ratios. The relative intensities (corresponding to the amplitudes) can be taken from [24] and the energy distance from values of [23]. A question should be in what way do we know the distance in channels before the actual energy to channel dependence determination. A method is to choose a value as close to the expected one as possible for the given gain setting, perform the fit and establish the dependence. With this linear coefficient we are able to calculate a new distance for the peaks and perform the fit again. This is repeated until the distance converges to one value, which is then used for the final energy to channel dependence determination, where the absolute coefficient is mainly observed as the linear one is now known, and deriving the unkown energy of L-9.4. As was examined in the previous chapter the L α lines of gold will interfere with L-9.4. The corresponding energies and relative intensities according to [23, 24] are presented in Tab L α2 line is much weaker compared to L α1. Nevertheless, it was decided to take its presence into account by fitting the doublet of gold with fixed amplitude ratio and distance in every L-9.4 analysis as again the fit showed the best stability. 22

23 CHAPTER 4. SHAPES OF SPECTRAL LINES Line type Energy [ev] Rel. intensity Au L α (33) 1.30(6) Au L α (34) 11.6(5) Table 4.1 Energies and intensities per 100 K atomic shell vacancies of the characteristic x-ray lines of Au [23, 24]. Standard deviations are given in brackets for the last digits. Coll. diameter l [ev] h [ev] Counts in max. none mm mm Table 4.2 Observed asymmetry values for given amplitude portion and collimator setup. The s denote distance of the chosen count value from the peak position. The l index states the lower energies part and h index states the higher part. Counts in maximum mean the value in the peak amplitude. 4.2 Asymmetry suppression Despite the developed description of the peak asymmetry behaviour it is profitable to decrease it by physical means. As the effect is caused mainly by the imperfect charge collection process, especially at the detector edges, a proper collimator, which deflects the radiation to as most suitable parts of the detector as possible, should be utilized. The aim is to pick up such collimator which successfully reduces the spectral lines asymmetries but which also does not lower detected counts to far too large extent. A very simple classification of the peak assymetry can be found by inspection of its sides. We choose some portion of the peak amplitude and note down the two energies on both sides where the counts dropped to this chosen value. These energies are then subtracted from the peak mean energy (peak position) and compared. For an ideal symmetric peak these values should be the same. This procedure was performed on the krypton K α1 line emitted from the Rb radioactive source for portion of its amplitude. The value was chosen because it showed an influence of the charge collection imperfections effects but was still clear of any parasitic lines, especially gold ones. Three setups were used - no collimator, an aluminium collimator with 6 mm inner diameter and a different aluminium collimator with 5 mm inner diameter, for more on the geometry see section 2.2. The material used for their manufacturing has been checked for impurities with means of the x-ray fluorescence analysis earlier. All three measurements were performed for 6 hours with dead time of 8.5 %, 7 % and 5.5 %. Obtained results are presented in Tab It is clearly seen that utilization of the 6 mm inner diameter collimator improved the symmetry of the peak to a great extent despite the counts reduction. On the other hand, application of the smaller diameter collimator did not improve the values at all, 23

24 CHAPTER 4. SHAPES OF SPECTRAL LINES but the number of counts dropped even more than in the first case. Therefore, for all further measurements the collimator with 6 mm inner diameter was chosen to be applied. 24

25 5 Measurements and analysis Equipped with proper spectra analysis tools we are now able to examine results from various combinations of elements undergoing fluorescence from 83m Kr/ 83 Rb radioactive source. A proper combination has to be finally chosen in order to establish the energy of L-9.4 gamma ray transition as presicely as possible. As a consequence several setups were ispected, each representing new experience for spectra fitting, L-9.4 energy determination, verification the final configuration is correctly chosen and results confidential. In addition, simulations were performed to determine a possible shift of L-9.4 energy if an unresolved peak arises in close proximity to the L-9.4. Elements for calibration have been used in a way that their corresponding x-ray energies are known to a very good precision according to [23]. Specifically, measurements with the following configurations have been done: radioisotopes 55 Fe and 83m Kr/ 83 Rb with manganese and krypton x-rays used for calibration; elements copper and arsenic with 83m Kr/ 83 Rb inducing Cu and As x-rays; elements nickel and arsenic with 83m Kr/ 83 Rb inducing Ni and As x-rays. Eventually, final configuration of L-9.4 energy measurement is stated and examined in the last section of this chapter. 5.1 Simulations of possible systematic errors We performed an analysis, with means of the analysing computer programme, of simulated spectra of a central peak and a small satellite peak positioned variously on the side of the central one with different amplitude ratios. The spectra were simulated in terms of channels and counts in channels. A linear dependence of energy to channel was assumed. The aim was to simulate the spectra to the most realistic extent and analyse them using a single Gaussian peak description only (with all its parameters free). Difference between obtained and simulated position of the central peak was then observed as well as influence of the Lorentzian shaping on the effect. The values presented here may be used as an estimation of potential systematic error of an analysed spectral line if we are aware of other lines presence nearby. Three groups of simulations together have been performed. The difference between them rests in Gaussian or Gaussian convolution with Lorentzian shaping combination of both peaks. This means that for the first group both lines were simulated as Gaussian with the FWHM, step and slope of the standard ones we obtain from real spectra. For the second the satellite peak was taken as the convolution with the Lorentzian width 25

26 CHAPTER 5. MEASUREMENTS AND ANALYSIS Distance [ev] Lorentz. width Amp. ratio Shift [ev] Shift [ev] Shift [ev] none none Γ s = 7.1 ev none Γ s = 7.1 ev Γ c = 3.6 ev 1/ / / / / / / / / / / / Table 5.1 Simulation analysis results for Gaussian shaping of both peaks, convolution of Gaussian with Lorentzian shaping of the satellite peak and convolution shaping of both peaks. Used Lorentzian widths are shown in the leftmost column; s index states for satellite and c for central peak. The observed shifts between simulated and analysed central peak position are given for a smaller and a larger region of fit, for further explanation see the text. of about 7.1 ev. For the third one also the central peak was taken as the convolution with Lorentzian width of about 3.6 ev. Results are presented for each group in Tab In the uppermost row the values for distance of the satellite peak, positioned to the lower side of energies, from the central one in ev are given. The second column from the left states amplitude ratios of the peaks, the satellite one having a smaller amplitude. Values inside the tables are then the observed shifts of the central peak position when the simulated spectrum was fitted with a single Gaussian line description only; negative values mean shift to lower energies. The first number to the left for a given distance and amplitude ratio corresponds to a fit region of about 430 ev to both sides of position of the central peak, the second number then corresponds to a region of about 715 ev. The table itself is divided into three parts which correspond to the three groups simulated in order as mentioned. The most important group of simulations is represented by the one with Lorentzian widths set for both peaks because it is the most realistic calculation. As it is clear from the table peaks with high count rate (to about one hundredth of amplitude of the central peak) should be undoubtably included in the fit if close enough or excluded if possible, otherwise a relatively very high error propagates into the obtained position. It was also found out that when the fitting interval is adjusted to exclude the satellite peak as far as possible, a shift of maximum 0.2 ev occurs in case of the highest amplitudes. In case of both small and large distance of the satellite from the central peak a 26