X-RayPhysicsMITDepartment of Physics(Dated: October17,2014)This experiment investigates the production and absorption of x rays. A high-precision solid-statex-ray detector is used to measure the spectra of x rays under a variety of circumstances that illustrateseveral oftheimportantphenomenaofx-rayphysics. Phenomenaobservedandmeasuredincludebremsstrahlung emission; uorescent excitation of x rays, which allows spectroscopic identication ofunknown elements in a sample; electron-positron annihilation; and the absorption and attenuation ofx-raybeamsbyphotoelectricinteractions,Comptonscattering,andpairproduction. Theenergiesof the Kx-raylines of numerous elements are measuredandcomparedwiththe predictions ofMoseleys law. The energy separations and relative intensities of the K and Klines are measuredandcomparedwiththetheoryofnestructureinthen = 2orbitals.PREPARATORYQUESTIONSPlease visit the X-rayPhysics chapter onthe 8.13rwebsiteatlms.mitx.mit.edutoreviewthebackgroundmaterial for this experiment. Answer all questions foundin the chapter. Work out the solutions in your laboratorynotebook;submityouranswersonthewebsite.SAFETYPersonal HealthandSafetyThecarcinogenicpropertiesofxraysandotherioniz-ingradiationshavebeenknownsincethe1940s. Expo-suressignicantlyexceedingthatduetonaturalsourcessuchascosmicraysandbackgroundradioactivitymustthereforebeavoided. Thesources usedinthepresentexperiment havebeenapprovedbytheMITRadiationSafetyProgramforeducational use. Theyarenotdan-gerous if handled with appropriate caution. You areurged to determine the exposures you may receive in var-iousmanipulationsofthelaboratorysourcesbymakingsuitable measurements with the laboratory radiation sur-veymeters.Thetwoprimarysources of radiationinthis experi-ment,241Am(analphaemitter)and90Sr(ahigh-energybetaemitter), shouldbetransportedfromtheirstoragelocker to the experiment quickly. For the safety of othersin the laboratory, they may never be left out unattended.Inparticular, the90Sr source must bepositioneddur-ingtheexperimentsuchthatitsbeamiswell containedaround the apparatus. Use lead shielding as necessary tominimizeradiationinanundesirabledirection.The90Sr source is contained in an aluminum and lead-linedcontainer (see Figure 3) whichcanbe placedonthesmallwoodenstandnexttothedetectorsothatthehole behind the lead shutter is aligned with the entrancewindowof thedetector. CAUTION: Avoidexpos-ingyour hands tothe radiationemergingfromtheholeintheleadlinedbox. The90Srsourceisquitestrong(several millicuries)andtheelec-trons which it emits readily bounce o lead nucleiinalldirections,includingoutthroughthehole.EquipmentSafetyThe detector used in this experiment has a few impor-tantoperatingrequirementstokeepinmindinordertoavoiddamagingitsdelicateandexpensivecomponents.Pleaseobservethefollowingprecautions:1. Nevertouchthecarbonberwindow. Leavethe polyethylene cover on. It only attenuates x raysbelow10keV.2. The eld eect transistor in the preamplierattachedtothedetector is easilydamagedandcostlytoreplace. Besurethepreamplierispowered(fromthebackof theNIMbin)beforeturningonthehighvoltagebias.3. Slowlyraise the bias voltage to about +3000 VDC.(Besureofthepolarity!) Becarefulwhenyouap-plythisandtake standardelectricalsafetyprecau-tions.4. Askaninstructortooverseeyourrstuseof thesystemandensurethereisenoughliquidnitrogeninthecryostat.I. INTRODUCTIONIn1895, WilhelmConradRontgen(orRoentgeninanglicized typography) discovered that a high voltage dis-chargebetweenelectrodesinagasatverylowpressureproduces a penetrating radiationwhichcauses certainmaterialstouorescevisiblelight[6]. Heobservedthatif the voltage exceeds about 30 kV, then the radiation whichhecalledxrayscanpenetrateahand, castingshadows of thebones onauorescent screen. It sooncametobeunderstoodthatelectrons, emittedfromthenegativeelectrode(cathode)of thedischargetube, andacceleratedbytheappliedvoltage,emitelectromagneticradiation (bremsstrahlung x rays) when they collide withthepositiveelectrode(anode)orthewallsofthetube.Id: 31.xrays.tex,v1.222007/08/2916:33:57sewell ExpId: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 2Theconsequences of Rontgens discoveryfor physicswere profound. Six years previously Hertz had discoveredelectromagnetic radiation(gigahertz radiowaves) withwavelengths amilliontimes longer thanthat of