Czech Technical University in PragueFaculty of Nuclear Sciences and Physical Engineering

Department of Physics

Study of the properties of the83Rb/Kr source used to calibrateand monitor the spectrometer in the international neutrino

experiment KATRIN

Bachelor’s Thesis

Author: Miroslav KrusSupervisors: RNDr. Milos Rysavy, CSc.

RNDr. Drahoslav Venos, CSc.Academic year: 2005/2006

Abstract

The KArlsruhe TRItium Neutrino (KATRIN) experiment is a next-generation direct neu-trino mass experiment designed to investigate the fundamental mass scale of neutrinos withsub-eV sensitivity in a model-independent way. It combines an ultra-luminous molecularwindowless gaseous tritium source with a high resolution electrostatic retarding spectrom-eter (MAC-E filter system) to measure the spectral shape ofβ-decay electrons close to thetritium end point at 18.6 keV. The determination of neutrino mass requires the precise knowl-edge of the retarding voltage in the analyzing plane of the main spectrometer. Therefore,among others, the energetically well-defined and sharp electron sources will be used to mon-itor its stability. For example, the very appropriate are the K-conversion electrons of83mKrthat have the energy of 17.8 keV. Owing to the short half life of83mKr (1.83 h), a long-termcontamination of the apparatus does not threaten. On the other hand, it also means that re-plenishment of83mKr is necessary. Therefore a solid83Rb/83mKr electron source is underdevelopment which continuously provides83mKr. The aim of this work is to determine therelease of83Rb which would lead to contamination of spectrometer by long-lived83Rb (halflife 86.2 days).Key words: neutrino, experiment KATRIN, monitoring and calibration,83Rb/Kr source

Abstrakt

Experiment KATRIN (KArlsruhe TRItium Neutrino) je vysoce citlivy, modelove nezavislyexperiment urceny ke zmerenı hmotnosti neutrina z tvaru konceβ spektra tritia. Kom-binuje bezokenkovy plynny tritiovy zdroj s elektrostatickym spektrometrem typu MAC-E. Pro urcenı hmotnosti neutrina je nutna presna znalost brzdıcıho napetı. K merenı sta-bility brzdıcıho napetı se krome nekolika dalsıch metod vyuzije energeticky dobre defino-vanych a ostrych zdroju elektronu. Pro tentoucel jsou naprıklad vhodne K-konverznı elek-trony izomernıho prechodu v kryptonu83mKr, ktere majı energii 17,8 keV. Dıky tomu, ze83mKr ma polocas rozpadu pouze 1,83 h, nehrozı dlouhodoba kontaminace spektrometru, nadruhou stranu je ovsem nutna casta vymena kryptonoveho zdroje. Proto se pripravuje zdroj83Rb/83mKr v pevnem skupenstvı. Rozpadem rubidia tak neustale bude vznikat krypton.Cılem teto prace je urcit, jestli se rubidium neuvolnuje z podlozky, coz by vedlo k zamorenıspektrometru dlouhozijıcım rubidiem (polocas rozpadu 86,2 dne).Klıcova slova: neutrino, experiment KATRIN, monitorovanı a kalibrace,83Rb/Kr zdroj

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Contents

1 Introduction 41.1 Neutrino properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 History of neutrino physics . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Implications of neutrino mass . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Double beta decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 The kinematic investigation of neutrino mass . . . . . . . . . . . . . . . . 7

1.5.1 Time-of-flight method . . . . . . . . . . . . . . . . . . . . . . . . 71.5.2 Measurement of the shape of end of spectrum . . . . . . . . . . . . 7

2 The experiment KATRIN 122.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Windowless gaseous tritium source (WGTS) . . . . . . . . . . . . . . . . . 122.3 Transport system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Electrostatic spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Pre-spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Main spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Monitoring and calibration 173.1 Precise retarding voltage measurement . . . . . . . . . . . . . . . . . . . . 183.2 Energetically well-defined and sharp electron sources . . . . . . . . . . . . 18

3.2.1 Conversion electrons from83mKr . . . . . . . . . . . . . . . . . . 183.2.2 Gaseous83mKr source . . . . . . . . . . . . . . . . . . . . . . . . 183.2.3 Quench-condensed83mKr source . . . . . . . . . . . . . . . . . . 193.2.4 Solid83Rb/83mKr source . . . . . . . . . . . . . . . . . . . . . . . 193.2.5 241Am/Co photoelectron source . . . . . . . . . . . . . . . . . . . 193.2.6 109Cd Auger electron source . . . . . . . . . . . . . . . . . . . . . 19

3.3 Monitor spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Absolute energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Electron flux monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 The study of the rubidium release from the83Rb electron source 214.1 Production of83Rb and83Rb/83mKr electron source . . . . . . . . . . . . . 224.2 The gamma spectrometer and the efficiency curve of the detector . . . . . . 224.3 The study of the sample of rubidium source No. S007 . . . . . . . . . . . . 264.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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1 Introduction

1.1 Neutrino properties

Neutrinos, in standard theory, are electrically neutral particles without magnetic moment.Spin of neutrino is equal to1

2. No other interaction of neutrinos, than weak, have been

registered. There are at least three species (or flavors) of neutrinos,νe, νµ, andντ , whichare left-handed1, and their antiparticles, which are right-handed. Electron type neutrinos andantineutrinos are produced in nuclearβ± decay, in particular in the neutron decay process

n → p + e− + νe,

they are also produced in muon decays

µ± → e± + νµ (νµ) + νe (νe),

and as a subdominant mode, in pion decays

π± → e± + νe (νe).

The elementary processes responsible for the nuclear beta decays or pion decays are quarktransition

u → d + e+ + νe

andd → u + e− + νe.

Muon neutrinos and antineutrinos are produced in muon decays, pion decays

π± → µ± + νµ (νµ)

and tau neutrinos are produced in tau decays, e.g.

τ− → e− + νe + ντ .

1.2 History of neutrino physics

Neutrino was first postulated by Pauli [1] in 1930 as an attempt to explain the continuous en-ergy spectrum observed in beta decay [2] under the assumption of energy conservation. Pauliproposed that an undetected particle was carrying away the observed differences between theenergy and angular momentum of the initial and final particles. He assumed that neutrino isa neutral weakly interacting particle with a spin1

2and the mass smaller than electron mass.

The name neutrino was introduced by Fermi2 (in 1933) who developed the first theory de-scribing the neutrino interactions. The first method of the measurement of neutrino mass

1The ”handedness” of a particle describes the direction of its spin along the direction of motion. The spinof a left-handed particle, for example, always points in the opposite direction to its momentum.

2Neutron was discovered several years ago and in Italian it means neutral and big, neutrino means neutraland small.

