Modeling of electron emission processes accompanying Radon- α -decays within electrostatic spectrometers
N. Wandkowsky, G. Drexlin, F.M. Fränkle, F. Glück, S. Groh, S. Mertens
MModeling of electron emission processesaccompanying Radon- α -decays within electrostaticspectrometers N. Wandkowsky , G. Drexlin , F.M. Fr¨ankle , , F. Gl¨uck , , S.Groh and S. Mertens , KCETA, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany Department of Physics, University of North Carolina, Chapel Hill, NC, USA Research Institute for Nuclear and Particle Physics, Theory Dep., Budapest,Hungary Institute for Nuclear & Particle Astrophysics, Lawrence Berkeley NationalLaboratory, CA, USAE-mail: [email protected]
Abstract.
Electrostatic spectrometers utilized in high-resolution β -spectroscopystudies such as in the Karlsruhe Tritium Neutrino (KATRIN) experiment have tooperate with a background level of less than 10 − counts per second. This limit canbe exceeded by even a small number of , Rn atoms being emanated into thevolume and undergoing α -decay there. In this paper we present a detailed modelof the underlying background-generating processes via electron emission by internalconversion, shake-off and relaxation processes in the atomic shells of the , Podaughters. The model yields electron energy spectra up to 400 keV and electronmultiplicities of up to 20 which are compared to experimental data. a r X i v : . [ phy s i c s . i n s - d e t ] A p r INTRODUCTION
1. Introduction
The Karlsruhe Tritium Neutrino experiment (KATRIN) is a next generation, large-scaletritium β -decay experiment designed to determine the effective electron (anti-)neutrinomass m ¯ ν e with a sensitivity of 200 meV (90% C.L.) [1]. It is currently being assembledby an international collaboration at the Karlsruhe Institute of Technology (KIT) inGermany.KATRIN will investigate the kinematics of tritium β -decay with unprecedentedprecision in a narrow region close to the β -decay endpoint E ≈ . m ¯ ν e . An essential pre-requisite to obtain the reference sensitivity of 200 meVis a low background level of < − counts per second (cps) in the signal region close to E . The KATRIN setup is described in detail in [1]. It consists of a windowlessgaseous tritium source providing > β -decays per second, a differential and cryogenicpumping section to eliminate the injected tritium molecules from the beam line, aswell as an electrostatic spectrometer acting as high-pass energy filter of unprecedentedprecision, and finally a position sensitive detector to count transmitted electrons. Thiswork is focused on background processes in the large spectrometer section.In a previous publication [3] we have reported on measurements with the KATRINpre-spectrometer in a test set-up configuration where α -decays of , Rn atoms inthe volume of an electrostatic spectrometer of the MAC-E filter type ‡ [4, 5, 6] wereidentified as significant source of background. These atoms originate mainly from thenon-evaporable getter material which is used as a chemical pump to obtain ultra-highvacuum (UHV) conditions of p ≤ − mbar [7], but also from other auxiliaryequipment within the spectrometer vessel and from the stainless steel vessel hull itself.In particular, we could demonstrate that a single radon α -decay can produce up toseveral thousands of detector hits in the energy region-of-interest over an extended timeperiod of up to several hours. This background originates from the emission of electronsin the energy range from eV up to several hundreds of keV, which is caused by a varietyof processes related to the emission of the energetic α -particle as well as the subsequentreorganization of the atomic shells. Almost all of these electrons are trapped in thesensitive volume of the spectrometer due to the known magnetic bottle characteristicof a MAC-E filter [8, 9]. Owing to the excellent UHV conditions in this part of thesetup, electrons remain trapped over very long time periods, so that they can producesecondary electrons via ionization of residual gas molecules. A significant fraction ofthese secondaries can reach the detector, resulting in a background rate exceeding theKATRIN design limit of 10 − cps.In this paper we describe a detailed model of electron emission processes following α -decays of the isotopes , Rn. In a separate publication [10] we in detail validatethis model experimentally by making use of precise electron trajectory calculations in a ‡ Magnetic Adiabatic Collimation with Electrostatic filter
ELECTRON EMISSION ACCOMPANYING RADON α -DECAY , Rn α -decay, namely internalconversion, inner shell shake-off, relaxation and atomic shell reorganization. Theimplementation of this model into our simulation software will be discussed in section 3.Within section 4 we will outline the importance of the physics model implemented inthis work in the light of our attendant publications [10, 9, 14].