visiblelight. Rontgensworkshowedhowtogenerateelectro-magnetic radiation with wavelengths ten thousand timesshorter. Suchwavelengthsarecomparabletoatomicdi-mensions. Asaconsequence,xraysprovedtobeapow-erful means for exploringtheatomicstructureof mat-teraswell asthestructureof atomsthemselves. Overthenext30yearsthediscoveryandmeasurementof x-rayphenomenaplayedacentralroleinthedevelopmentofthemodernquantumtheoryofmatterandradiation.RontgenwasawardedtherstNobelPrizeinPhysicsin1901[6].Inthepresentexperimentyouwill useagermaniumsolid-statex-rayspectrometertostudyavarietyofphe-nomenainvolvingthe interactions of high-energypho-tons andmatter. Theintroductorypart is astudyofxrayproductionbyirradiationof matter byelectronsandxrays. It is intendedtofamiliarizeyouwiththeequipmentandsomeofthebasicphysicsofxrays. Therest is a menu of possible studies you can pursue as timepermits.II. THEORYThesub-disciplineof x-rayphysicsinvolvesacertainamount of nomenclature and notation that you will needto become familiar with before performing this lab. Muchof the older literature in the eld uses the so-called Sieg-bahnnotationtodescribexraysemittedduringtran-sitionsbetweenatomicelectroncongurations. Atermi-nology diagram showing the transitions giving rise to theK,L,andMlinesappearsinReference[7,p.630]andisreproduced in Figure 1. Table I further explains the cor-respondence of the level naming scheme to electronic con-gurations. Inmorerecenttimes, amoreintuitiveIU-PAC notation has become dominant (see Reference [3]).Inthissystem, transitionsbetweenx-raylevelsarede-notedbythelevelsymbolsfortheinitialandnalstatesseparatedbyaminus sign. Theinitial stateis placedrst, irrespectiveof theenergeticordering. Youshouldbecome familiar with converting between both notations.TableIIshowsthecorrespondencebetweenthetwono-tations. As anexample: KL3inIUPACnotationisK1intheSiegbahnnotation. Either way, it denotesthellingofa1sholebya2p3/2electron.II.1. ProductionofEnergeticPhotonsThenamexrayisgenerallygiventoaphotonifitis emittedbyafreeor boundelectronandhas anen-ergyintherangefromabout0.1keVtoabout100keV.Photons emitteddirectlybynuclei aregenerallycalledgammaraysevenif theirenergyisintheconventionalTABLEI.Correspondencebetweenxraydiagramlevelsandelectroncongurations. The 1superscriptinthe electroncongurationindicatesasingleelectronvacancyinamany-electronsystem. Thistablefollowsthatfoundin[3].Level Electron Level Electron Level Electroncong. cong. cong.K 1s1N1 4s1O1 5s1L1 2s1N2 4p1O2 5p1L2 2p1N3 4p13/2O3 5p13/2L3 2p13/2N4 4d13/2O4 5d13/2M1 3s1N5 4d15/2O5 5d15/2M2 3p1N6 4f15/2O6 5f15/2M3 3p13/2N7 4f17/2O7 5f17/2M4 3d13/2M5 3d15/2TABLE II. Correspondence between the Siegbahn (older) andIUPAC(newer) notations. Amore complete table canbefoundin[3].Siegbahn IUPAC Siegbahn IUPACK1 KL3 L1 L3M5K2 KL2 L2 L3M4K1 KM3 L1 L2M4KI2KN3 L2 L3N5xrayrange. The high-energyphotonproductionpro-cessesyouwillexploreare:Bremsstrahlung: (braking radiation) An energeticelectron which undergoes a sudden accelerationcausedbyinteractionwithahigh-Znucleushasahigh probability of emitting a bremsstrahlung pho-tonwithanenergyrangingfromzerotothefullkinetic energyof the electron. The spectrumofthexraysradiatedfromthetargetof anelectronbeam consists of a bremsstrahlung continuum withamaximumenergycutoequal tothekineticen-ergy of the electrons in the beam. For example, forelectrons of charge e accelerated by an applied volt-age V , the maximum energy in the bremsstrahlungspectrumwouldbe V e. Inthis experiment, thesource of energetic electrons is a millicurie-levelsampleof90Sr, whichbeta-decayswitha29-yearhalflifeandmaximumelectronenergyof0.5MeVto90Ywhichinturnbetadecayswitha64-hourhalflifeandmaximumelectronenergyof2.3MeVto90Zr.X-rayuorescenceviachargedparticles: Whenan energetic electron or other charged particle(e.g. an alpha particle) interacts with an atomit may eject an electron fromone of the innershells. Theresultingionrelaxes fromits excitedId: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 3K :m:: T lt Mm: lll' 'Y I .lI lit Nx il 'VL VD 'I lI om N v 'I pn JI[ ,, 'Tls-np K 0.1.. I ! JrII II I I 11I1II L r,,1f.'6'3