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was proposed in 1933 by Fermi [3] and Perrin [4], who suggested to search for effects ofneutrino mass via detailed investigation of the high-energy parts ofβ-spectra.Another method of neutrino detection was suggested by Pontecorvo [5]. He proposed to usechlorine-argon reaction

νe + 37Cl → 37Ar + e−

and discussed the possibility of registering solar neutrinos. This experiment was performedby Davies [6] in 1968.In 1934, Bethe and Peires estimated that the cross section for the neutrino should be small,of the order of 10−43 cm2 for a 1 MeV . Reines and Cowan [7] discovered electron neutrinos(or more precisely antineutrinos) emitted from a nuclear reactor in 1956.The neutrino ”handedness” was measured in 1958 in Goldhaber experiment [8] in Brookha-ven National Laboratories. In this experiment the circular polarization ofγ-quanta fromchain of the reactions

e− +152 Eu → νe + 152Sm∗

152Sm∗ → 152Sm + γ,

was measured. The measurement of the polarization of theγ-quanta allowed to determine thelongitudinal polarization of neutrino. It was found that neutrino is the left-handed particle.Lederman, Schwartz and Steinberger showed in 1962 that more than one type of neutrinoexists by first detecting interactions of muon neutrino. In 1989 the LEP accelerator experi-ments [9, 10] at CERN based on the measurement of the decay width of Z0-boson determinedthat there were just three neutrino species. These experiments gave the following number ofdifferent neutrino species:

Nν = 2.993± 0.011.

In 1957 - 58 Pontecorvo [11, 12] proposed that, in direct analogy with (K0-K0)-

oscillations, neutrinos may also oscillate due to (ν − ν)-transformation. After it was con-firmed thatνe νµ are different particles [13], Maki, Nakagawa, and Sakata [14] suggested thepossibility of neutrino flavor oscillations,νe ↔ νµ. In Super-Kamiokande [15, 16] strongevidences for neutrino oscillations were obtained in their atmospheric neutrino data in 1998.Tau neutrino was firstly detected in the DONUT (Direct Observation of the NU Tau) experi-ment [17] at Fermilab in 2000.

1.3 Implications of neutrino mass

• Particle physicsThe Standard Model (SM) describes present experimental data on electroweak scale.In SM charged fermions acquire mass by Yukawa-coupling to Higgs boson. This cou-pling is arbitrary in theory, but the observed pattern of masses and mixing of chargedfermions has no natural explanation in the SM. Therefore the experimental evidencesfor neutrino masses and mixing are the first clear hints of physics behind the SM. Sincethe neutrino masses are much lower than the masses of other fermions, the knowledgeof absolute magnitude of neutrino mass is crucial for understanding the masses offermions in general.

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• Cosmology and astrophysicsNeutrinos play very important role in astrophysics and cosmology. They carry awayup to 99 % of the energy released in the type II supernova explosion and thereforethey dominate the supernova energetics. Neutrino reactions play a crucial role in themechanism of supernova explosions.

It is generally believed that the stellar energy is produced by thermonuclear reactions.For so-called main sequence stars (to which our sun belongs), the main result of thesereactions is a fusion of hydrogen into helium:

4p + 2e− → 4He + 2ν + γ + 26.73 MeV. (1)

The main reaction chain in which the fusion process (1) occurs in the sun is the so-called pp cycle, whereas the so-called CNO (Carbon Nitrogen Oxygen) cycle is re-sponsible for less than 2 % of solar energy. Neutrinos are emitted in six reactionsof the solar pp cycle, they are produced in nuclear beta decay or electron capture re-actions, and their energy spectra are well known. Three of these reaction - pep andthe electron capture into two different final states of7Be - produce monochromaticelectron neutrino lines, whereas the neutrinos born in other reactions have continuousenergy spectra. The fluxes of the solar neutrino are calculated in the framework of thestandard solar models.

Since there are109 times more neutrinos than baryons from Big Bang in the Universe,these neutrinos can play an important role as neutrino hot dark matter (νHDM) in theevolution of large scale [18] structures. Neutrinos of the mass mν ∼ 1 eV could con-stitute the so-called HDM and may be important for galaxy formation. Cosmologicalmodels of forming structure strongly depend on relative amount of dark matter andνHDM in the universe. Therefore the determination of neutrino contributionΩν to to-tal dark matterΩDM in the universe is very important for our understanding of forminglarge-scale structures.

The Big Bang nucleosynthesis depends sensitively on neutrino interactions and onthe number of light neutrino species. Neutrinos may also play an important role inbaryogenesis: the observed excess of baryons over antibaryons in the universe may berelated to decay of heavy Majorana neutrinos.

1.4 Double beta decay

In some cases when the ordinaryβ decay processes are energetically forbidden, the doubleβ decay processes, in which a nucleusA(Z, N) is converted into an isobar with the electriccharge differing by two units, may be allowed:

A(Z, N) → A(Z± 2, N∓ 2) + 2e∓ + 2νe(2νe).

Double decays are processes of second order in weak interactions, and the correspondingdecay rates are very low: typical lifetimes of the nuclei with respect to the 2β decay areT > 1019 years.Doubleβ decays [19, 20] with the emission of two electrons were experimentally observedfor a number of isotopes with half-lives in the range1019 - 1021 years, e.g.48Ca, 76Ge, 100Mo.

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There are very few candidate nuclei for doubleβ+ decay, but the experimental observationof this process is difficult because of the very small energy release.If the lepton number is not conserved, the electron neutrino or antineutrino emitted in one ofelementaryβ decay processes forming the doubleβ decay may be absorbed in another (thismeans that neutrino is identical to antineutrino), leading to the neutrinoless doubleβ decay

A(Z, N) → A(Z± 2, N∓ 2) + 2e∓.

Such processes would have very clear experimental signature: since the recoil energy ofdaughter nucleus is negligibly small, the sum of the energies of the electrons (or positrons)in the final state should be equal to the total energy release, i.e. should be represented by adiscrete energy line. This is the only known process enabling experimentally testing whetherneutrino is Majorana particle.For example, one of the experiments searching for the neutrinoless double beta decay of

76Ge → 76Se + 2e−

is the Heidelberg-Moscow experiment [21, 22] in the Gran Sasso Underground Laboratory,since 1990.

1.5 The kinematic investigation of neutrino mass

In contrast to double beta experiments, the kinematic investigations of neutrino mass do notdepend on any assumptions on the neutrino type (Majorana or Dirac particle). The kinemat-ics experiments can be classified into two categories. Both are based on the relativistic energymomentum relationE2 = (pc)2 +(mc2)2 as well as on energy and momentum conservation.

1.5.1 Time-of-flight method

Measurement by this method uses a very large distance between source and detector. Thedistances of several kpc allows the investigation of small TOF effect resulting from non-zero neutrino mass. It also requires very intensive sources of neutrinos which are providedby cosmic cataclysmic evens like supernovae. The Supernova TOF studies are based onthe observation of energy-dependent time delay of massive neutrino relatively to the lightfrom supernova. The observation of about 20 neutrinos from Supernova 1987A yields theupper limit of the electron neutrino massmν < 23 eV by measuring correlations betweenthe energy and arrival time of the supernova neutrinos. These neutrinos are detected by largeunderground experiments, e. g. Super-Kamiokande, SNO.

1.5.2 Measurement of the shape of end of spectrum

These methods are model independent.The best limits forνe come from observation of the tritium decay

3T → 3He + e− + νe.

There are other neutrino experiments than those with tritium exploiting single-β decay,among those using the sources14C, 35S, 55Fe,63Ni, 71Ge,135I and177Lu.