2. Electron emission accompanying radon α -decay An essential design feature of high-resolution tritium β -spectroscopy by a MAC-E filter isan excellent UHV in the pressure range p ≤ − mbar, so that background-generatingionization processes of β -decay electrons during the filter process are minimized. In thecase of the KATRIN spectrometers, this is achieved by non-evaporable getter (NEG)strips totalling a length of 3 km in the main spectrometer and 100 m in the pre-spec-trometer. As shown in [3], the large surface of the porous NEG strips gives rise toemanation of radon atoms associated with the primordial Th,
U and
U decaychains (see figure 1). Furthermore, the large stainless steel surface of the spectrometervessel (main spectrometer: 650 m , pre-spectrometer: 25 m ) and auxiliary equipmentattached to it also contributes to radon emanation due to small quantities of radonprogenitors contained near the surface.Due to its long half-life ( t / ( Rn) = 3 .
82 d [15]), compared to the pump outtime of radon in the KATRIN spectrometers ( t prespec ≈
25 s, t mainspec ≈
360 s), theisotope
Rn is essentially being pumped out of the spectrometer before it decays.Therefore, its background contribution can be neglected. The short-lived isotopes
Rn( t / = 3 .
96 s) and
Rn ( t / = 55 . α -decay uniformly over theentire spectrometer volume ( V prespec = 8 . , V mainspec = 1250 m ) to their respectivedaughter nuclei Po and
Po (see figure 1). The important fact for our investigationshere is that all α -decays are accompanied by the emission of atomic shell electrons fromthe eV up to the multi-keV scale (the α -particle as well as X-ray fluorescence photonsare of no interest for our background studies, see [9]). If these electrons are emittedinto the sensitive volume of the spectrometer, they can contribute significantly to thebackground rate via secondary processes.There are various processes which can result in the emission of up to more thana dozen electrons in a single α -decay. If the α -decay populates an excited level of thedaughter nucleus, the process of internal conversion, as described in section 2.1, willresult in the emission of electrons with energies of up to several hundreds of keV. Also,the α -particle itself can interact with electrons of the inner atomic shells, leading to so ELECTRON EMISSION ACCOMPANYING RADON α -DECAY U t =7.1 10 a . ... Pa Rn t =3.96 s Th t =1.4 10 a . ... Rn t =55.6 s , Po Po * 216 Po Po eeee shake-off conversion e e relaxation ... t =3.3 10 a . preceding decay chainsinside spectrometer Figure 1: Top: In the KATRIN spectrometers, non-equilibrium decay chains lead toemanation of the two short-lived radon isotopes
Rn and
Rn. Bottom: radon α -decay processes inside the spectrometer and subsequent electron emission processesresulting from shake-off (both isotopes), conversion (mainly Rn) and shell relaxation(following conversion and shake-off processes).called shake-off processes, detailed in section 2.2. Both processes produce vacancies inthe electron shells. These are successively filled by atomic relaxation processes, whichare the focus of section 2.3. Finally, the shell reorganization process of outer shellelectrons is described in 2.4.
In an internal conversion (IC) process the excited level of the daughter nucleus, whichis populated by the α -decay process, interacts electromagnetically with an inner-shell ELECTRON EMISSION ACCOMPANYING RADON α -DECAY P ( IC ) ∝ Z ) [16, 17], as isthe case for polonium ( Z = 84). In addition, the probability of IC decreases for largertransition energies, so it is relevant only for low-lying levels. In our specific case, ICprocesses are thus of importance only for Rn → Po ∗ decays, where significantbranching ratios lead to the two excited levels (7 / + , 271.2 keV and 5 / + , 401.8 keV)shown in figure 1. In case of Rn → Po decays, the even-even nucleon configurationof the
Po daughter creates a paucity of low-lying excited states, implying that ICprocesses following α -decays of Rn are exceedingly rare processes.In an IC process, an inner-shell electron with binding energy E b is emitted into thecontinuum with a kinetic energy of E kin = E ∗ − E b , (1)where E ∗ denotes the excitation energy of the nucleus. For our specific case of , Po ∗ daughters, conversion electron energies between about 40 keV and 500 keVare observed [18, 19].The total conversion probability amounts to about 3.3% when integrating over allelectron shells in the case of Po ∗ . The probability is largest for K-shell electrons(2%) as they are closest to the nucleus. Table 1 lists the dominant electron emissionprobabilities and electron energies for the decay Rn → Po ∗ [18]. Our model allowsfor consecutive IC processes in case the initial de-excitation process does not result in aground state configuration of the polonium daughter. We also include the rare IC processof the decay Rn → Po ∗ [19], but its contribution is negligible for the investigationsin [10, 9]. As mentioned above, the emission of a conversion electron leaves a vacancyin the electron shell, leading to subsequent complex atomic shell relaxation processes,which are described in sections 2.3 and 2.4. A nuclear α -decay leads to a perturbation of the atomic shells, as the electrons experiencethe passage of the outgoing α -particle through the atomic orbitals, as well as the suddenchange ∆ Z = Z (cid:48) − Z of the Coulomb potential of the nucleus (initial state: Z = 86 forradon, final state: Z (cid:48) = 84 for polonium) [20]. The impact of both processes on inner-shell (K, L, M) electrons is different than on outer-shell (N or higher) electrons dueto the largely different orbital velocities. For inner-shell electrons, the orbital periodis much larger than the orbital passage time of the α -particle ( v α /v e ≈ .