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5i ' Frn.VIII-17.QualitativetermdiagramforX-raylevels,showinglinesintheK,L,and Mseries.No attempt hasbeen made to plotthe energy levelsto scale. FIG.1. Qualitativeterminologydiagramfrom[7,p.630].statebyacascadeoftransitionsinwhichelectronsfromouter shells fall inward until no vacancyremains. Eachtransitiongives rise to a photonwithacharacteristicenergy. Aphotonproducedwhen an outer electron falls into a hole in then=1, 2, or3shell iscalledaK, L, orMxray,respectively. These characteristic energies areuniquetoindividualelements.X-rayuorescenceviaxrays: Aphotonwithsu-cient energymayinteract withanatomtoejectanelectronfromaninner shell inwhat is calledaphotoelectricabsorptionprocess. Thesubse-quent relaxationof the excitedionproduces thesamecharacteristicxraysasinelectronbombard-ment.Emissionofphotonsviaexcitednucleidecay:One example of this process is the decayof theexcitednucleusof133Cecreatedbythebetadecay(K-electroncapture) of133Ba. Inthiscase, boththenucleusandtheelectronsareleftinanexcitedstateof133Ce, resultingintheemissionofnucleargammarays as thenucleus relaxes toits groundstate and the emission of a 31 keVcesiumKxrayastheatomicelectronsrelaxtotheirgroundstate.Annihilationofelectron-positronpairs: Some un-stablenuclei (e.g.22Na)undergoaninversebeta-decayprocessinwhichaprotoninthenucleusistransformedintoaneutronwiththeemissionofapositron(anti-electron) andanelectronneutrino.Theejectedpositroneventuallyinteractswithanelectroninthesurroundingmaterial, annihilatingId: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 4intophotons. Suchannihilationsusuallyyieldtwophotonswhich,inthecenterofmassframe,travelinexactlyoppositedirectionsandwitheachcarry-inganenergyofpreciselymec2inaccordancewiththeconservationofmomentumandenergy.II.2. InteractionsofXRayswithaSolidStateCrystalAn x-ray photon can interact with the germanium crys-talusedasadetectorinthisexperimentby:1. Photoelectricabsorptionbyanatom, resultinginthedisappearanceof thephotonandthecreationof an excited ion through ejection from the atom ofan electron with an amount of kinetic energy equalto the original energy of the photon less the energyrequiredtoremovetheelectronfromtheatom.2. Comptonscatteringbyalooselyboundelectron,resulting in a recoil electron and a scattered photonofloweredenergywhichmayescapethecrystal.3. Paircreation, iftheenergyoftheincidentphotonis suciently large (h> 2mec2). The result is thedisappearanceof thephotonandthematerializa-tion of an electron and positron with an amount ofenergyapproximatelyequaltothatoftheincidentphotonlesstherestenergyoftwoelectrons.4. Coherentscatteringbytheboundelectronsof anatom, resultinginascatteredphotonof slightlyreducedenergy,whichmaybeneglectedhere.Interactionof anincidentphotonbyprocess1, 2, or3is the start of acomplexdegradationprocess that in-volves multiple Coulombinteractions of the Compton-recoil, photoelectric-ejected, or pair-created electronswithatoms of thecrystal, as well as interactionor es-capeofphotonsthatmayemergefromtheinteractions.TheCoulombinteractions excitevalenceelectrons intothe conduction band, thereby giving rise to mobile chargethatissweptbythebiasvoltageontotheemitteroftheFETinthepreamplier.Inthecaseofaprimaryphotoelectricinteraction,theexcitedion, missinganinner-shell electron, decays byacascade of transitions inwhichelectrons fromoutershells fall inward, terminatingnallywiththecaptureof astrayelectronintothe valence shell. Eachdecaytransitionproducesaphotonof acertaincharacteristicenergy, which may then further interact with the crystal.In pair production, if the positron comes to rest in thecrystal it will combinewithanelectronandannihilatewith the production of two photons traveling in oppositedirections. If all the energy of the original photon nallyappearsasthekineticenergyof secondaryelectronsinthecrystal, thentheamplitudeof theresultingchargepulse will be accurately proportional to the energy of theincident photon; this is the ideal situation desired in x-rayspectroscopy. Ontheotherhand, if oneormoreof thesecondary photons escapes from the crystal, the resultingcharge pulse will be smaller, resultinginabroadenedspectral line or, more importantly, in a separate escapepeakinthe spectrum, corresponding to the escape ofprecisely one energetic photon such as the K x-ray photonemitted by a germanium atom that has photoelectricallyabsorbedtheincidentphoton.II.3. MoseleysLawTheoryMoseleydiscoveredthatthewavenumbersk 1ofcharacteristicx-raylinesemittedbytheelementsunderelectronbombardmentarerelatedtotheatomicnumberZbyequationsoftheformk = C(Z ), (1)whereCisacoecientwithunitsoflengththatde-pendsonthetypeofx-rayline,andisaunitlessvaluethat accounts for electronshielding, makingZ aneectivenuclearcharge.HemeasuredthewavenumbersdirectlybyBraggre-ectionspectrometry, usingcrystalswithknownlatticespacings. The x-ray energies are related to wave numbersbythePlanckformulaE= hck, (2)wherehisPlancksconstantandcisthespeedoflight.Intermsofx-rayenergies,theMoseleyrelationreadsE= C