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Very low endpoint energy E0 is required in kinematic experiments3. This requirement isfulfilled by 187Re and3T which have the two lowest endpoint energies of E0 = 2.6 keV andE0 = 18.6 keV, respectively. Although tritium has a higher endpoint energy as compared to187Re its use has several advantages:

• Tritium decays by super-allowed transition into its daughter nucleus with a half lifeof 12.3 years, compared to the primordial half life of the forbidden transition of187Reof 5×1010 years. The short half life yields a high specific activity and minimizes theinelastic processes of beta electrons within the tritium source.

• Tritium has the simplest atomic shell thus minimizing the necessary corrections due tothe electronic final states or inelastic scattering in the beta source.

In 1991 and 1994 two new experiments started data taking at Mainz and at Troitsk. Theyused a new type of electrostatic spectrometer, so-called MAC-E-Filters, which were superiorin energy resolution and luminosity with respect to the previous magnetic spectrometers.

MAC-E-Filter (Magnetic Adiabatic Collimator followed by an Electrostatic Filter) Thisnew type of spectrometer is based on early works by Kruit [23] and was later redevelopedfor the application to the tritium beta decay at Mainz and Troitsk independently [24, 25].MAC-E-Filter combines high luminosity at low background and a high energy resolution.Both features are essential to measure the neutrino mass from the endpoint region of a betadecay spectrum. The main features of the MAC-E-Filter are illustrated in figure 1. Two su-perconducting solenoids are producing a magnetic guiding field. The beta electrons, whichstarted from the tritium source in the left solenoid into the forward hemisphere, are guidedmagnetically on a cyclotron motion along the magnetic field lines into the spectrometer, thusresulting in an acceptance solid angle of nearly 2π.The magnetic gradient force transforms most of the cyclotron energy E⊥ into longitudinalmotion. This is illustrated in figure 1 at the bottom by a momentum vector. Due to theslowly varying magnetic field the momentum transforms adiabatically keeping the magneticmomentumµ constant (equation given in non-relativistic approximation4)

µ =E⊥B

= const. (2)

This transformation can be summarized as follows: the beta electrons, isotropically emittedfrom the source, are transformed into a broad beam of electrons flying almost parallel to themagnetic field lines. This parallel beam electrons are energetically analyzed by electrostaticpotential created by a system of cylindrical electrodes. All electrons, which have enoughenergy to pass the electrostatic barrier, then are reaccelerated and collimated onto a detector,all others electrons are reflected. Therefore the spectrometer acts as an integrating high-energy pass filter, the relative sharpness of this filter is given only by the ratio of the minimum

3On the other hand, very smallness of the decay energy implies that the Coulomb interactions betweenthe outgoing beta electron and the atomic electron in the final daughter ion may play a significant role inthe interpretation of the experiments. The strength of this Coulomb interaction is governed by the parameterη = α

v , whereα is fine structure constant andv is velocity of the emitted beta electron. For example, near thetritium endpoint,η ≈ 0.03.

4for relativistic particlesµ = (γ + 1)E⊥B

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Figure 1: Principle of the MAC-E-Filter. Experimental setup (top), Momentum transforma-tion due to the adiabatic invariance of the magnetic orbit momentumµ in the inhomogeneousmagnetic field (bottom).

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magnetic field Bmin in the analyzing plane in the middle and the maximum magnetic fieldbetween beta source and spectrometer Bmax:

∆E

E=

Bmin

Bmax

. (3)

The beta spectrum can be measured by scanning the electrostatic retarding potential. Bothexperiments at Mainz and Troitsk used similar MAC-E-Filters, which differed slightly insize: the diameter and length of the Mainz (Troitsk) spectrometer are 1 m (1.5 m) and 4m (7 m), respectively. In order to suppress electrons which have a very long path withinthe tritium source and therefore exhibit a high scattering probability, the electron source isplaced in magnetic fieldBS (fig. 2), which is lower than the maximum magnetic fieldBmax.This restricts the maximum accepted starting angle of the electronsθmax by the magneticmirror effect to:

sin θmax =

√BS

Bmax

.

Up to now, direct kinematic searches of neutrino mass produced only the upper limits

mν1 < 2.05 eV at 95% CL (Troitsk [26])

< 2.3 eV at 95% CL (Mainz [27]) (4)

mν2 < 170 keV at 90% CL (PSI [28]; π+ → µ+ + νµ) (5)

mν3 < 18.2 MeV at 95% CL (ALEPH [29]; τ− → 5π + ντ ), (6)

whereν1, ν2,andν3 are the primary mass components ofνe, νµ, andντ . The limits in eqs. 5,6 come from comparison of the total energy release with the energy of decay products. Thelimits in eq. 4 are obtained from the tritium beta decay experiments and are based on theanalysis of the so-called Kurie plot (fig. 3). The electron spectrum in the allowed beta decayis

Ne(Ee)dEe ∝ F (Z,Ee)√

E2e −m2

eEe(E0 − Ee)√

(E0 − Ee)2 −m2νdEe (7)

hereF (Z, Ee) is the Fermi function describing the electromagnetic interaction between theemitted electron and the daughter nucleus andE0 is the released energy. The shape of thebeta spectrum near the endpoint depends on whether or not neutrinos have mass.It follows from the equation that the plot of the Kurie function

K(Ee) =

√√√√ Ne(Ee)

F (Z, Ee)peEe

(8)

versusEe should be straight line whenmν = 0 but should have a different shape close to theendpoint of the spectrum whenmν 6= 0. However, all the experiments showed some excessof the number of the electrons near the endpoint of the spectrum rather than a deficiency thatis expected ifmν 6= 0. This excess is most likely due to unknown systematic effects.

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Figure 2: Schematic view of magnetic fields of a tritium beta decay experiment consistingof a source, a spectrometer of MAC-E-Filter type and a detector (omitting an optional pre-spectrometer).

Figure 3: Kurie plots formν = 0 (solid line) andmν 6= 0 (dashed line)

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2 The experiment KATRIN

2.1 Overview

The tritium beta experiments at Troitsk and Mainz almost reached their limits of sensitivityto the neutrino mass. To decrease the limit into sub-eV region, a new experiment with muchhigher neutrino mass sensitivity is needed. The prepared experiment KATRIN [30, 31, 32](KArlsruhe TRItium Neutrino) is based on long-term experience with present spectrometersof MAC-E type and it is prepared by groups from Bonn, Fulda, Karlsruhe, Mainz, Munster,Rez, Seattle, Swansea, and Troitsk. The setup of KATRIN corresponds to∼ 70 m long linearconfiguration with about 40 superconductive solenoids, which adiabatically guide electronsfrom source to detector. The whole configuration of KATRIN (fig. 4) can be grouped intofour major functional units:

• a high luminosity Windowless Gaseous Tritium Source (WGTS) and Quench Con-densed Tritium Source (QCTS)

• an electron transport and tritium pumping section, containing an active differentialpumping section and a passive cryogenic pumping section

• a system of two electrostatic retarding filters with a smaller pre-spectrometer for pre-filtering and a larger main spectrometer for energy analysis of electrons

• a semi-conductor high-resolution low background detector to count the electrons trans-mitted through the electrostatic filters.

