Alpha-Gamma Correlations

Reiss Moore (in collaboration with Luke Arnell)

Abstract

By looking at the correlations between the alpha and gamma decays in heavy nucleiit was possible to deduce a number of their nuclear properties. Such nuclei used wereamericium-241 and thorium-228. The lifetime of the intermediate state of the mostcommon correlated alpha-gamma decay in Am-241 was determined by using a fasttiming circuit. This resulted in data representing a series of exponentially decayinggaussian curves from which we could deduce a half-life by optimising a convolution tothe raw data. A half-life of 70.7 6.5 ns was measured. By also observing the angu-lar correlation of the same decays, the spin of the intermediate state was determined,although results were inconclusive. Finally the coincidences of alpha and gamma tran-sitions were observed in Th-228. By comparing coincidence energy spectra with thegeneral energy spectrum of Th-228, combined with measurements at different angles,it is possible to observe the relaxation of spin alignment with time, although theseresults were also deemed inconclusive.

1 Introduction

For a long time there have been a variety of ways to determine the quantum mechanicalproperties of many heavy nuclei. Many of the older methods prove to be just as effectivetoday. By looking at the correlated alpha and gamma decays of heavy nuclei, it is possibleto determine properties such as the lifetime of particular states and their spin.1 Thisexperiment does exactly that by observing the time between correlated alpha and gammadecays to measure the lifetime of the intermediate state that the alpha decay populates.Triggered by the initial alpha decay, a timing circuit is used to detect the number ofcorrelated decays for different time intervals. A similar timing circuit is used to also lookat the angular correlation between these transitions. By fixing the axis of an initial alphadecay, a subsequent gamma decay has some angular distribution, which can be observed byrecording the same information required to determine the lifetime of the intermediate state,but at different angles between the respective alpha and gamma detectors. This allowsdetermination of the gamma transition character. Finally, coincidence measurements wereused to look at spin relaxation. Details will be given on all of the equipment used, how itwas used, and the results and discussion of the experiment.

2 Theory

2.1 Alpha-Gamma Correlation

When a nucleus decays by alpha emission, it can populate many different states as well asthe ground state, in a newly created excited nucleus, with each emission having a differentdecay probability. The daughter states are at a higher energy than the ground state, soin order to reach the ground state gamma emission will also occur via a number of lowerenergy states, or often straight to the ground state. By combining a charged particledetector with a gamma ray detector, it is possible to detect the gamma ray that is theresult of a particular alpha decay.

Americium-241 (52+

) decays by alpha emission, with the majority of decays populating the

excited states of neptunium-237. The most prominent of these is the decay to the 52

59.54keV level, at a probability of 84.5%. Subsequently, gamma radiation is emitted in order toreach the 52

+ground state from the 59.54 keV level. These two decays can be described as

correlated. The intermediate state has a half-life of 67 ns. Similarly, thorium-228 decaystotally by alpha emission, populating the excited states of radium-224, which itself alphadecays to the ground and 240.99 keV levels of radon-220. The alpha emission of Th-228 isprimarily to the ground state (73.4%), with 26% of the decays to the 84.37 keV state of Ra-224 that in turn gamma decays to the ground state. Although 94.7% of the alpha decays

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of Ra-224 are to the ground state, 5.25% are to the 240.99 keV level. Th-228 thereforeshows two significant correlated alpha-gamma decays that can readily be observed.

2.2 Lifetime

The lifetime of a particular populated state is determined by Heisenbergs uncertaintyprinciple:

Et ~2

(1)

where E is the uncertainty in the states energy, and t is the uncertainty in the statesassociated time. The uncertainty in energy is representative of the energy width of thestate, , which itself is related to the mean lifetime of the state, :

E =

2=

~2

(2)

Rearranging this relationship, we can see the equation used to measure the lifetime ofexcited states:

=~

(3)

In alpha decay, the associated state lifetimes are relatively long when compared to gammaray transitions that tend to occur for short-lived states.2 For these shorter lifetimes it isnot possible to calculate the lifetime from the exponential behaviour of the activity as afunction of time. By measuring the time interval between the formation of an intermediatestate and its subsequent decay instead, we get the same exponentially decaying behaviourfor the survival probability of a state, and we see the second decay transition shortly afterthe intermediate state is formed.3 By comparing the time interval and the number ofcounts for each time interval, a graph similar to that in Figure 1 can be produced.

