Lab 5 Lifetime of the 14.4keV Level in Fe57

Lifetime of the 14.4keVLevel in Fe-57Ainsley Niemkiewicz

Introduction•Co57 decays intoFe57 at the 136keVlevel by k-electroncapture–proton in the nucleusFigure 1: The decay scheme for Co-57.captures an electron from the k shellp + e− → n +υ–#p decreases & #n increases–Co-57 → Fe-57•An electron from the l shell fills the hole left bythe electron that was captured–An x-ray is emitted (detected)

Introduction•Fe57 either decaysFigure 1: The decay scheme for Co-57.–directly to the ground state and emits a 136keV γ-ray (11%)or–decays to the 14.4keV level and emits a 122keV γ-ray (89%)•Detected γ-ray = “start”•14.4keV level decays to the ground state either–directly, emitting a 14.4keV γ-ray or–internal conversion•nucleus gives some of its energy to an electron in the k shell•the electron is ejected from the atom•The hole is filled by an l shell electron•X-ray is emitted–Detected γ-ray or x-ray = “stop”

Method•Co57 source–placed on an Fe substrate–located between twoscintillators–faces the scintillator onthe right (scintillator 2)•minimize the effects of absorptionin the substrate•2 Scintillators–when struck by a particle, absorb the energy from that particle–reemit the energy in the form of light–Scintillator 1 (left)•1” thick plastic–Sufficient counting efficiency with 1” thickness–Detects photoelectric and Compton effects wellFigure 2: A diagram of the apparatusused for this experiment .•Detects the 122keV γ-rays emitted when Fe-57 decays from 136keV to the14.4keV level (start)–Scintillator 2 (right)•1/8” thick plastic with 5% Pb (Bicron)–Increases the efficiency for 14.4keV γ-rays»counting efficiency = 77% for 14.4keV γ-rays» counting efficiency = 93% for 6.4keV x-rays•density = 1.1g/cm^3•Detects the decay of the 14.4keV level to the ground state (stop)

Method•Photomultiplier tubes (RCA 8575)–Light from the scintillators produces a current–photomultiplier tubes multiply this current 10^7times–Voltage across the tube=2.02kV (trials 1&2), 2.12kV(trial 3)•Amplifier-Discriminators (ELSCINT)–Amplifier gain = 4 (“gain 1”, scintillator 1), 20 (“gain5”, scintillator 2)–Discriminators convert an electronic pulse into astandardized output pulse•only when the input pulse amplitude > threshold–Adjust threshold in terms of scintillator output bychanging the gain and photomultiplier tube voltage•threshold for scintillator 1 > 14.4keV•threshold for scintillator 2 > 6-10keV (weak or strong source)

Method•Time to Amplitude Converter (TAC)–Discriminator 1 → start of the TAC–Discriminator 2 → delay → stop of the TAC•Delay=200ns•Can see prompt peak/coincidences•Can see the decay data left of the prompt peak (136keV levellifetime)–TAC changes the time between the start and stoppulses into a voltage•amplitude proportional to time (lifetime)–amplitude conversion = 2,000ns for trial 1 and1,000ns for trials 2 and 3•Multichannel Analyzer (MCA)–sorts the data into a histogram–voltages (bins) = x-axis and # of counts = y-axis–Conversion gain = 1024 channels

Data & AnalysisGraph 2: Calibration 2 with pulses sent in multiples of 160ns,without the delay, and TAC set at 1,000ns.Graph 1: Calibration 1 with pulses sent in multiples of 160ns, connected to the delay, and TAC set at 2,000ns.• Calibration– Time calibrator sent pulses of integer multiples of 160ns– 1 st calibration• with the delay• TAC = 2,000ns– 2 nd calibration• without the delay• TAC = 1,000ns– slope of linear curve fits = conversions from channel # to time

Data & AnalysisGraph 3: Trial 1 exponential decay of the 14.4keV level in Fe 57 .Graph 4: Trial 1 exponential decay of the 136keV level in Fe 57 .• 3 trials (24 hours, 24 hours, 5 hours)• Exponential curve fit:± xf(x)=Aeτ+ c– A = area under the curve, τ = lifetime, and c = background– Points were binned by 4 (14.4keV level)• Small # of counts in each binτ

Data & Analysis3Trial #Lifetime12Level in Fe 57 Weighted Average142.9±0.52(ns)Channel Number (#) 76.25±0.36 150.6±0.9 149.2±3.2Time (ns) 144.7±0.68 140.5±0.84 139.2±2.914.4keVAccepted Value 1 (ns)141.5Level in Fe 57 Weighted Average12.32±0.14(ns)Channel Number (#) 6.607±0.09 12.33±0.29Time (ns) 12.54±0.17 11.50±0.27136keV13.98±0.4613.04±0.43Accepted Value 1 (ns)12.55Table 1: A table of the results from the graphs.

Data & AnalysisGraph 11: Plot of χ 2 vs. the lifetime for trial 2,which shows the best estimate for the lifetime.Graph 9: Plot of χ 2 vs. the lifetime for trial 1, which shows the best estimate for the lifetime.• Same exponential curve fit: f(x)= eτ+ c• Fixed lifetime (τ)τ– 120-160ns, steps of 5ns• χ^2 values vs. lifetime• Minimum=best estimate for the lifetime• (minimum χ^2+1)=standard deviation for the lifetimeA± x

Data & Analysis2LifetimeTrial #1Fe 57 Weighted142.3±0.24Average (ns)Channel 76.59±0.4Number (#) 1Time (ns)145.3±0.7814.4keVLevel inAcceptedValue 1 (ns)141.5150.3±0.69140.2±0.64Table 2: A table of the results from the χ2 vs. lifetime graphs.• The natural linewidth of the 14.4keV level wasdeterminedh−9−9∆E= = 4.625×10 ± 0.0078×10 evτ• Accepted value=4.66x10^(-9)ev

Uncertainties• Χ^2 values ≈ (# of data points - degrees offreedom)Trial #Lifetime12314.4keV χ 2 (experimental) 292.4238.9261Level inFe 57 χ 2 (expected)394284289136keV χ 2 (experimental) 6.611126165.8Level inFe 57 χ 2 (expected)21207196Table 3: A table of the χ 2 values and the expected values.• Curve fits are okay, but not perfect• Background– flat– adds a constant (c) in the curve fit equation• Scatter– Ex. particle Compton scattering in one detectorand then the scattered photon being detected bythe other detector– Scatter from all over the room

Conclusion• Good Results– Lifetime of the 14.4keV (141.5ns) and 136keV(12.55ns) levels were determined• Two methods– Curve fit» 142.9±0.52ns (14.4keV)» 12.32±0.14ns (136keV)– Fixed lifetime (minimum value)» 142.3±0.24ns– Natural linewidth (4.66x10^(-9)ev) of the14.4keV level was calculated• 4.625x10^(-9)±0.0078x10^(-9)ev– All the values are reasonable compared to knownvalues• some are a few standard deviations away