1, with v e :electron orbital velocity, v α : α -particle velocity). For outer-shell electrons, this ratio isreversed ( v e /v α ≈ . p for radon) and will only slowly rearrange to thedaughter orbitals (6 p for polonium), see section 2.4.For inner shells, electron shake-off (SO) is caused by the direct collision process [20,21, 22]. In this case, the α -particle, which has already gained 99% of its final kinetic ELECTRON EMISSION ACCOMPANYING RADON α -DECAY P i (per α -decay) ofthe dominant IC lines and of the corresponding electron energies E kin for Rn, asmeasured by [18]. The electron energy is given by eq. (1) and can thus be attributedto specific excited levels of energy E ∗ via the known values of the binding energy E b (K: 93.1 keV, L: 16.9 keV, M: 4.1 keV, N: 1 keV). Only electron lines with an emissionprobability larger than 0.05% are given. In our model we incorporate the possibilityof consecutive IC processes within a single α -decay in case that the 401.8 keV level of Po ∗ is populated and de-excites to the 271.2 keV level. E kin [keV] P i [%] shell E ∗ [keV]37.5 0.4 K 130.6113.7 0.13 L 130.6178.13 1.27 K 271.2254.29 0.74 L 271.2267.08 0.19 M 271.2270.24 0.064 NP 271.2308.71 0.233 K 401.8384.87 0.102 L 401.8energy inside the mean radius of the K-shell, can exchange energy with an electron viathe Coulomb interaction when passing in the vicinity of the corresponding orbital, and,consequently, it can kick out the inner shell electron into the continuum. The decayenergy is shared between the α -particle and the emitted electron. The latter carriesonly a small fraction, usually of the same order of magnitude as the shell binding energy E b . Therefore, in the adiabatic transition, the shake-off process results in a continuous,steeply falling energy spectrum. In this work we use the parameterization of Bang andHansteen [23] to determine the emission probability for a SO electron with a certainkinetic energy E shake : N ( E shake ) = (cid:18) E b E b + E shake (cid:19) . (2)The SO probabilities for Po have been measured [24, 25, 26] and calculated [21, 27]and are used as a good approximation for the , Po isotopes which are consideredhere. The values, which are listed in table 2, underline the well-known fact that theejection probability strongly increases for higher shells. For the M shell, only the totalemission probability is listed. In our model, we do, however, consider the 5 subshellsindividually, adapting the corresponding emission probabilities. Since there was noexperimental data available for the individual subshells, we used an equal distributionamongst the subshells as an approximation.
ELECTRON EMISSION ACCOMPANYING RADON α -DECAY Po, asmeasured by [24, 25]. shell probabilityK [24] 1 . · − LI [25] 5 . · − LII [25] 0 . · − LIII [25] 1 . · − M [25] 1 . · − An electron, which is emitted via an IC or SO process, will leave a vacancy in an innershell, as shown schematically in figure 2. As a consequence, the electron structure of theatom has to rearrange, thereby releasing binding energy. This can be either in the formof a fluorescence photon (radiative transition), which is of no concern for this work, orin the form of an Auger electron, if the electron filling the vacancy originates from adifferent shell, or a Coster-Kronig electron, in case it is emitted from a sub-shell of thesame level (non-radiative transition) [28]. In case of a radiative transition, the initialvacancy is transferred to a higher atomic shell, while for non-radiative transitions theatomic shells are left with two vacancies. The relaxation processes then propagate upto the outermost shell. In heavy atoms such as polonium, large cascades are observedwhen inner-shell vacancies are successively filled by non-radiative transitions (“Augerexplosions”). Consequently, highly charged polonium ions are created, which cannot beneutralized when propagating in the spectrometer UHV environment § .An electron emitted in a non-radiative transition will receive a distinct kineticenergy. In the example of figure 2, the Auger electron energy can, in a firstapproximation, be determined by E kin = ( E b , L1 − E b , M1 ) − E b , M4 , (3)where E b ,i are the binding energies of the involved shells i . In case of a radiativetransition, the photon would have received the energy difference E γ = E b , L1 − E b , M1 .The above approximation neglects two effects [29]: • A pair of holes in the atomic orbitals retains interaction energy. • The relaxation of the atomic orbitals results in a lowering of the final state energy,which alters the ionization energies of electron shells containing holes.The Auger electron energies, which are applied in our model, are indeed correctedfor the aforementioned effects, using the intermediate coupling model of [29]. In the § The highly charged Po-ion will be neutralized when hitting the spectrometer vessel.