The graph allows for the calculation of the mean lifetime of an intermediate nuclear state.It represents a sum of exponentially decaying Gaussian peaks, and obeys the followingequation:

N(t) = A+Bt

exp texp(t t)2

2(4)

where N is the number of counts, A represents the background radiation, B is somenormalisation factor, is the state decay constant, t represents a point along the curve,t is the time of the interval mentioned previously and is the time resolution. From thedecay constant it is possible to calculate the mean lifetime of the nuclear state, as seen inEquation 5:

=1

(5)

3

Figure 1: An example of a plot for the time interval (x-axis) vs. the number of counts per each timeinterval (y-axis). The time resolution shown should be less than or similar to the state half-life.

The state lifetimes are often quoted as half-lives, t1/2, so the following equation can beused for conversion between the two:

t1/2 = ln2 =ln2

(6)

2.3 Angular Correlation

For gamma radiation, it is possible to work out the multipole order of a particular transitionby looking at the angular correlation between two subsequent decays.4 For a situationwhere there exists an equal substate population (e.g in a large sample of nuclei), whenwe average over the angular distribution we find that it is isotropic for a single transition.For a nucleus that decays by two successive radiations to the ground state, however, whenthe first decay is observed it implies that the angular momentum of the nuclear statebetween the two has some orientation. As such, the following decay will have some angulardistribution about the initial decays direction.5

The angular correlation between the alpha and gamma decays, W(), can be representedby:

W () =k=0

AkPk(cos) (7)

where k = 0, 2, ..., kmax (i.e even due to conservation of parity), is the angle between thetwo decays, and Pkcos() are the Legendre polynomials. Ak accounts for the multiplicity ofthe observed radiation and the angular momenta that the involved nuclear levels possess. Ifwe introduce conditions that result in unequal populations of the nuclear states, W() is nolonger constant. One such condition is when a strong magnetic field and low temperatures

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are introduced. A reduction in temperature causes the populations to become unequal as adirect result of the Boltzmann distribution.6 Another way is to look at the two successiveradiations and observe the angular distribution of the second around some axis defined bythe first transition. This definition of a fixed axis means that for the first transition =0,and as a result a decay between states of the same angular momentum cannot occur in thatparticular direction.7 The resulting secondary transitions have a non-isotropic distributionin order to conserve angular momentum, a result of the spin orientations in the nucleus.The shape of the correlation function is determined by these spins.8 As such it is possibleto deduce the spins of the states involved in the correlated transitions from the angularcorrelation function.

2.4 Spin Relaxation

Spin relaxation occurs when spins interact with the surrounding thermal environment torestore equilibrium. It can be split into two types: spin-lattice (longitudinal) relaxation,and spin-spin (transverse) relaxation, each of which has a respective time constant. Theformer relates to the Boltzmann distribution of the spin populations, and the latter isrelated to the decay of equal spin state populations, which form spin coherences.9 Toobserve both of these, similar methods to those in Section 2.3 can be used. The creationof unequal substate populations produces a non-zero net magnetisation of the spins inan excited nucleus. This magnetisation will decay over the same time constant describedabove, which defines the length of time it takes for the spin orientations to return to theequilibrium state.10

3 Equipment

This section will introduce and explain the equipment that has been used to carry out thisexperiment.