(Z ). (3)This equation can be used to predict the characteristic x-ray energies for elements as a function of atomic number.Moreover,measurementsofphotonenergiescanbeusedtodeterminetheidentityofanunknownmaterial. Thisisthebasisofx-rayspectroscopy.III. APPARATUSFigure 2is ablockdiagramof the electronic equip-ment. ThedetectorisaCanberramodel BE2020high-purity germanium broad energy x-ray detector connectedthroughapreampliertoanamplier, andthencetoamultichannel analyzer(MCA). Thepreamplierisper-manently mounted on the detector. The amplier isaspectroscopygradeunit, withcoarsegainvariableinsteps anda continuous ne gaincontrol. The signalpulses from the preamplier are positive. Positive pulsesfromthe amplier are feddirectlyto the ADCinputof theMCAwhichtakes010voltpositivepulseswithwidthsgreaterthan2s. (Useofthebipolaroutputas-sures that the baseline is restored after each pulse, but isdiscouragedunlessyouencounterextremelyhighcountId: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 5Detector Pre-amplifierPulserDetectorBias SupplyAmplifier MCA (in PC)TE-700 VDC BiasFIG. 2. Schematicdiagramof thecircuitarrangementforx-rayspectroscopy,includingtheCanberraBE2020detector.rates.) The MCA sorts the pulses according to their am-plitudes and records the number of pulses in each of 2048amplitudeintervals knownas channelsor bins. Ahistogramdisplayof thesenumbersisgeneratedbytheMCA and represents the energy spectrum of the detectedxrays.III.1. DetectorThedetector is asinglecrystal of p-ndopedgerma-niummountedbehindathincarbonberwindowinavacuum. Toreducethermal noise, itisconnectedtoacoppercoldngerwhichdipsintoliquidnitrogencon-tained in a large Dewar below the detector. This arrange-mentconductsheatawayfromthecrystalandkeepsthedetectoratatemperaturenear80K, assuringthattherate at whichelectrons are thermallyexcitedintotheconductionbandof thecrystal isverylow. Thecrystalisreverse-biasedbymorethan+3000VDCinordertosweepout anyconductionelectrons that appear. Thedepletionzoneinthe biasedcrystal is eectivelyaninsulator. Onlyphotoelectronsejectedfromgermaniumatomsexcitedbyincidentxrays(orasaresultof rarethermal excitations)will conduct, thusproducingasig-nal. Around1.8eVisneededonaveragetoproduceanelectron-holepairinagermaniumcrystal.III.2. StartingUpWhenever you start up the system or make a change itiswisetochecktheproperfunctionofthepreamplier,amplier, andMCAbyexaminingwithanoscilloscopethepulsesattheoutputof amplier, andtochecktheoverall performance of the systemwiththe aidof thepulser. Inparticular, youshouldcheckthat theshapeandpolarityofthepulsesinto eachunitarecorrect,andthat the amplitudes of the pulses you wish to analyze areintheproperrangeastheyentertheMCA(010V).Theoutputcurrentfromthedetectorisaccumulatedonasmall capacitorconnectedtotheemitterofthein-put FET in the preamplier. The capacitor is dischargedautomatically by an auxiliary circuit whenever the accu-mulatedchargeexceedsacertainlimit. Eachdischargeproducesapulseof xedheightthatappearsinoneortwochannelsoftheMCAatthehighenergyendofthespectrum. Therateofthesedischargesvariesaccordingtotheintensityof theradiationbeingmeasured. Caremust be taken not to mistake the resulting spectrum fea-tureforalineinthex-rayspectrumbeingrecorded.TurnontheNIM-binpowersupply, thePC, andtheoscilloscope. ConnecttheamplieroutputtotheMCAandtheoscilloscope. Turnonthehighvoltagesupplyandgraduallyapplythebiasvoltageofabout+3000Vwhile monitoring the detector output on the oscilloscope.Be sure you apply a positive bias voltage; a negative highvoltagebiaswilldamagethedetector.Place a22Na source a few inches in front of the Ge de-tector window (The windows is made of very thin carbonber. Aguardhasbeenplacedoverittopreventacci-dental touchingandbreakingof the fragile foil, whichmust be as thin as possible to allow low energy x-rays