Figure 4: The 70m long KATRIN reference setup with its major components: a) the window-less gaseous tritium source WGTS, b) the transport elements, containing an active pumpingpart and a passive cryotrapping section, c) the two electrostatic spectrometers and d) thedetector forβ-counting .

2.2 Windowless gaseous tritium source (WGTS)

The WGTS allows the measurement of the endpoint region of the tritium beta spectrumand consequently the determination of the neutrino mass with a minimum of systematicuncertainties from the tritium source. It consists of a 10 m long cylindrical tube of 90 mmdiameter, filled with molecular tritium gas of high isotopic purity (>95%).

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The tritium will be continuously fed through a capillary to an injection chamber in the middleof the tube where it is injected through more than 250 holes of diameter of 2 mm thusavoiding gas jets. The tritium molecules freely stream to both ends and there they are pumpedaway by a series of differential turbomolecular pump station. The working temperature of27 K and central tritium pressurepin = 3.35×10−3 mbar at the injection point result in a totaltritium column density ofρd = 5 × 1017 molecules/cm2. This calculation assumes that thepressure at the ends is zero. The real pressurep at the ends will be0.035 pin < p < 0.05 pin.The stability of the temperature to 0.1 %, which is achieved by a boiling liquid neon cryostatsurrounding the tritium tube, is very important for the stability of the column densityρd . Themagnetic field over the full volume of the tritium source (BS = 3.6 T) guides the electronsadiabatically to both ends of the cylindrical tube.

2.3 Transport system

The electron transport system adiabatically guides beta decay electrons from the tritiumsources to the spectrometer, while at the same time it eliminates any tritium flow towardsthe spectrometer, which has to be kept practically free of tritium for background and safetyreasons. The tritium flow (T2 and HT molecules) into the pre-spectrometer should be smallerthan10−14 mbar l/s to limit the increase of background caused by decay of tritium moleculesin the pre-spectrometer as well as in the main spectrometer to10−3 counts/s.Fig. 5 shows the electron transport system schematically. Differential pumping sectionDPS2-F is followed by two cryo-pumping sections (CPS1-F and CPS2-F).

Figure 5: Schematic drawing of the Transport System.

The CPS1-F cryostat also houses a split coil magnet for insertion of Quench CondensedKrypton Source (QCKrS).

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DPS2-F [33] The differential pumping section consists of five 1 m long beam tubes of 75mm diameter within a superconductive solenoids of 5.6 T field. The magnetic flux of 191T cm2, which is needed to transport electrons from the WGTS to the pre-spectrometer andmain spectrometer, requires a diameter of 66 mm thus leaving more than 4 mm of radialclearance.

The cryo-pumping section (CPS1-F and CPS2-F) [34, 35] In the next part of the trans-port system, the cryosorption section, all remaining traces of tritium will be trapped onto theliquid helium cold surface of a transport tube surrounded by transport magnets. It is con-sidered to cover the tube surface with a condensed argon polycrystal layer or graphite forbetter trapping. The cryopumping section consists of two parts, CPS1-F and CPS2-F. Eachsection consists of three individual transport elements of again 1 m length and 75 mm diam-eter within superconducting coil with central magnetic field of 5.6 T. The different tubes aretilted by 20 to each other, thus prohibiting a direct line of sight.

2.4 Electrostatic spectrometers

As mention above, the electrostatic filter system of KATRIN consists of two spectrome-ters of MAC-E-Filter type: the pre-spectrometer and the main spectrometer (fig. 6). Thepre-spectrometer, working at a fixed retarding energy of approximately 300 eV below theendpoint of the beta spectrum, allows only electrons with the higher energies to pass into themain spectrometer. The main spectrometer analyzes the kinetic energy of electrons with aresolution of 0.93 eV. The main task of the pre-spectrometer is to limit the number of elec-trons, which might scatter on the residual gas molecules in the main spectrometer, therebyincreasing the rate of background events. The high resolution of the main spectrometer re-quires large dimensions. The diameter of main spectrometer is 10 m and length is 23.3 m.Both spectrometers are connected by two 1 m long superconductive transport magnets.

2.4.1 Pre-spectrometer

The pre-spectrometer plays a major role both in the developmental phases and during tritiummeasurements. It fulfills several tasks:

• It serves as a prototype for the main spectrometer, verifying the extreme high vac-uum (XHV) concept, testing the reliable operation of the heating/cooling system andinvestigating the performance and properties of the new electro-magnetic design.

• During normal tritium measurements it will operate as a pre-filter, reducing the incom-ing flux of electrons into the main spectrometer from 1010 s−1 to 104 s−1.

The requirements on the energy resolution of the pre-spectrometer are moderate, becausea resolution of∆E ≈ 300 eV is sufficient to reduce the flux of beta electrons by a factorof 106. This reduction factor can be achieved by fixing the retarding energy at about 300eV below the tritium endpoint energy E0. The lower flux minimizes the chances to createbackground by ionization of residual gas molecules in the spectrometers.The pre-spectrometer is a cylindrical tank with a length of 3.38 m and the inner diameter of1.68 m. The dimensions are comparable to the MAC-E-Filters at Mainz and Troitsk. The

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Figure 6: The electrostatic filter system of KATRIN consists of a pre-spectrometer to rejectall low energy electrons, followed by a large main spectrometer with an energy resolution of0.93 eV . Both spectrometers are connected by two superconducting transport solenoids.

walls of the vessel are made of 10 mm thick stainless steel.The whole pre-spectrometer is a small copy of the KATRIN main spectrometer. All essen-tial technical challenges of the KATRIN main spectrometer (for example XHV less than10−11 mbar, high-voltage on the hull of the vessel up to 35 kV and the nearly massless innerelectrode system) have also to be met for the pre-spectrometer. Therefore the KATRIN col-laboration decided to build the pre-spectrometer at an early stage of the experiment to testthe new ideas and their technical solutions.

2.4.2 Main spectrometer

The main spectrometer will be the key component of the KATRIN experiment. It is a largeelectrostatic spectrometer with diameter of about 10 m and total length of 23.3 m. Two su-perconductive solenoids will generate a strongly inhomogeneous magnetic field guiding theelectrons through the spectrometer. Additional air coils will alow fine-tuning of the magneticfield in the centre and compensate the earth magnetic field. Like the pre-spectrometer, theouter hull of the main spectrometer will be on high potential, serving as a guard electrodefor more accurate high voltage on the inner wire electrodes. This high resolution MAC-E-Filter will allow the tritium beta decay endpoint to be scanned with higher luminosity and aresolution of 0.93 eV, which is a factor of 5 better than previous MAC-E-Filters.Since the background rate has a direct influence on the sensitivity of KATRIN on the neutrinomass, the vacuum requirements for this big vessel are very demanding. The main vesselwill be manufactured from stainless steel sheets selected both for its strength and excellentmagnetics properties. The weight will be approximately 200 tons. The thickness will vary

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from 25 mm to 32 mm.The properties of the vessel are:

• inner diameter of the cylindrical section: 9.8 m

• total length: 23.28 m

• inner surface: 650m2

• volume: 1400m3

2.5 Detector

All electrons passing the retarding potential of the main spectrometer are re-accelerated totheir initial energy and magnetically guided by 2-solenoids detector transport system to thefinal plane detector. This detector has to detect

• electrons from tritium beta decay with energies up to 18.6 keV

• conversion electrons from83mKr with energies from 17.8 keV up to 32 keV (used forcalibration)

• electrons from a high rate (∼ 100 kHz) electron gun

The detector background is defined as the remnant background, when there is no directconnection between the detector and the main spectrometer. This background comes fromthe following components:

• Background due to radioactive contaminations in the material used, in particular dueto events from the238U and232Th decay chain.