ELECTRON EMISSION ACCOMPANYING RADON α -DECAY KLMAuger electron Coster-Kronig electronKLM
Figure 2: Sketch of a relaxation process. An inner shell vacancy is filled by an electronfrom an outer shell or a neighboring sub-shell, thereby releasing the correspondingbinding energy difference. This energy can be transferred to another electron, which isthen ejected from the atom. Depending on the origin of the electron filling the vacancy,the emitted electrons are called Auger electrons or Coster-Kronig electrons.case of polonium, relaxation electron energies can reach up to about 93 keV, whichapproximately corresponds to the K-shell binding energy.Sudden changes of the atomic potentials occur during vacancy cascade development,which can lead to the emission of electrons [30]. However, due to their relatively lowemission probabilities, this effect is only of minor importance and is neglected in ourmodel.Furthermore, as the number of vacancies in the atomic shells increases, the electronbinding energies decrease which can lead to the closure of some Coster-Kronig channels,reducing the average charge state of the daughter atom [30]. In fact, here we arenot interested in obtaining an exact multiplicity distribution of emitted electrons(predominantly of exceedingly low energies <
100 eV), because the subsequent ionizationprocesses of high-energy IC and inner-shell SO electrons in collisions with residual gaswill produce several hundred or even thousand secondary electrons due to their magneticstorage in the spectrometer.
In the above described processes the atomic shell of the polonium daughter is left inan excited state, and the de-excitation follows a rather complex scheme involving manydifferent pathways within relaxation cascades. If the α -decay process leaves the atomicshell unperturbed, or if the SO process of the α -particle involves outer shell (N or higher)electrons, the relaxation processes are much less complex. The underlying effect is thatthe outer-shell electron wave function cannot adjust adiabatically to the final state dueto the fact that the outer-shell electron velocity is much smaller than the α -particlevelocity. In any case the atomic system will relax to the smaller ( Z −
2) nuclear chargeof the daughter nucleus.There is a gradual transition of α -decay processes resulting in a highly excited final IMPLEMENTATION INTO THE SIMULATION SOFTWARE p ) has to adjust to the groundstate shell configuration of polonium (6 p ). In our model we treat both processes in anidentical manner.The change in nuclear charge ( Z −
2) in the α -decay Rn → Po results in a change∆ E = 37 . E is composed of the suddenenergy exchange component ∆ E sud and the much slower rearrangement component∆ E R [22]. As the fast inner electrons can adjust adiabatically to the effective nuclearcharge reduction by rearranging to daughter orbitals, almost all of ∆ E occurs suddenly(∆ E sud ) and has to be supplied by the outgoing α -particle, which results in an equivalentretardation. The remaining small fraction ∆ E R is retained by the atom as temporaryexcitation energy for the much slower shell rearrangement in the outer shells. We employa scenario where the average atomic rearrangement energy ∆ E R (6 p → p ) of about250 eV [22] is shared statistically by two electrons from the outermost shells. If theirkinetic energy is larger than the polonium ionization energy for P-shell electrons (1-9 eV), they are emitted into the continuum. This results in a flat energy spectrum oflow-energy “shell reorganization” electrons.As the probability for inner shell SO (see table 2) and IC (see table 1) is notdominating, the above described atomic shell reorganization (SR) in the ground stateconfiguration is the most frequent electron emission process accompanying α -decay. If,however, the electron shell in the final state is an excited state, caused either by IC orby inner shell SO, we calculate the full atomic relaxation, which will be described indetail in section 3.1.