3.1 Surface Barrier Detector

Silicon diode detectors are used to detect charged particles due to their availability andoperation at normal temperature (some other semiconductor detectors require cooling e.g.HPGe). A surface barrier detector is an example that, in this case, contains a silicon PINdiode. A PIN diode contains a p-type region, an n-type region, and an intrinsic layerbetween the two. The p- and n-type regions are heavily doped, creating an acceptor levelnear the valence band, and a donor level near the conduction band respectively. Thiscreates a large potential barrier between them, giving a depletion region that is depleted of

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electrons and holes, used for the detection of charged particles. The intrinsic layer is lightlydoped, usually with silicon that is either slightly n- or p-type. PIN diodes are favoured overPN junctions due to the intrinsic region providing a larger volume over which electron-holepairs can be produced, as well as offering a low capacitance and high breakdown voltage.11

By altering the size of the intrinsic region, once can change the capacitance and quantumefficiency of the diode. The signal produced is a quantity of charge, Q, determined by thefollowing equation:

Q =E e 106

(8)

where E is the energy if the alpha radiation (in MeV), e is the electronic charge and is the energy needed to create an electron-hole pair. It is important that a high-voltagereverse bias is applied to the detector. The reverse bias acts to increase the width of thedepletion region through to the underlying layer, making it the same width as the intrinsicregion.12 Any bias applied must not be too high as this will deplete the PIN junction ofall charge carriers.13

Radiation damage can limit the operation of any semiconductor detector. Incoming ra-diation can give rise to defects in the detector material, which allows different levels toform that can trap decays and limit the semiconductors charge carriers. As such energyresolution is decreased with the possibility of leakage current increasing.14

3.2 Plastic Scintillation Detector

Figure 2: Schematic of a scintillation detector.

Plastic scintillation detectors are most commonly used to detect gamma rays. A schematicof a typical detector can be seen in Figure 2. When gamma radiation enters the scintillator,their energy is absorbed by exciting the scintillator molecules. As these states decay backto the ground state fluorescence occurs, which is then transmitted to a photomultipliertube (PMT) that multiplies the current produced by the fluorescence for suitable detectionand analysis. It is important to note that all of the fluorescence transitions occur ata lower energy than that required to initially excite the electronic configuration. This

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means that there is little, to no self-absorption of the produced fluorescence. Generallyscintillation detectors have a fast response time, making them excellent for the study ofdifferent gamma decays that occur within short time periods of one another. Plastic isoften used for due to its flexibility, fast signal processing and high light output.15 Aplastic that has cross sections of the photoelectric and pair production effects larger thanthat of Compton scattering should be used to maximise efficiency, since gamma rays arenot totally absorbed when they undergo Compton scattering, giving rise to detections atdifferent energies to those true to the nucleus begin studied.16

In order to discriminate between different radiation types, a scintillator relies on its depen-dence on the energy loss of particles, dE/dx, as they enter the material. The light emissionthat occurs in a scintillator can be split into relative fast and slow decay components, eachdependent on dE/dx, which determine the decay time of the light emission. This providesthe discrimination between different radiation types, since different radiations have differentdE/dx, and therefore different ratios between the fast and slow components. For plastic,a particle that goes through a large energy loss produces excited molecules at a high den-sity. This results in more intermolecular interactions, and radiative states produced (fastcomponent) can lose their energy in a number of ways. The slow component is representedby metastable excited states. For gamma rays, the fast component is significantly largerthan the slow component.17

The primary components of a PMT are a photocathode, a dynode and an anode.18 Thephotocathode converts incident light from the scintillator into electrons by transferring theenergy of a photon, h, to an electron, which drifts and escapes from the photocathodesurface if h is greater than the work function of the photocathode material. Acceleration ofthe electrons is then applied by an electrode, directing them to strike the dynode. As theydo, secondary electrons are released that are in turn accelerated to another dynode so moreelectrons are released, and this continues until they reach the anode. An amplified current isproduced for analysis. Mu-metal shielding protects the PMT from low frequency magneticfields that may influence the low energy electrons that travel through the PMT system.19

Typically, NaI is used as the scintillator material, since it easily grown to large sizes andshapes. It also has a relatively large atomic number, giving a reasonable interaction crosssection. A dopant of thallium is often used to provide wavelength shift, which reduces thelikelihood of excitation emissions being reabsorbed.20

The transmission of light between a scintillator and PMT must be maximised to maintainefficiency. As such, silicon is used as the contact for organic scintillators and a PMT sincethe refractive indices of all three are similar.21 For timing measurements, the PMT isheld at a high negative voltage. The size of the voltage determines the gain of the signalproduced.