• Cosmic induced background from prompt events (e. g. muons, neutrons).

16

3 Monitoring and calibration

The determination of neutrino mass from the measurement of the tritium beta spectrum nearthe endpoint by the KATRIN experiment requires the precise knowledge of the energyEret

in the analyzing plane of the main spectrometer. This energy is determined by the retardingelectrostatic potential at the analyzing plane and the scanning potential Us applied to thesource.KATRIN needs not only a very high short-term stability of the retarding voltage, but alsoa method to measure it with a 50 mV precision for at least three years data taking. For aretarding voltage of 18.6 kV this corresponds to a long-term relative precision better than 3ppm. The precise measurement of the scanning voltageUs, which will not exceed 100 V,does not represent any problem.On the other hand, the numerical studies [36] have shown that an unrecognized shift of Eret

by 0.05 eV would result in the systematic error of the fitted neutrino mass as large as 0.04eV which is a substantial part of the expected KATRIN sensitivity to mν .One will utilize several methods to monitor the retarding potential in the KATRIN experi-ment to achieve a high degree of redundancy:

• Direct retarding voltage measurementA high-precision voltage divider will divide the retarding voltage U down to about 10V, which is then measured with a high-precision digital voltmeter.

• Monitor spectrometerCalibration measurements in the main system cannot take place concurrently with tri-tium measurements. However, it is necessary to monitor the stability of the retardingvoltage during tritium runs. There the retarding voltage of the main spectrometer willalso be applied to a third electrostatic analyzer of the MAC-E type. The task of thismonitor spectrometer is to measure the energy of a well-defined sharp photoelectron-or conversion electron line which is compared to the retarding energy of the KATRINmain spectrometer. The use of monitoring data for the absolute calibration of retardingvoltage of the main spectrometer will be also considered.

• Direct calibration of the main spectrometerThe spectroscopy of photoelectrons from241Am/Co source or of conversion electronsfrom a83mKr source will be done repeatedly with KATRIN main spectrometer to ab-solutely calibrate the retarding energyEret under measurement conditions.

All the three methods will be used not only to monitor the stability of the KATRIN retardedenergy, but also to perform an absolute energy calibration repeatedly. The absolute calibra-tion is necessary not only to check the stability of all monitor systems, but also to compare theendpoint energy E0 obtained by fitting the measured tritium beta spectrum with the helium-tritium mass difference∆m (3He - 3H), determined by cyclotron resonance measurements inPenning traps [37]. Any significant difference would point towards an unrecognized system-atic error.

17

3.1 Precise retarding voltage measurement

The retarding voltage of the KATRIN main spectrometer will be reduced by a precision high-voltage divider [38] down to a voltage below 10 V which is ideally suited for state-of-the-arthigh precision digital voltmeters. Whereas suitable voltmeters are commercially availablewith a precision and long-term stability at the ppm-level, voltage dividers are commerciallyavailable only with a stability and precision of 10−5, too low to be suited for KATRIN.Therefore, with support from the German Physikalische - Technische Bundesanstalt (PTB)in Braunschweig, a high precision high voltage divider is developed. The aim is a long-termstability and precision at the 1 ppm level for a maximum voltage of 35 kV.

3.2 Energetically well-defined and sharp electron sources

To calibrate the KATRIN retarded energy absolutely and to check the stability of the high-voltage measurement setup, energetically well-defined and sharp electron sources are needed.There can be applied several kinds of sources:

• conversion electrons from83mKr in different physical states

• photoelectron sources with well-defined photon energies

• Auger electrons from109Cd

3.2.1 Conversion electrons from83mKr

The K-conversion electron line of the 32 keV transition in83mKr (K-32) has the energy of17.8 keV and natural width of 2.8 eV [39]. Since this energy differs by only 0.8 keV fromthe endpoint energy of the tritium spectrum, the K-32 line is well suited for the tasks ofabsolute calibration and monitoring of the spectrometer energy scale. Although the strongL3-32 line has an energy of 30.5 keV, well above the tritium beta decay endpoint, it may beadvantageous for special investigations due to its natural width of 1.2 eV [40]. The half lifeof 83mKr is only 1.83 d. On one side this avoids any danger of a long-term contamination ofthe apparatus, but it also means that replenishment of83mKr is necessary.The gaseous83mKr will be utilized in the first application to check the properties of theWGTS as well as for absolute energy calibration of the apparatus. For the latter task theenergy of this conversion line has to be known with high precision.

3.2.2 Gaseous83mKr source

Even more important than the absolute energy calibration is the use of gaseous83mKr withinthe gaseous tritium determining the distribution of the electric potential within the WGTSprecisely. For this purpose the WGTS will run with a83mKr admixture to gaseous tritium.To avoid freeze-out of the krypton it is needed to increase the WGTS temperature to 120 -150 K.

18

3.2.3 Quench-condensed83mKr source

A small vacuum vessel containing83Rb implanted into polyamide foil generates gaseous83mKr emanating from the foil. The krypton gas is purified by a cold trap and quench-condensed on a highly oriented pyrolytic graphite (HOPG) substrate. The advantages of thissource are its very easy maintenance, the isotropic electron emission, the possibility of veryhigh count rates, the constant electron emission rate, which is only governed by the 1.83 hhalf life, and compatibility with UHV requirements.

3.2.4 Solid83Rb/83mKr source

To avoid the necessity to repeat the83mKr film quench-condensation every few hours due tothe short half life of83mKr, one is considering to build a solid83Rb/83mKr electron source.83Rb is evaporated in vacuum onto HOPG or metal backing.83Rb decays with a half life of86 days, thereby continuously generating83mKr. Such a source would be more convenientfor handling due to its compactness. (See chapter 4)

3.2.5 241Am/Co photoelectron source

Precise energy calibration of electron spectrometers at energies up to several keV is oftenperformed by means of photoelectrons induced by X-rays. However, increasing the naturalwidth of exciting X-radiation from heavier elements decreases the accuracy of this methodat higher electron energies. Therefore theγ rays will be used from a241Am-source hit-ting a thin cobalt foil. The photoelectrons ejected by 26 344.6± 0.2 eV [41] gamma-ray photons of241Am from the atomic K-shell of metallic cobalt with binding energy of7 708.78± 0.02 eV [42] have a kinetic energy near the endpoint of the tritium beta spec-trum. The241Am/Co photoelectron source would be suitable for our purpose:

• the energy of monitoring photoelectrons, 18.636 keV differs from the tritium endpointonly by about 60 eV and the calibration line is above the beta spectrum (that meanswithout background)

• the natural width of exciting gamma-rays, its Doppler broadening at 300 K and recoilenergy are less than 0.02 eV, i.e. completely negligible for our purpose.