3. Implementation into the simulation software
To study the event topologies of electrons from the α -decay of , Rn atoms, andto estimate background rates and characteristics due to their subsequent trapping (fordetails, see [10, 9]), a detailed code for particle trajectory calculations in the complexelectromagnetic field configuration of the KATRIN spectrometer is required. Thischallenging task is met by the KATRIN simulation package
Kassiopeia [32], whichallows to track electrons over long periods of time with machine precision. For thepurpose of this work a Monte Carlo event generator to describe electron emissionfollowing , Rn α -decay was developed and is described in section 3.1. Section 3.2then gives a short overview of the output of this generator. The detailed physical model for signal events and background processes is implementedinto the
Kassiopeia package via MC-based event generators. For the investigationsof this paper, a radon background generator was developed to describe the processes
IMPLEMENTATION INTO THE SIMULATION SOFTWARE α -decay, such as internal conversion (IC), shake-off(SO), relaxation (RX) and shell reorganization (SR) which are described in the previoussection 2.Figure 3 shows a flowchart of the radon event generator. no InitializationSO active?SO process yes e - emitted? yes RX active?RX process yes
IC active?IC process yes e - emitted? yes RX active?RX process yesnono
SR active?SR process yes
Finalization nonono no
Figure 3: Event generator flowchart: After initialization of the generator, the differentphysical processes (SO: shake-off, IC: internal conversion, RX: relaxation, SR: shellreorganization), represented as solid boxes, are processed according to the model, whichis described in more detail in the main text. The user has the possibility to configure thegenerator, e.g. turn on or off certain processes to study specific aspects. Correspondingdecision points are given in dashed boxes.The simulation can be configured by the user to study the impact of differentprocesses on the background. The following choices are available (options in brackets): • activate/deactivate individual physical processes (SO, IC, SR, RX) • enforce physical processes (SO, IC) • select radon isotope (219, 220)During initialization, all data files required for the computation of the various physicalprocesses for a specific isotope are read in. Enforcing SO and IC processes can be usefulbecause they are rather rare (up to few %). If this option is enabled, it is assured thatthe according processes are executed within every generated event by scaling up theemission probabilities of the individual shells until their sum totals 100%.The first physical process to be carried out (if activated by the user) is the SOprocess, as it is directly caused by the passage of the α -particle through the atomic IMPLEMENTATION INTO THE SIMULATION SOFTWARE ω i and the Auger yield α i of the shell i which is underinvestigation to determine the transition type. For K- and L-shell vacancies the dataof [36], and for M- and N-shell vacancies those of [37, 38] is used. If a radiative transitionis diced, the vacancy is simply transferred to a higher shell, where the new vacancy isdetermined from the available final states according to their relative probabilities. Non-radiative transitions up to and including the M-shell result in two vacancies, whileseveral vacancies can be created by N-shell vacancy de-excitation due to super-Coster-Kronig transitions, i.e. all transitions happen within the N-shell. The described processis repeated until all vacancies reach the outer O- or P-shells or until no further de-excitations are energetically possible. As we do not take into account small modificationsof the energies of electron shells due to the actual relaxation process, the de-excitationsresult in discrete energy lines.After the RX process was completed, or if, initially, the SO process was deactivated,the IC process is performed (if activated by the user). This specific ordering is justifiedby the fact that shell relaxation processes are completed on a much faster time scale(10 − s) [39] than internal conversion processes (10 − s) [40]. As in the SO subroutine,a random number is used to initiate an IC process with the correct probability. Becausethe excited nucleus can decay into an intermediate energy state instead of the groundstate, this has to be taken into account by allowing consecutive IC processes (so calleddouble conversion [22]). The interrelated energy levels are marked as such in the inputfile, which allows for reliable bookkeeping of the involved states. The IC electron energydepends solely on the decaying nuclear state and the binding energy of the emittedelectron, resulting in discrete IC lines.The final process to be carried out is the SR process. At first, the SR subroutinechecks if any SO or IC processes occurred previously. If this is the case, the SR process isskipped because the Po daughter has already relaxed via the above mentioned processes.Otherwise, an unperturbed shell is assumed, which results in the excitation of twoelectrons, statistically sharing the shell reorganization energy of ∆ E R = 250 eV (shellbinding energy to be deducted). These electrons are actually only emitted from the atomif their energy exceeds the outer shell binding energy of about 1 eV (first ionization) or9 eV (second ionization).In the final step of the event generation, all electrons generated by a single α -decay IMPLEMENTATION INTO THE SIMULATION SOFTWARE
Kassiopeia simulation software.
Figure 4 shows the energy spectra and energy-dependent emission probabilities asobtained with our event generator. The discrete IC and relaxation lines, as well as the energy [keV] -3 -2 -1
10 1 10 d N / d E -7 -6 -5 -4 -3 -2 -1 Shake-OffConversionRelaxationShell Reorganization Rn energy [keV] -3 -2 -1
10 1 10 d N / d E -7 -6 -5 -4 -3 -2 -1 Shake-OffConversionRelaxationShell Reorganization Rn Figure 4: Event generator: energy spectra of IC, inner-shell SO, relaxation and SRelectrons for the case of Rn → Po (top) and Rn → Po (bottom) α -decay. SRelectrons, which originate from unperturbed atomic shell relaxation, are distinguishedfrom K-, L- and M-shell SO electrons. The electron energy axis is subdivided into 250intervals between 1 eV and 500 keV with logarithmically increasing bin size.higher-order potential dependence of the SO spectrum can be clearly identified. The flatenergy spectrum dominating the low-energy part is originating from our model of SR IMPLEMENTATION INTO THE SIMULATION SOFTWARE p → p ), as the two electronsstatistically share an energy of 230-250 eV. Due to their identical nuclear charge, theinner-shell SO and SR contributions of the two polonium isotopes are assumed to beidentical. The SO probability is negligible for the inner K-shell. Therefore, the low-energy part of the relaxation spectrum results mainly from L-shell (or higher) SO, andhence reaches up to about 17 keV (L-shell binding energy). As stated above, the ICprocess is of importance only in the decay Rn → Po ∗ . In this case, there is a highprobability for vacancies in the inner K-shell, leading to the high-energy part (up toabout 90 keV) of the relaxation spectrum.The total probability for electron emission by a specific process can be obtained byintegration over the whole energy spectrum. The corresponding results are summarizedin table 3.Table 3: Electron emission probabilities P per decay, depending on the emission process,based on the Rn and
Rn event generators of this work.