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3.3 Charge Sensitive Preamplifier

Signals from semiconductor detectors are generally weak, so they are amplified by pream-plifiers. Charge sensitive preamplifiers have a lack of sensitivity to varied capacitancesassociated with temperature changes making them ideal for use with semiconductor de-tectors.22 This can be demonstrated by looking at a schematic of the charge sensitivepreamplifier circuitry in Figure 3.

Figure 3: Charge-sensitive preamplifier schematic.

The governing equation is simply related to the capacitance of the preamplifier, Cf :

V0 =Q

Cf(9)

where V0 is the output voltage, and Q is the charge from the surface barrier detector. Assuch there is no dependence on detector capacitance. The preamplifier collects charge onthe capacitor Cf and converts it to a voltage. Combining Equations 8 and 9, a relationshipbetween the incoming charged particle energy and voltage produced as a result can be seenin the following equation:

V0 =E e 106

Cf(10)

The amplitude of this voltage is therefore directly proportional to the incoming alphaenergy, and as such one can then either view the output on an oscilloscope or amplifythe signal for further uses. Equation 11 shows the equivalent noise charge, ENC, for apreamplifier. Noise must be limited to maximise detector resolution.

ENC = eVrmsw

C (11)

where C is the total detector and preamplifier capacitance, w is the energy required toproduce an electron-hole pair, and Vrms is the output voltage noise level.

Bias for the detector is supplied via the preamplifier. A connection between the preamplifierand detector facilitates the voltage supply to the detector plus the signal from the detectorto the input of the preamplifier.23

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3.4 Fast Timing Amplifier

For timing experiments, a fast timing amplifier must be used. It is an example of aNuclear Instrument Module (NIM), which also applies to the remainder of equipment to beexplained. Timing amplifiers act to reproduce the incoming signal with a higher amplitudewhilst retaining the primary shape. The rise times of the signal produced are in the lowor sub-nanosecond region, making them perfect for timing measurements. The resultingpulse also has its polarity reversed, although a switch can provide the opposite. Othercontrols on a timing amplifier include gain adjustment, and integration and differentiationtime constant selection. The former allows the size of the incoming signal to be adjustedon a coarse or fine scale, and the latter provide pulse shaping to optimise the signal fortiming measurements

3.5 Slow Spectroscopy Amplifier

Slow spectroscopy amplifiers, or linear amplifiers, provide optimisation of the size and shapeof incoming signals for energy spectroscopy, whilst achieving a high energy resolution.Typically the input is a preamplifier signal, which can often be irregular. Pile-up canoccur whereby signals occur before the tail of an initial signal has reached the baseline,thus altering the amplitudes of the signal. A shaping time can be defined to ensure thatthe tail is shortened and this overlapping effect does not occur.24

3.6 Discriminators: Leading Edge and Constant Fraction

Fast timing discriminators generate an output dependent upon whether or not we are inter-ested in a certain signal that the discriminator receives. For example, it will only output asignal when the alpha decay signal from a fast timing amplifier is above a chosen thresholdvalue25. A logic pulse is then created that is related in time to an event occurrence. Thetiming resolution is affected by three main elements. The first is walk, where variations inthe incoming pulses shape and amplitude cause the output pulse to move from the pick-offelement, relative to the input pulse. The second is drift, a result of temperature variationsand component degradation, giving a long-term timing error. The third is jitter, caused bynoise and statistical fluctuations that increase the timing uncertainty of the pick-up signal.Both the jitter and walk can be seen in Figure 4.26

Leading edge discriminators look at the leading edge of a signal and check when it crossesa particular threshold level. Once the threshold is reached the output logic pulse is given.The threshold is adjusted via a potentiometer. The main problem, however, is that walkis very prominent since only the leading edge is used. Frequent changes in the pulseamplitudes coming into the discriminator mean that the corresponding outputs occur at

9

Figure 4: Graphic of the jitter and walk effects in discriminators.

different times. For detectors that produce a large number of signals of varying amplitudes,the result is poor time resolution and a lack of accuracy in timing measurements.