• the natural width of atomic K-shell in cobalt is 1.3 eV

• the241Am half life of 432 y is practical for long term monitoring

3.2.6 109Cd Auger electron source

Another monitoring source could be109Cd. The important properties of cadmium nucleusare:

• electron capture decay into109Ag [43]

• only low X-ray energy emission

19

• emits in 9 % of decays KL2L3(1D2) Auger electrons of 18 511.7± 1.3 eV [44]

• the natural width of the KL2L3 line is 11.2 eV [40]

• half life of 463 days

Although the line width of the KL2L3 (1D2) is rather broad compared to 50 mV, the requiredlong term stability of the KATRIN filter voltage, it can be used at least complementary tothe other envisaged nuclear standards. It is expected that thin metallic sources of more than200 kBq can be made. Since the source is metallic one, it is suitable for UHV applications,although it should not be heated to more than 100 - 200C since cadmium melts at 320Cand is easy to oxidize.

3.3 Monitor spectrometer

The spectrometer of the former Mainz Neutrino Mass Experiment is available for KATRIN.The energy resolution of this spectrometer is 4.8 eV, this value has been chosen as a compro-mise between energy resolution and luminosity for tritium beta spectrum measurements. ForKATRIN, the existing Mainz spectrometer will be upgraded into a high resolution one. Theenergy resolution will be improved by factor 5 down to 1 eV. The corresponding luminositydoes not play a role for calibration and monitoring purposes.

Figure 7: Setup of the monitor spectrometer beam line with a calibration source followingan atomic/nuclear standard and fed with the main spectrometer retarding potential.

The idea is to apply the retarding voltage of the KATRIN main spectrometer to this moni-tor spectrometer (Fig. 7). A well-defined electron source will then be measured by varying

20

the voltage of the electron source allowing practically continuous monitoring of retardingvoltage. Such low voltages well bellow 1 kV can be measured very precisely and reliably.The work functions of the monitor spectrometer and the main spectrometer are very sim-ilar (practically identical) as in both cases stainless steal under XHV conditions is used.Absolute calibration additionally requires the precise knowledge of the parameters of bothsources and the potential distribution in the analyzing plane of both spectrometers. Electronsources which may fulfill the above requirements are the241Am/Co photoelectron source,the quench-condensed83mKr source or the83Rb/83mKr source.

3.4 Absolute energy calibration

One will use the gaseous83mKr source in the WGTS as well as the condensed83mKr sourceand the241Am/Co source at the position of the alternate QCTS in the split coil magnet tocalibrate the main spectrometer directly. Although in contrast to calibration of the highvoltage at the monitor spectrometer these measurements require parts of the time availablefor tritium beta decay measurements, they are more direct and give redundant information,e.g. they probe also time variations of the work function of the main spectrometer.The conversion and photoelectron sources will be used not only to monitor the stability ofthe high-voltage systems and work functions. For an absolute calibration of the retardingenergy, the fitted beta endpoint will be compared with the tritium-helium mass difference∆m(3He− 3H)[37], determined by cyclotron resonance measurements in Penning traps.Any significant difference will point to unaccounted systematic errors.

3.5 Electron flux monitor

The WGTS strength will be frequently monitored by lowering the retarding potential tofacilitate rapid determination of the electron flux from the source with precision better than10−3. Additionally electron flux monitors will be installed behind the source to monitorthe electron flux over wide ranges of beta energies and to check the stability of the sourceoperation.

4 The study of the rubidium release from the83Rb electronsource

In order to avoid the contamination of the electron spectrometer by long-lived83Rb, theevaporated open83Rb/83mKr source has to be tested on the release of the83Rb. This test wasrealized by the measurement of activities of the source in different times. From compari-son of these activities with the exponential decay law can be established the amount of thereleased rubidium. The activity of83Rb was measured by means of the gamma spectrometry.83Rb decays by electron capture with a half-life of 86.2 d into the short-living isomeric state83mKr (1.83 h), i.e. the83mKr isomer is continuously generated by the decay of83Rb.

21

4.1 Production of 83Rb and 83Rb/83mKr electron source

The production of the83Rb was carried out at the U-120M cyclotron with a H− ion beam viareactionnatKr(p, xn)83Rb using a krypton gas target. The pressurized krypton gas (absolutepressure 7.5 bars, 22 cm3) was exposed to the external 6µA proton beam for 10 h (totalcharge of about 220 mC). The effective energy used for the production reaction was in therange 19.2 - 21.7 MeV. This range is optimal for83Rb production rate, and minimizing theamount of84Rb.The rubidium water solution contained an admixture of rubidium isotopes with mass num-bers A = 83, A = 84 (T1/2 = 32.9 d), and A = 86 (T1/2 = 18.66 d). The relative abundance ofisotopes83Rb, 84Rb and86Rb amounted to 10:1:0.2. The admixture will play no role if theKATRIN WGKrS or QCKrS are used, as the admixed isotopes decay into stable krypton andstrontium nuclei. A mixture of rubidium isotopes, that was absorbed at surface of the targetchamber, was eluted from it by 25 ml of distilled water.This water solution was filled into a quartz glass vessel. During the heating of the solutionwith an infralamp the rubidium was deposited on the walls of the vessel. The deposition waswashed with a smaller amount of distilled water. Further concentration and purification wasdone with a chromatography column. Finally, several drops (4.5µl) of the water solutionwere moved into the tantalum evaporating boat and gradually dried at room temperature.Then this boat was fixed in vacuum evaporating apparatus. At first, the boat was heated upto 200C for about ten minutes with a shutter between the boat and a substrate, in order torelease the impurities. Then the shutter was moved and the boat was heated up to 800C forabout one minute, in order to evaporate rubidium onto the 50µm thick aluminium substrate.

4.2 The gamma spectrometer and the efficiency curve of the detector

The gamma rays were detected by commercial apparatus. A HPGe detector (Schlumberger)of N type with relative efficiency of 22.3% and with resolution of 1.8 keV at 1.3 MeV wasused. The electronic chain was supplied by company Nuclear Data. The signal from thepreamplifier output was processed by amplifier ND591 and further digitized by ADC con-vertor ND581. The measured spectra were stored in PC equipped with Accuspec acquisitioninterface board. The detector high voltage of 4 kV was supplied by high voltage instrumentND360.In the measurement we have used Accuspec in-built system of live time, i. e. the apparatusdead time was taken into account.At first, the absolute efficiency of the detector in dependence on energy for suitable geometrysource - detector was measured. Theγ ray standards152Eu and133Ba (Tab. 1) were used forthe determination of the efficiency curve of the HPGe detector. The relevant activityA wascomputed for the date of measurement from the formula

A = A0

(1

2

) tT1/2

,

whereA0 is the activity related to reference date,T1/2 is half life of 83Rb, andt is elapsedtime. The error of the activity∆A was computed from the formula derived according to the

22

error propagation law

∆A =

√√√√(

∂A

∂A0

)2

(∆A0)2 +

(∂A

∂T1/2

)2 (∆T1/2

)2.