tobedetectedandyetstrongenoughtoholdthevacuum.)Adjust the gain of the amplier so that at its output theprominent511keVlineappearsontheoscilloscopeasaconcentrationof pulseswithamplitudesnear5V. RuntheMCAcontrol softwarecalledMaestroforWin-dowsfromthedesktop. AccumulateaspectrumwiththeMCA, andadjust thegainsothat the22Nasignalappearsasalineinthemiddleofthedisplay. Youmayhave tocut out noise bysuppressingthe lowest MCAchannels. Thenplacethe133Bagamma-raycalibrationsource in the front of the detector window. Check the lin-earity of the MCA channels from the energy of the knownlines. CalibratetheMCAbydeterminingthechangeinenergyperchannel. MakesuretorecalibratetheMCAwheneveryouchangetheampliergain. (Infact,recali-brating often throughout the experiment,at least on the22Na511keVline,isagoodidea.)Youarenowreadytogo. Keepnotesof thesettingsused in all your measurements so you can return to themquicklyifdesired.IV. MEASUREMENTSInthisexperiment,youwillexplorethefollowing:thenestructuresplittings of theKandLshellenergylevels;the use of x-rayspectroscopyinidenticationofunknownmaterials;the Eversus Zrelations (Moseleys law) for thevariousseriesofcharacteristicKandLx-rays(seetheoriginalpapersinReferences[8,9]);attenuation cross sections of various metals forxraysofseveraldierentenergies;andavarietyofotherphenomena.Analyzethespectraasyoutakethembyusingthecur-sor to determine peak position and the full width at halfId: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 6slot for lead targetslot for absorberlead shieldinglead shutter90Sr beta sourceFIG. 3. Arrangement for producing bremsstrahlung x rays byhighenergyelectronsemittedinbetadecayof90Srand90Y,andstudyingtheabsorptionofthexraysbyvariousmateri-als. Thisisalsothearrangementforirradiatingsamplestoproduceuorescentxrays.maximum (FWHM), and the region of interest (ROI) fea-ture to determine total counts and area under the peaks.YoumayalsosavethedatalefromtheMCAforfur-ther analysis. As always, do notleave simple analysis foraftertheconclusionofyourlabsession. Plotsimplere-lationsamongdataasyouacquirethemtoconrmthattheexperimentisproceedingaccordingtoexpectations.Record pertinent details about all saved data les in yournotebook.IV.1. ProductionofBremsstrahlungandCharacteristicLineRadiation.Place the90Sr source (asource of highenergybetaparticles)sothattheholeisfacingthegermaniumde-tector. Observethespectrumof pulseswithnothinginthe45slot(seeFigure3). Thenputathin(1/4inchthick)slabofleadinthe45slotsothatthebetaparti-cles (energetic electrons) emitted by the source strike theslab. Observe the spectrum of the pulses produced by thebremsstrahlungradiationfromtheleadtargetandiden-tify the characteristic x rays of lead. The most prominentpeaksareprobablytheKlines. SmallerpeaksmaybeLlinesorbackgroundradiationfromweakradioactivityinthe room. Identify the energy (with an error estimate) ofthehigh-energycutooftheBremsstrahlungspectrum.Thisshouldcorrespondtothemaximumenergyof theincidentelectrons.Replace the lead slab with other materials and observetheircharacteristicxrays. The90Srsourceisshieldedintheleadcontainer soas toconnethedirections ofits emissions tothe target area. However, some scat-teredelectrons emerge fromthe target alongwiththebremsstrahlung. Youcanestimatetheelectroncontami-nationintheexitbeambymeasuringthechangeinthecountingratewhenthin(about1mm)layersof plasticare inserted between the window and the detector,or bydeecting the electrons with a strong permanent magnet.IV.2. X-rayInducedFluorescenceMeasuretheuorescentradiationemittedbydierenttarget materials when they are irradiated by x rays fromthe241Amorthe90Srsource. Arrangethegeometrysothat the target is as close as possible tothe detector,but the x rays from the source can not enter the detectordirectly. Identify the features you see. What is the lowestenergy K line you are able to detect?The highest?Whatarethelimitingfactors?Place an object of unknown composition in front of thex-ray source. There are many objects of unknown compo-sitionprovidedforthisexperiment. Recordthespectrafor these unknown materials, and identify locations of thepeakstocomparethemwithknownvalues.IV.3. MoseleysLawAdjustthegainsothattheKlinesofleadareatthefar right end of the MCA histogram and record their po-sitions. Thevariablex-raysourceusedinthis