To overcome this, a constant fraction discriminator (CFD) can be used. Instead of justusing the leading edge of the incoming signal, a CFD takes the whole signal and separatesit, with one part being reduced in amplitude by a factor f, and the other being inverted anddelayed. The sum of the two is then taken to produce the constant fraction signal, witha zero-crossing time corresponding to the time at which the pulse reaches the fraction, f(same as the amplitude reduction factor), of its final amplitude. The zero-crossing time andpulse amplitude are independent, and so the crossing gives a time marker at the optimumpulse height fraction.27 As such, there is little walk with a CFD and the timing resolutionis greatly improved when jitter is reduced, making them much more suitable for timingexperiments. A CFD unit will have an input for a signal from a timing amplifier, twoinputs to introduce the delay that is required for a CFD to work, a monitor output thatshows the combination of the two initial, and then altered split signals, and a number ofoutputs for use with further equipment. Also included are three potentiometers: the Tscrew provides adjustment of the threshold level, the Z screw provides adjustment of thewalk, and the W screw allows the output width to be adjusted.

In order to correctly set a leading edge discriminator, the threshold level should be set aslow as possible so as to minimise walk, but also at a steep slope to ensure that jitter is alsominimised. To optimise a CFD, first the threshold should be adjusted to minimise the noiseand low-energy pulses. Next, the walk should be optimised by viewing the signal from theCFD monitor output and adjusting the walk potentiometer so that all of the signals thatare seen have the same zero-crossing time28. Figure 5 shows the ideal threshold and walkadjustments.

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(a) (b)

Figure 5: CFD optimisation, where (a) shows the ideal threshold adjustment, and (b) shows theideal walk adjustment.

3.7 Time-to-Amplitude Convertor (TAC)

A TAC is a timing module that outputs a pulse with an amplitude that is proportional tothe time interval that it records.29 A start pulse triggers the TAC to start, for example theCFD output from an alpha detector, which is then stopped by another signal, for examplethe CFD output from a related gamma detector. For recording decay correlations, it isimportant that a delay is applied to the second decay to ensure that the TAC is stopped asa direct result of the same decay that triggered the TAC to start. The primary control ona TAC is the range selection, which is used to select the time interval between the signalsthat start and stop the unit. Given options of 50, 100 and 200 ns, a multiplier allowsfurther range selection. A range should be selected that is related to the time intervalsthat will be measured.

3.8 Coincidence Unit

A coincidence unit requires at least two signal inputs from a discriminator. Provided theincoming signals are of a good width (roughly 100 ns), and they overlap when the rise timeof the second input is more than 5 ns after the first signal, the coincidence condition ismet (see Figure 6).30 The result is a logic pulse, which indicates that a coincidence hasoccurred.

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(a)(b)

Figure 6: (a) shows the steps and signals required to correctly calibrate the coincidence unit. (b) isan example of the coincidence output signal.

3.9 Gate and Delay Generator

Gate and delay generators produce a logic pulse with adjustable width and delay. They aretriggered by an incoming pulse, giving a logic output that is wider than typical logic pulsesmaking them useful for event windowing. The output can be used as a gating signal foran MCA (see following section) when combined with the signal from a spectroscopy ampli-fier.31 The gating signal should overlap the signal from the spectroscopy amplifier.

3.10 Multichannel Analyser (MCA)

An MCA is an Analog-to-Digital Convertor (ADC) that stores the information in its inter-nal memory, based on a count-by-count system. An input pulse has some amplitude andthe ADC converts this amplitude into a digital number. The number of pulses that theanalyser records over a given time gives the total number of counts over all memory. Byconnecting it to a computer it is possible to record quantitative information from detectorset-ups and analyse the recordings using MCA emulation software. It is also possible togate the MCA, which prevents certain pulses from being recorded by the ADC when it isin the process of recording a previous pulse. A logic signal holds the input gate open whenthe ADC is not busy.32

For timing measurements the MCA should be calibrated so that the relationship betweenthe channel number and the time interval recorded is known.