The absolute efficiencyε of detector was computed from the formula

ε(E, P, p) =P

p100

tA, (9)

whereP represents number of counts for transition energyE (area of relevant peak in thespectrum),p is probability of transition per decay in %,t is time of measurement, andA isthe activity of the source. For the efficiency error, the formula was obtained according to theprescription

∆ε =

√√√√(

∂ε

∂A

)2

(∆A)2 +

(∂ε

∂P

)2

(∆P )2 +

(∂ε

∂p

)2

(∆p)2.

Table 1: Theγ ray standards and the basic information about the measurement

152Eu 133Ba

half time T1/2[y] 13.537(6) 10.51(5)

number of standard 957-02 837-12

activity A0[kBq] 547.50 (error 2.2%) 208.10 (error 1%)

ref. date 18. 6. 1986 7. 3. 1986

date of measurement 27.10. 2005 27.10. 2005

exposure time [h] 5 5

geometry cylinder 173 mm+lid+paper cylinder 173 mm+lid+paper

elapsed time t [y] 19.358 19.64

activity A [kBq] 203.2(45) 58.98(67)

The numerical results of calculation and analysis are presented in Tab. 2 and Tab. 3The efficiency curve is plotted in the Fig. 8. The plotted data were smoothed by a polynomialtrend for energies from 50 keV to 300 keV and by a power trend for energies from 200 keVto 1600 keV.

23

Table 2: The measured areas and computed values of efficiencies for133Ba

Energy Area error probab. error efficiency error

of trans.

[keV] [count] [count] [%] [%] [10−3] [10−3]

53.1610 47195 661 2.1990 0.0220 2.0925 0.0382

79.6140 80233 3771 2.6200 0.0600 2.9857 0.1446

80.9970 1045600 12547 34.0600 0.2700 2.9930 0.0502

160.6100 20815 687 0.6540 0.0080 3.1030 0.1087

223.2300 10962 285 0.4500 0.0040 2.3750 0.0678

276.4000 145830 875 7.1640 0.0220 1.9846 0.0262

302.8500 341900 2051 18.3300 0.0600 1.8186 0.0240

356.0200 987070 6909 62.0500 0.1900 1.5509 0.0212

383.8200 132850 797 8.9400 0.0300 1.4488 0.0191

Figure 8: The efficiency of HPGe detector measured by152Eu and 133Ba nuclear standards.

24

Table 3: The measured areas and computed values of efficiencies for152Eu

Energy Area error probab. error efficiency error

of trans.

[keV] [count] [count] [%] [%] [10−3] [10−3]

121.7817 3494467 45485 28.5800 0.0600 3.3430 0.0855

244.6975 623871 1903 7.5830 0.0190 2.2494 0.0500

295.9392 30745 492 0.4470 0.0050 1.8806 0.0512

344.2785 1590694 8004 26.5000 0.4000 1.6412 0.0370

367.7887 48491 679 0.8610 0.0050 1.5399 0.0402

411.1163 113112 566 2.2340 0.0040 1.3843 0.0312

443.9650 145829 875 2.8210 0.0019 1.4134 0.0322

488.6792 17482 507 0.4190 0.0030 1.1407 0.0415

503.4740 6420 302 0.1490 0.0080 1.1781 0.0611

563.9900 18414 368 0.4890 0.0060 1.0295 0.0306

566.4300 5537 233 0.1290 0.0019 1.1735 0.0556

586.2648 16482 396 0.4590 0.0050 0.9818 0.0320

674.6750 5878 200 0.1720 0.0040 0.9344 0.0378

678.6230 14516 319 0.4710 0.0040 0.8426 0.0262

688.6700 26759 375 0.8570 0.0080 0.8537 0.0223

719.3490 9723 301 0.2780 0.0080 0.9562 0.0364

778.9040 361750 1085 12.9420 0.0190 0.7642 0.0170

810.4510 9253 361 0.3200 0.0030 0.7906 0.0354

867.3780 107843 647 4.2450 0.0190 0.6946 0.0158

919.3300 10461 272 0.4270 0.0060 0.6698 0.0228

926.3170 6650 206 0.2780 0.0050 0.6540 0.0249

964.0790 337871 1042 14.6050 0.0021 0.6325 0.0141

1005.2720 18215 328 0.6460 0.0050 0.7709 0.0219

1085.8690 212640 851 10.2070 0.0210 0.5696 0.0127

1089.7370 36766 294 1.7270 0.0060 0.5821 0.0136

1109.1740 4659 168 0.1860 0.0080 0.6848 0.0289

1112.0740 277280 1133 13.6440 0.0210 0.5556 0.0123

1212.9480 27018 270 1.4220 0.0060 0.5195 0.0126

1299.1400 29421 294 1.6230 0.0080 0.4956 0.0120

1408.0060 349656 1070 21.0050 0.0240 0.4551 0.0101

1457.6430 8146 163 0.5020 0.0050 0.4436 0.0132

1528.1030 4582 160 0.2810 0.0050 0.4458 0.018425

4.3 The study of the sample of rubidium source No. S007

This measurement was done in different times and in the same geometry as the absoluteefficiency measurement. The strongest gamma peak of 520.39 keV and probability of transi-tion (0.447(22)) was used for the determination of the activity of83Rb. Two programs wereutilized to evaluate the area of this peak.At first, the program ’Deimos’ [45] was used. This is user friendly interface, but with theGaussian shape for fitting gamma spectra line. Due to high count rate in our spectra, thenatural asymmetry of gamma lines was pronounced. Therefore the level ofχ2 was high.High χ2 enlarged errors at the program output. For this reason, we have used another com-puter program ’Area’ [46]. This program sums up the counts of the peak and it subtractsbackground.The numerical results analyzed by program Deimos are in Tab. 4

Table 4: Activity of rubidium - measured data and computed activity

date time time dead P ∆ P A ∆ A name of

of of [s] time [count] [count] [Bq] [Bq] spectrum

measurement measurement [%] file

25.10.2005 11:39 300 8.54 72042 432 472317 2843 Gf0018

25.11.2005 8:20 1800 6.88 335790 1678 366912 1843 Gf0022

9:23 1800 6.83 334297 2340 365280 2563 Gf0023

Due to determination of the release of rubidium per month, the activities were recounted onthe date 25.11.2005 9:23 (see Tab. 5 and Tab. 7). For more precise value of activity of 25.11., we made two measurements and we establish the weighted mean from this values (seebelow).