P >
Rn) P (
Rn)inner-shell SO 2 . · − . · − IC 3 . · − . · − relaxation 2 . · − . · − SR 1 .
89 1 . Due to the complex nature of the response of the atomic shells during and after theemission of an α -particle, it is of vital importance to compare the present model withindependent measurements. Generic parameters for comparison are:( i ) the final charge state of the daughter atom, because it is highly sensitive to a correctdescription of processes such as atomic relaxation, and( ii ) the electron energy spectrum in the multi-keV range, which can be estimated fromthe number of secondary electrons produced in the electrostatic spectrometer [10].Figure 5 shows the polonium charge state following Rn and
Rn decays as obtainedwith the generator of this work, in comparison to the independent measurement reportedin [26]. There is good agreement between measured and simulated frequencies ofoccurrence of different
Po charge states, which underlines the basic validity of ourmodel. We attribute the deviations occurring at charge states ≥ IMPLEMENTATION INTO THE SIMULATION SOFTWARE polonium charge state -2 0 2 4 6 8 10 12 14 16 18 no r m a li z ed i n t en s i t y -4 -3 -2 -1 Rn) measurement (Rn) simulation ( Rn) simulation (
Figure 5: Charge states of
Po (daughter of
Rn) and
Po (daughter of
Rn),as obtained with our generator. The simulation is compared to an independentmeasurement of the
Po charge state [26]. The values obtained with the
Rngenerator were normalized to the overall rate of non-zero charge states as theexperimental precision for the detection of neutral daughter atoms was rather limitedin [26]. For the
Rn results, the same normalization constant was used to emphasizethe difference between the two isotopes.generator we note that the detection of neutral daughter states, as outlined in [26],was rather challenging. We thus ascribe the discrepancy to experimental difficulties inassessing the efficiency in detecting neutral atoms after α -decay.The significant difference between the two simulated isotopes in electronmultiplicities, and correspondingly in the charge distribution of the daughter ion, isdue to IC processes in the case of Rn → Po ∗ . As they are emitted from innershells, highly charged final states result from complex relaxation cascades.The second important parameter which is of key importance to validate our model isthe energy spectrum of the emitted electrons in the multi-keV range. In an electrostaticspectrometer of the MAC-E filter type, this parameter cannot be measured directly,as electrons are trapped over long periods of time [3, 9, 10, 11, 12, 13]. However,an indirect method to assess the energy of stored multi-keV electrons is to make useof their subsequent cooling via ionization of residual gas and to count the number ofproduced secondary electrons in a detector. A single radon α -decay can lead to alarge number of detector hits N det (up to 1500 hits corresponding to a single eventwere observed at the KATRIN pre-spectrometer). There is a good correlation betweenprimary electron energy (shown in fig. 4) and N det , which is, however, not strictlylinear due to competing energy losses by synchrotron radiation and due to non-adiabaticeffects at higher energies. In fig. 6 we display the number of detector hits following single IMPLEMENTATION INTO THE SIMULATION SOFTWARE α -decays in the KATRIN pre-spectrometer in an experimental configuration whereionizing collisions with residual gas (Ar at p = 2 · − mbar) were maximized at theexpense of synchrotron losses. The measured spectrum is compared to correspondingMonte-Carlo simulations with the radon generator of this work. There is good agreementbetween experimental data and MC simulation, taking into account the limited numberof radon α -decays (127 events) accumulated over a measuring period of about 500 hours.The simulation reproduces the main features of the measured distribution: a largenumber of Rn-events