portionoftheexperiment(AmershamAMC.2084)isdetailedinFigure4. ItsemissioncharacteristicsaredetailedinTa-bleIII.TABLEIII. X-rayenergiesproducedbyAmershamvariablex-raysource. FromDataSheet11196.Target Energya(keV) PhotonyieldbK K (sec1sr1)Cu 8.04 8.91 2,500Rb 13.37 14.97 8,800Mo 17.44 19.63 24,000Ag 22.10 24.99 38,000Ba 32.06 36.55 46,000Tb 44.23 50.65 76,000aweightedmeanenergiesbthephotonyieldwasdeterminedusingahighresolutionSi(Li)x-rayspectrometer;thephotonoutputishighlycollimatedlimitingemissiontoabout0.5steradians.Placethevariableenergyx-raysource(seethespeci-cationsheettapedtothewall nexttotheradioactivesource storage cabinet) in front of the detector and recordthe channel numbers of the Klines of terbium(Tb),barium(Ba), silver(Ag), molybdenum(Mo), rubidium(Rb), and copper (Cu). In each case, obtain about 10,000counts in the major peak and measure as precisely as youcan the peak position, the FWHM and the total count un-dereverysignicantpeakobserved. Youmayseepeaksfromtheamericiumgammarays, neptuniumxrays, es-cape peaks, etc. Search for L lines at low energies for thehigher-Zelements. Ineachcase,printtheMCAdisplay,documentingtheruninyournotebook.Tosimplifytheanalysis,trytocoverthetotalenergyrange of the various spectra with one setting of the gain.Id: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 7FIG. 4. Diagramof the Amershamvariable energy x-raysource. The primary source is 10mCi of americium-241(1/2=433 yr), consisting of a ceramic active component inaweldedstainless steel capsule, withintegral tungstenalloyrear shielding. Themaximumsurfacedoserate(excludingemissionaperturewherethedoseratewillvarywiththetar-get in use) is less than 0.1 mR/h. The principal alpha energiesfromAm-241are5.442MeV(12.5%)and5.484MeV(85.2%).Gamma energies are 59.5 keV (35.3%). Also emitted are someneptuniumLx-rayswithenergiesbetween11.922.2keV.Itiswisetorunthroughtheseriesquicklyseveraltimesuntilyougetthesettingsjustright, andthentakeyournaldata. Fortheterbiumspectrum,recordthecountsperchannel overtheKLandKMpeakregions, in-cludingthewingsofthepeaks, sothatyouwill beableto make a detailed analysis of the structures of the lines.Togetdataonleadandotherhigh-Zelementsyoucanuse the90Sr bremsstrahlung generator with various mate-rialsplacedinthebeam. Youcanalsoexciteuorescentx-rayemissionfromhigh-Zelements withthe gammaraysfromthecalibrationsources. Tostudyuorescentemissioninlow-Zelements, increasethegaintoplacethecopperKlinesattherightendofthedisplay. Notethatduetotheplasticshieldingonthedetector, itwillbediculttomeasureenergiesbelow10keV.Ifyoufeeltheneedtoremovetheplasticcover, pleasetalktoaninstructor.IV.4. AttenuationCoecientsMeasure the attenuation coecient of x-rays of severalwidelydierentenergiesinseveral metalsof widelydif-ferentatomicnumberZbyinsertingthinsheetsof themetalbetweenasourceofmonoenergeticxraysandthedetector. (The Amersham variable x-ray source is a con-venientsourceofmonochromaticx-rayswithenergiesinthe range from 6 keV to about 60 keV: see Figure 4. Thegammaraycalibrationsources providemonochromaticphotonsupto1.3MeV.)A typical measurement might be carried out as follows.PlacetheAmershamhowitzerabout10cmfromthede-tectorwiththedial turnedtoAg. MeasuretherateofpulsesinthesilverKLandKMlinesusingthefacil-ities of theMCA. Placeafoil of metal withmeasuredthicknessbetweenthesourceandthedetector, ascloseas possible tothe source. Measure the reducedcountrate. (Agoodchoiceofthicknessisonethatreducestheratebyafactorof about2.) Repeatthemeasurementwithasecondandthirdfoil. Repeatthismeasurementfordierentmetals. If timepermits, changetheAmer-sham setting and check the count rate at dierent photonenergiesaswell.IV.5. EmissionofNuclearGammaRaysandCharacteristicXRaysPlace the133Ba gamma-ray calibration source in frontofthedetectorwindow. Adjustthegainsothattheen-ergy spectrum utilizes the full dynamic range of the MCA(2048 channels). Measure the spectrum and with the aidof Reference[4] identifyasmanyof itsfeaturesasyoucan.IV.6. e+eAnnihilationRadiationPlacethe22Nagamma-raycalibrationsourcenearthegermaniumdetector. Turnthegaindownbystepsuntilthespectrumof pulsesproducedbyphotonswithener-gies in the energy range from 01.5 MeV can be seen. Ac-cumulatethespectrumuntil thestatistical uctuationsare well smoothedout. Identifythe lines andexplaintheir origins. Identifythecontinuaof pulses producedby Compton scattering of