Table 5: The activity of the rubidium recounted according to the decay law on the date25.11.2005 9:23

A [Bq] ∆A [Bq]

368404 2218

366777 1842

365280 2563

The weighted mean of activity on last two values from Tab. 5 is A = (366.3± 2.1) kBq (C.L.99%)The release of rubidium can be computed as a difference between ’primary’ activity (from themeasurement of 25.10.) and activity from 25.11. The release activityArel = (2.1± 7.0) kBq(C.L. 99%).The numerical results analyzed by program Area are in Tab. 6The weighted mean of activity on last two values from the Tab. 7 is A = (367.51± 0.60) kBq(C.L. 99 %)

26

Table 6: Activity of rubidium - measured data and computed activity

date time time dead P ∆ P A ∆ A name of

of of [s] time [count] [count] [kBq] [kBq] spectrum

measurement measurement [%] file

25.10.2005 11:39 300 8.54 72065 270 472464 1785 Gf0018

25.11.2005 8:20 1800 6.88 336653 583 367854 662 Gf0022

9:23 1800 6.83 336157 584 367312 663 Gf0023

Table 7: The activity of the rubidium recounted according to the decay law on the date25.11.2005 9:23

A [Bq] ∆A [Bq]

368518 1392

367715 662

367312 663

The release of rubidium can be again computed as a difference between ’primary’ activity(from the measurement of 25.10.) and activity from 25.11. The release activityArel = (1.0± 4.2) kBq(C.L. 99%).

4.4 Conclusion

In this work, we should determine the release of the rubidium from the solid83Rb/83mKrelectron source. Within the frame of error, we cannot establish the quantity of releasedrubidium. However, we can say that release, if it exist, is less than 5.2 kBq. This release inactivity units in one month is compatible to zero release.This conclusion means that we trust areas yield by program ’Area’.For the more accurate determination of the release of the rubidium, one should carry outmore measurements.

Acknowledgement

I am very grateful to both my supervisors, Milos Rysavy and Drahoslav Venos for lendingarticles and books and above all for their help in preparing this thesis. Also, I would liketo thank Otokar Dragoun and Antonın Spalek for their valuable conversations which havethe significant influence on this work.

27

References

[1] W. Pauli, in letter to participants of the Conference in Tubingen (1930); Septieme Con-seil de Physique Solvay 1933, Noyaux Atomiques, 324 (1934).

[2] J. Chadwick, Verh. d Deutschen Phys. Ges. 16 (1914) 383.

[3] E. Fermi, Ricerca Scientifica 2(1933) N12; Z.Physik 88 (1934) 161.

[4] F. Perrin, C.R. 197 (1933) 1625.

[5] B. Pontecorvo, Chalk River Report PD-205, 20 November, 1946.

[6] R.J. Davis, D.S. Harmer and K.C. Hoffman, Phys. Rev. Lett. 20 (1968) 1205.

[7] F. Reines and C.L. Cowan, Nature 178 (1956) 446; C.L. Cowan, F. Reines, F.B. Harri-son, H.W. Krise, A.D. McGuire, Science 124 (1956) 103.

[8] M. Goldhaber, L. Grodzins and A.W. Sunyar, Phys. Rev. 109 (1958) 1015 .

[9] Particle Data Group, European Physical Journal C 15 (2000) 1.

[10] Particle Data Group, C. Caso et al., Eur. Phys. J. C3 (1998) 1.

[11] B. Pontecorvo, J.Exptl. Theoret. Phys. 33 (1957) 549 [Sov. Phys. JETP 6 (1958) 429].

[12] B. Pontecorvo, J.Exptl. Theoret. Phys. 34 (1958) 247 [Sov. Phys. JETP 7 (1958) 172].

[13] G. Danby, J.M. Gaillard, K. Goulianos, L.M. Lederman, N. Mistry, M. Schwartz, andJ. Steinberger, Phys. Rev. Lett. 9 (1962) 36.

[14] Z. Maki, M. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28 (1962) 870.

[15] Y. Fukuda et al., Phys. Rev. Lett. 85 (2000) 3999

[16] Super-Kamiokande, Y. Fukuda. Phys. Rev. Lett 81 (1998) 1562; ibid. 82 (1999) 2644;ibid. 82 (1999) 5194; arXiv:hep-ex/9908049

[17] B. Lundberg, Fermilab seminar, July 21, 2000, http://fn872.fnal.gov/

[18] S. Hannestad, astro-ph/0404239

[19] S.R. Elliott, J. Engel, J. Phys. G: Nucl. Part. Phys. 30 (2004) R183

[20] H.V. Klapdor-Kleingrothaus, “60 Years of Double Beta Decay - From Nuclear Physicsto Beyond the Standard Model”, World Scientific, Singapore (2001)

[21] H.V.Klapdor-Kleingrothaus, Int. J. Mod. Phys. A 13 (1998) 3953; Proc. Lepton andBaryon Number Violation, IOP Bristol & Philadelphia 1999, Eds. H.V. Klapdor-Kleingrothaus, I. Krivosheina, 205-301

[22] Heidelberg-Moscow collab., Phys. Rev. Lett. 83 (1999) 41

28

[23] P. Kruit and F.H. Read, J. Phys. E16 (1983) 313

[24] A. Picard et al., Nucl. Inst. Meth. B63 (1992) 345

[25] V.M. Lobashev, Nucl. Inst. and Meth. A240 (1985) 305

[26] V.M. Lobashev et al., Phys. Lett. B460 (1999) 227

[27] C. Weinheimer et al., Phys. Lett. B460 (1999) 219

[28] K. Assamagan et al., Phys. Rev. D53 (1996) 6065

[29] R. Barate et al., Eur. Phys. J. C2 (1998) 395

[30] A. Osipowicz et al., hep-ex/0109033, FZKA scientific report 6691

[31] T. Thummler et al., FZKA scientific report 6752

[32] KATRIN collaboration, KATRIN Design Report, Report FZKA 7090, NPIRez EXP-01/2005, MS-KP-0501.

[33] Ansaldo Superconduttori S.p.A., 16152 Genova, Italy, http://www.as-g.it/

[34] R.A. Haefer, ’Kryo Vakuumtechnik’, Springer Verlag, 1981.

[35] C. Benvenuti et al., J. Vac. Sci. Technol. 13,6 (1976) 1172

[36] J. Kaspar et al., Nucl. Instr. and Meth. A527 (2004) 423

[37] R.S. van Dyck et al., Phys. Rev. Lett. 70 (1993) 2888

[38] R. Marx, IEEE Trans. Instr. Meas. Vol. 50, No. 2, 2001

[39] A. Picard et al., Z. Phys. A342 (1992) 71

[40] J.L. Campbell, T. Papp, Atom. Data Nucl. Data Tables 77 (2001) 1

[41] R.G. Helmer, C. van der Leun, Nucl. Instr. Meth. A450 (2000) 35

[42] R.D. Deslattes et al., Rev. Mod. Phys. 75 (2003) 3

[43] R. R. Kinsey et al., The NUDAT/PCNUDAT Program for Nuclear Data, pa-per submitted to the 9th International Symposium of Capture Gamma-Ray Spec-troscopy and Related Topics, Budapest, Hungary, October 1996. Data ex-tracted from the NuDat2—Decay Radiation database version of 12/10/2004http://www.nndc.bnl.gov/nudat2/dec searchi.jsp

[44] H. Kawakami et al., Physics Letters A 121 (1987) 414

[45] J. Frana, Program DEIMOS32 for Gamma-ray Spectra Evaluation, J. Radioanal. Nucl.Chem. Vol. 257, No. 3, (2003) 583

[46] D. Venos, private communication, 2006

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