with rather few detector counts, caused by the low-energy plateauof the shake-off events, and a steep decrease (tail of the shake-off spectrum) towardsa flat plateau of very few events featuring a large number of detector hits (caused byconversion electrons). number of detector hits simulationmeasurement average equivalent primary energy (keV) nu m be r o f r adon e v en t s Figure 6: Comparison of measured and simulated numbers of detector hits produced byindividual radon α -decay events within the KATRIN pre-spectrometer. An equivalentenergy scale can be reconstructed when using average energy losses due to scatteringand synchrotron radiation [10]. The non-linearity of the energy scale results fromthe decreasing scattering cross section for higher energies in combination with linearlyincreasing synchrotron losses.A thorough understanding of radon-induced background is crucial for a successfulneutrino mass determination with the KATRIN experiment. Therefore, furtherdetailed background studies comparing measurements and simulations with differentexperimental conditions were carried out in [10]. A combination of the model ofthis work with precise electron trajectory calculations provides the necessary thoroughunderstanding in order to reduce the background level below the required limit. CONCLUSIONS
4. Conclusions
In the course of this work we have developed for the first time a comprehensiveand detailed model of electron emission processes following the α -decays of the tworadon isotopes Rn and
Rn. These investigations were motivated by our earlierobservations, reported in [3], of periods with significantly enhanced background rates atthe KATRIN pre-spectrometer measurements.The background model incorporates various processes such as internal conversion,shake-off and relaxation of the atomic shells during or after the α -emission. The resultingelectron energies cover a wide range between a few eV up to several hundred keV, andinvolve highly charged polonium daughter ions. Our model successfully reproducesexperimentally observed polonium charge multiplicities as well as electron energies inthe multi-keV range, as shown in this work. Further experimental validation of ourcomplete physics model was performed in a separate work [10], where the backgroundbehavior observed within test measurements at the KATRIN pre-spectrometer could bewell described.It is only by developing and by validating detailed models of background processesthat the KATRIN experiment can realize its full physics potential in measuring theabsolute mass scale of neutrinos. Acknowledgement
This work has been supported in parts by the Bundesministerium f¨ur Bildungund Forschung (BMBF) with project number 05A08VK2 and the DeutscheForschungsgemeinschaft (DFG) via Transregio 27 “Neutrinos and beyond”. We alsowould like to thank the Karlsruhe House of Young Scientists (KHYS) of KIT for theirsupport (S.G., S.M., N.W.).
References [1] “KATRIN Design Report (FZKA Report 7090),” tech. rep., , KIT,2004.[2] G. Drexlin et al. , “Current Direct Neutrino Mass Experiments,”
Adv. in High Energy Phys. ,vol. 2013, ID 293986, 2013.[3] F. Fr¨ankle et al. , “Radon induced background processes in the KATRIN pre-spectrometer,”
Astropart. Phys. , vol. 35, no. 3, pp. 128–134, 2011.[4] G. Beamson, H. Q. Porter, and D. W. Turner, “The collimating and magnifying properties of asuperconductiong field photoelectron spectrometer,”
J. Phys. E , vol. 13, no. 64, 1980.[5] V. M. Lobashev and P. E. Spivak, “A method for measuring the electron antineutrino rest mass,”
Nucl. Instrum. Meth. A , vol. 240, no. 2, pp. 305–310, 1985.[6] A. Picard et al. , “A solenoid retarding spectrometer with high resolution and transmission for keVelectrons,”
Nucl. Instrum. Meth. B , vol. 63, no. 3, pp. 345–358, 1992.[7] J. Wolf, “Size matters: The vacuum system of the Katrin neutrino experiment,”
Journal of theVacuum Society of Japan , vol. 52, pp. 278–284, 2009.