the monoenergetic gamma raysinthegermaniumcrystal. Measuretheenergiesof theComptonedges. Explaintherelationbetweentheener-giesofthephotopeaksandtheComptonedgesintermsofthetheoryofComptonscattering.Dothe same withthe60Cosource. Withsucientstatisticsyoumayseeatinyblipinthespectrumnear0.511MeV.Howdoyouaccountforthat?Id: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 8IV.7. ChallengeProjects1. Placea137Cscalibrationsourceclosetothedetec-torwindowandreducetheampliergainsoastoplacetheneedle-sharp661.63keVgamma-raylinenear the right-hand side of the MCA display. Dontbe confusedbythe higher level reset pulse fromthe detector preamplier. Accumulate the spec-trumfor about onehour. Measurechannel posi-tions of all the features you can discern. Downloadthe spectrum for later detailed analysis. Try to pro-videaphysicsexplanationforeachofthefeatures,makinggooduse of the dataongamma-rayandx-rayenergiesintheCRCHandbook.2. Dothesamewiththe133Bacalibrationsource.3. With the system calibrated by x rays of known en-ergy, trytodeterminetheelemental compositionof the United States quarter coin by measuring thespectrumofitsuorescentxrays.4. Using the Ag source in the Amersham source, com-paretheabsorptioncrosssectionsofcadmiumandpalladiumfor theKLandKMlines of silver.Canyouexplainthedierenceinlightof thefactthat cadmium and palladium do not dier much inatomicnumber? Youcanobserveasimilardier-encebetweentheabsorptioncrosssectionsof var-iousmetalswithZnear25forxraysfroma55Fesource.5. Place a lead sheet in the beam of electrons emittedby90Srintheplasticboxtoproduceacontinuumspectrum of bremsstrahlung radiation. Insert a foilofmolybdenumintheslotbetweentheleadtargetandthedetector. Observethedetailsofthespec-trum in the range of energies around the KL (K)lineofmolybdenum. ObservetheKLabsorptionline, andexplainhowitsplaceinthespectrumisrelatedtotheKLline.V. ANALYSISV.1. BremsstrahlungAnalysisUsing the KL lines of lead and the 511 keV line fromthe22Na calibrationgamma-raysource as calibrators,determinethehigh-energycutoof thebremsstrahlungspectrum. Howdoesitcomparewiththeendpointoftheenergyspectrumofthebetaraysfrom90Srand90Y(consulttheCRCtables)?V.2. FluorescenceAnalysisTrytoidentifyall the lines foundinthe various x-rayspectra. Use the calibrationtoidentifythe ener-giesof theselines. Comparetheseenergiestothechar-acteristic energies of the metal fromwhichthey wererecorded. Thencheckthe energies fromthe unknownmetals. Usethemeasuredcharacteristicx-rayenergiesandcount rates toidentifythepercent compositionofthemetal.V.3. MoseleysLawAnalysisThe essential features of Moseleys laware revealedbyaplot of the square root of the measuredchannelnumbers against the atomic numbers of the emitting ele-ments. Makesuchplotsfortheeachdistinctsetoflines(KL3,KN3,LM,etc.),anddeterminethevaluesofCnandineachcase.1. Convertall yourpeakpositionsandFWHMmea-surements to energies in keV with estimated errors.Dothiswiththehighestprecisionthatyourdatajustify, andcompareyour results withthevaluestabulatedintheCRChandbook. Determinetheenergies of the germaniumKlines fromdataontheidentiedescapepeaks.2. Determinetheratiosof theintensitiesof theK1and K2lines and compare with the theoretical ex-pectationsbasedonconsiderationofthestatisticalweightsoftheparentL3andL2states(seeRefer-ence[7,pp.646655]).3. According to an approximate treatment of the spin-orbit interaction(see Reference [7, p. 606]), thedoublet separationinenergyshouldvarywithZas (Z )4. Comparethis predictionwithyourdata.4. Theoretical challenge: For the case of Tb, verifythat the magnitude of the spin-orbit splitting isthatgivenbyperturbationtheory. Whatquantumrule forbids the transition from L1to K? Given thisfact, howcouldyoudetermineexperimentallythevalueoftheenergyL1levelofTb?V.4. AttenuationCoecientsAnalysisPlot the natural log of the count rate against the thick-nessoftheattenuator. Checkwhetherthedataconformtotheformulaforexponentialattenuation,namelyI(x) = I0exln

I(x)I0