3.11 Arrangement

The NIM modules are slotted into a NIM bin that supplies them with power. DifferentNIMs require different voltages, defined by the pin arrangements of the connectors on

12

the back of the modules. Depending on the function of each module and the desiredarrangement, they can be connected together by using coaxial cables, which are suitableto carry the signals involved in typical nuclear experimental systems.

4 Method

Initially it was essential to determine the correct bias that should be applied to the chargesensitive pre-amplifier that was connected to the surface barrier detector. This was simplydone by measuring the background fluctuations and the amplitude of the signal producedas the bias voltage is incrementally increased. By striking a balance between the two, theoptimal bias voltage can be found. The MCA was also calibrated by comparing an initialrecording from the TAC, with a delayed version of the original. The shift in the peakposition corresponds to the delay time used and as such the number of nanoseconds perchannel can be deduced.

Source

PMT Timing Amp Discriminator Delay

TAC

Detector Preamplifier Timing Amp Discriminator

MCA

Figure 7: Schematic of the first and second experiments.

To measure the lifetime of Am-241, it is possible to look at the coincidence between twodecays linked as described in the Section 2.1. The surface barrier detector, which has tobe connected to a charge sensitive preamplifier first, and PMT are each connected to afast timing amplifier. These signals are then connected to a discriminator each. Initiallythey were connected to leading edge discriminators, but for reasons explained in Section3.6 CFDs were used for the remainder of the experiment. The gamma signal must thenbe delayed to ensure that the gamma decay that is definitely detected after the initial

13

alpha decay. By using a TAC, it is possible to measure the difference in time at which thetwo decays occur. The TAC is started when an alpha decay to the intermediate state isdetected, and subsequently stopped when the correlated gamma decay to the ground stateis detected. By running the TAC signal through an MCA for a chosen amount of time(the longer the time, the better the results), a distribution of the counts against time canbe analysed to determine the lifetime of the state (as discussed in Section 2.2). The rawdata given by the MCA can be interpreted using the relationship in Equation 4. Initiallya rough fit of the equation to the data can be applied, with a code designed to apply achi-squared analysis used to minimise the equation to the raw data by changing the A, B, and components of Equation 4.

To determine the best threshold for the leading edge discriminators, recordings were takenfor different settings and the results compared by looking at the overall shape and resolutionof each. The same method was used to optimise the settings of the constant fractiondiscriminators, although more data was needed due to there being more settings to controlwith the CFDs. A combination of leading edge and CFDs was also used to provide amiddle-ground comparison between the two types of discriminator.

For the second part of the experiment it was necessary to alter the angle between the twodetectors in order to deduce the spins of the nuclear states involved in the correlated decayof Am-241. The set-up was exactly as it was in the first part of the experiment, with anglesof 180, 135 and 90 between the two detectors being measured. It was important thatthe experiment for each angle was run for a lengthy amount of time to ensure that suitablecomparison could be achieved between the different angles, since the data created for eachcan be very similar.

The third part of the experiment involved looking at the coincidences of the alpha andgamma decays at different angles, from which the spin relaxation time can be deduced. Inthis case Th-228 was used since it is easier to differentiate between the singles and coinci-dence conditions than with Am-241. All of the equipment previously used is kept the sameexcept for the TAC and delay units. By first tuning the CFDs for the alpha and gammadecays from the Th-228 source, the outputs were connected to a coincidence unit, whichin turn was connected to a Gate Delay Generator. This signal was then used to gate theADC within the MCA unit, with a signal from a slow spectroscopy amplifier attached tothe alpha detector used as the ADC input. A schematic is shown in Figure 8.

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Source

PMT Timing Amp Discriminator

Coincidence

Detector Preamplifier Timing Amp Discriminator

GDG MCA

Spec. Amp

Gate

ADC input

Figure 8: Schematic of the third part of the experiment.