CONCLUSIONS [8] H. Higaki, K. Ito, K. Kira, and H. Okamoto, “Electrons Confined with an Axially SymmetricMagnetic Mirror Field,” AIP Conference Proceedings , vol. 1037, no. 1, pp. 106–114, 2008.[9] S. Mertens et al. , “Background due to stored electrons following nuclear decays at the KATRINexperiment,”
Astropart. Phys. , vol. 41, no. 52, 2013.[10] N. Wandkowsky et al. , “Validation of a model for Radon-induced background processes inelectrostatic spectrometers,” submitted to J. Phys. G: Nucl. Partic. , 2013.[11] F. Fr¨ankle,
Background Investigations of the KATRIN Pre-Spectrometer . PhD thesis, KarlsruheInstitute of Technology (KIT), 2010.[12] S. Mertens,
Study of Background Processes in the Electrostatic Spectrometers of the KATRINExperiment . PhD thesis, Karlsruhe Institute of Technology (KIT), 2012.[13] N. Wandkowsky,
PhD thesis in preparation . Karlsruhe Institute of Technologie (KIT), 2013.[14] S. Mertens et al. , “Stochastic Heating by ECR as a Novel Means of Background Reduction in theKATRIN spectrometers,”
JINST , vol. 7 P08025, 2012.[15] A. Sonzogni, “Interactive Chart of Nuclides,” National Nuclear Data Center: Brookhaven NationalLaboratory, .[16] K. Siegbahn, “Alpha-, beta- and gamma-ray spectroscopy,” vol. 2, pp. 894, North Holland Pub.Co. Amsterdam, 1968.[17] Ch. Theisen, A. Lopez-Martens and Ch. Bonnelle, “Internal conversion and summing effects inheavy-nuclei spectroscopy,”
Nucl. Instrum. Meth. A , vol. 589, pp. 230–242, 2008.[18] E. Browne, “Nuclear Data Sheets for A = 215 , , , , Nuclear Data Sheets , vol. 93,no. 4, pp. 763–1061, 2001.[19] S.-C. Wu, “Nuclear Data Sheets for A = 216,” Nuclear Data Sheets , vol. 108, no. 5, pp. 1057–1092,2007.[20] M. S. Freedman, “Ionization by Nuclear Transitions,”
Summer course in atomic physics, Carry-le-Rouet, France , Aug 1975.[21] J. S. Hansen, “Internal ionization during alpha decay: A new theoretical approach,”
Phys. Rev. A ,vol. 9, pp. 40–43, Jan 1974.[22] M. S. Freedman, “Atomic structure effects in nuclear events,”
Annu. Rev. Nucl. Sci. , vol. 24,pp. 209–248, 1974.[23] J. Bang and J. M. Hansteen, “Coulomb deflection effects on ionization and pair-productionphenomena,”
K. Dan. Vidensk. Selsk. Mat. - Fys. Medd. , vol. 31, no. 13, pp. 1–43, 1959.[24] M. S. Rapaport, F. Asaro, and I. Perlman, “ K -shell electron shake-off accompanying alpha decay,” Phys. Rev. C , vol. 11, pp. 1740–1745, May 1975.[25] M. S. Rapaport, F. Asaro, and I. Perlman, “ M - and L -shell electron shake-off accompanying alphadecay,” Phys. Rev. C , vol. 11, pp. 1746–1754, May 1975.[26] S. Szucs and J. M. Delfosse, “Charge Spectrum of Recoiling
Po in the α -Decay of Rn,”
Phys.Rev. Lett. , vol. 15, pp. 163–165, Jul 1965.[27] A. Migdal, “Ionization of atoms accompanying α - and β -decay,” J. Phys. (USSR) , vol. 4, pp. 449,1970.[28] E. H. S. Burhop, “The Auger effect and other radiationless transitions,”
University PressCambridge , 1952.[29] F. P. Larkins, “Semiempricial Auger-electron energies for elements 10 ≤ Z ≤ At. Data Nucl.Data Tables , vol. 20, no. 4, pp. 311–387, 1977.[30] E. Pomplun, “Auger Electron Spectra - The Basic Data for Understanding the Auger Effect,”
ActaOncologica , vol. 39, no. 6, pp. 673–679, 2000.[31] C.C. Lu et al. , “Relativistic Hartree-Fock-Slater eigenvalues, radial expectation values, andpotentials for atoms, 2 ≤ Z ≤ Atomic Data , vol. 3, pp. 1–131, 1971.[32] D. Furse et al. , “KASSIOPEIA - the simulation package for the KATRIN experiment,” to bepublished.[33] M. Mathsumoto and T. Nishimura, “Mersenne Twistor: A 623-dimensional equidistributed uniformpseudorandom number generator,”
ACM T. Model. Comput. S. , vol. 8, no. 1, pp. 3–30, 1998.
CONCLUSIONS [34] C. Robert and G. Casella, “Monte Carlo Statistical Methods,” Springer Texts in Statistics , pp. 47ff., 2004.[35] E. Pomplun, J. Booz and D. E. Charlton, “A Monte Carlo Simulation of Auger Cascades,”
RadiationResearch , vol. 111, pp. 533–552, 1987.[36] M. H. Chen and B. Crasemann and H. Mark, “Relativistic radiationless transition probabilities foratomic K- and L-shells,”
At. Data Nucl. Data Tables , vol. 24, no. 1, pp. 13–37, 1979.[37] E. J. McGuire, “Atomic M-Shell Coster-Kronig, Auger, and Radiative Rates and FluorescenceYields for Ca-Th,”
Phys. Rev. A , vol. 5, no. 3, pp. 1043–1047, 1972.[38] E. J. McGuire, “Atomic N-Shell Coster-Kronig, Auger, and radiative rates and fluorescence Yieldsfor 38 < Z <
Phys. Rev. A , vol. 9, no. 5, pp. 1840–1851, 1974.[39] M. Drescher et al. , “Time-resolved atomic inner-shell spectroscopy,”