= x, (4)wherexisthethicknessandisaconstantcalledtheattenuationcoecient. Dividingbythedensityofthematerial gives amore useful quantityknownas themassattenuationcoecient.Id: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 9Fitastraightlinetothelogplot. Fromtheslope,de-terminethemassattenuationcoecientandtheattenu-ation cross section. Repeat for each energy and each ele-ment,andsummarizeyourresultsintabularandgraph-icalform. Whatregularitiesdoyouperceive?(Youmaynd log-log plots of cross section versus energy or Zuse-ful).POSSIBLETOPICSFORORALEXAM1. Atomic structure and the explanation of the Mose-ley relation between K-line energies and atomicnumberZ2. Comptonscattering3. Classical theoryof the Thomsonscatteringcrosssectionoftheelectron,e.g.Reference[10]4. Thebremsstrahlungspectrum,e.g.Reference[11]5. Attenuationofanx-raybeaminmatter, e.g.Ref-erence[10]6. The theory of the high-purity germanium detector,e.g.Reference[2][1] A. C. Melissinos and J. Napolitano, Experiments inmodernphysics, (AcademicPress, 2003)Chap. 8.2.5,pp.312315.[2] G. F. Knoll, Radiationdetectionandmeasurement,(JohnWiley&Sons, 2000)Chap. 12, pp. 405426, 3rded.[3] IUPAC, Analytical compendium: X-rayspectroscopy,in Analytical Compendium (International Union ofPure and Applied Chemistry, 2003) Chap. 10.3.4.8,http://www.iupac.org/publications/analytical_compendium.[4] R. Deslattes, E. Kessler, P. Indelicato, L. de Billy, E. Lin-droth, J. Anton, J. Coursey, D. Schwab, K. Olsen, andR. Dragoset, X-raytransitionenergies (version1.0),(NIST, Gaithersburg, MD, 2004) http://physics.nist.gov/XrayTrans.[5] CRC Handbook of Chemistry and Physics, 84th ed. (CRCPress,20032004).[6] W. C. R ontgen, Nobel Lecture (1901), http://www.nobel.se/index.html.[7] A.H.ComptonandS.K.Allison,X-raysintheoryandexperiment, (D.VanNostrand,NY,1935)pp.590595,606,syics630,646655,2nded.[8] H. Moseley, Phil. Mag. 26, 1024 (1913), the High-FrequencySpectraoftheElements,PartI.[9] H. Moseley, Phil. Mag. 6, 27, 703(1913), the High-FrequencySpectraoftheElements,PartII.[10] R. D. Evans, The atomic nucleus, (Krieger, Fla, 1955)thismassivebookwaswrittenbyanMITprofessorforatwo-semester course inNuclear Physics in1955andcoversagreatdealofmaterial![11] B. Rossi, Highenergyparticles, (Prentice-Hall, NewYork, 1952)availabletoMITstudentsonlineviahttp://web.mit.edu/8.13.[12] K. M. G. Siegbahn, Nobel Lecture(1924), http://www.nobel.se/index.html.[13] A. H. Compton, Nobel Lecture (1927), http://www.nobel.se/index.html.[14] A. Compton, The Physical Reveiw, Second Series 22(1923).AppendixA: Historical ElementsofX-RayPhysicsThe signicance of Rontgens discovery for medical di-agnosis was quickly recognized. Kaisers, queens, andlesser folksharedthe wonder of gazingat the interiorstructureoflivingbodieswithoutcuttingthemopen. Inthe1930schildrencouldspendhoursattheshoestoreamusingthemselvesbywigglingtheirtoesinthex-rayuoroscopeusedtojudgethetofnewshoes. Millionshadtheirchestsregularlyexaminedbyhigh-dosex-rayphotographyforsignsoftuberculosis. Today,xraysareof critical importanceintheelds of medical imaging;material science, fordeterminingbothcompositionandstructure; transportationsecurity, for example airportbaggageinspection; microscopeswithsuboptical resolu-tion; astrophysicsandcosmology; crystallography, suchasthefamousexampleof RosalindFranklinsdiscoveryof the double helix structure of DNA; and observing fastreactionswithsynchrotronradiation.The classic waytogenerate xrays is tobombardametal target with a beam of energetic electrons. A typicalcommercial x-raygenerator, suchasoneusedbyaden-tistoranairportbaggageinspectionsystem, employsavacuum tube in which electrons emitted from a lament-heatedcathodeareacceleratedbyanelectriceldsup-portedbyahigh-voltage(say,50kV)powersupplyandstrikeametalanodetarget. Thespectrumofthexraysradiatedfromthe target consists of a bremsstrahlungcontinuumwithanenergycutoathc=V e(Visthevoltage of the power supply), and narrow lines with wave-lengthscharacteristicofthetargetmaterial.After Rontgens 1895 discoveryof xrays, the mostimportantlandmarksintheeldssubsequentdevelop-mentincludedvonLauesdiscoveryof x-raydiractionbycrystals, Moseleysdiscoveryof therelationbetweenatomicnumberandthewavelengthsof thecharacteris-ticxraysemittedbytheelements,Siegbahnsstudiesinx-rayspectroscopy[12] andComptonsdiscoveryof thequantumcharacterof thescatteringof xraysfromfreeelectrons[7,13,14].Id: 31.xrays.tex,v1.222007/08/2916:33:57sewell Exp 10Rontgen initially thought tentatively and incor-rectly that the newrays he had discovered werelongitudinal electromagneticwaves. Thehigh-frequencytransversewavenatureofxrayswasnallyprovedsix-teen years later by von Laues discovery of the diractionofxraysbycrystals.