5 Results and Discussion

Biases of 80.5 V and 1.33 kV were used for the alpha and gamma detectors respectively.An initial calibration of the MCA showed that each channel number had to be multipliedby 0.0265 to convert the scale to time.

5.1 Lifetime Measurement

Setting the gain of the timing amplifiers at 20.6 and 20.6, the integration time at 20 nsand 20 ns, and the differentiation time at 100 ns and 500 ns for the alpha and gammadetectors respectively, with the TAC set at a range of 200 ns and a delay of 48 ns appliedto the gamma signal, the leading edge discriminator was set-up using the steps describedin Section 3.6, with it optimised as described in Section 4. An optimum threshold of 0.7V was deduced for both the alpha and gamma detectors. The experiment was run for 24hours and the results show in Figure 9.

Minimising the fit of Equation 4 to the data, values of 1.52 0.02, 0.054 0.001, 0.012 0.001 and 5.54 0.08 for A, B, and respectively were produced, with the red line

15

Figure 9: Leading edge lifetime measurement. The blue lines show the measured data, and the redline represents the minimised fit to the data.

showing the optimised fit. The errors were produced by the applied minimising function inthe form of an error matrix. By using Equation 6, a half-life of 57.8 7.2 ns was calculated,with the uncertainty propagated form the error produced on . The actual lifetime of themeasured state is given in Section 2.2. Comparing the two we see a percentage differenceof 13.7%. The actual value does not lie within the error range and this can be accountedfor by the low time resolution of the leading edge discriminators.

CFDs were calibrated for the alpha and gamma detectors, with threshold values of 1.5 Vand 1.5 V, and walk values of 23 mV and 67 mV respectively determined. All other settingsremained the same, apart from the range, which was 500 ns. The results are shown in Figure10. Values of 7.15 0.05, 1.39 0.02, 0.098 0.001, and 1.31 0.02 were deduced forA, B, and respectively. The resolution is markedly improved when comparing thegraphs and values, with a steeper rise shown in Figure 10 and CFD < LE . CFDs areclearly more suitable for timing measurements. Equation 6 gives a half-life of 70.7 6.5ns, which is an improvement in comparison to the leading edge results. This clearly showsthat CFDs are the best discriminators to use when measuring lifetimes of transition statesdue to their superior time resolution.

To confirm the resolution improvement, a leading edge was used for the gamma detector,and a CFD for the alpha detector, with all other settings as they were. The fit produceda value of 3.24 for , which clearly lies between the values found for the leading edge andCFD measurements.

16

Figure 10: CFD lifetime measurement. The blue lines show the measured data, and the red linerepresents the minimised fit to the data.

5.2 Angular Correlation Measurements

To compare the results of the angular correlation measurements, they had to be normalisedfor the number of counts. The data for the 180 measurement gave the most counts dueto the lack of attenuation, and so the 135 and 90 data was normalised to match thecounts of the 180 data by adjusting the normalisation factor B. The results are shown inFigure 11. After normalising the 135 and 90 data, the results from the 90 arrangementclearly do not line up with the rest of the data. This is a result of attenuation. At anglesof 180 and 135, the emitted gamma rays have to propagate through less of the materialcontaining the source. The time taken for the gamma rays in the 90 arrangement to reachthe detector is therefore increased, which we see as a reduced number of counts as thetime interval between the correlated decays is increased. To correct this, the data wasnormalised relative to the other graphs, with the corrected data shown in Figure 12. Themeasured number of counts, N , is subject to some statistical uncertainty, determined byN . Accounting for this, it is clear to see that the results produced could be a result of

statistical fluctuations, with values of roughly 6 counts given forN at the peaks for each

angle.

It is important to note that the number of counts reduced significantly compared to previousparts of the experiment, as seen by comparing Figures 10 and 11/12, which were run for asimilar amount of time. The distance between the two detectors was adjusted but the countrate was not improved by brining them closer together. There is a possibility of equipmentdegradation and it would have been useful to analyse the resolution and efficiency of both

17

Figure 11: Angular correlation measurement, comparing the data for different angles between thetwo detectors. The data has been normalised for the number of counts at each angle.

Figure 12: The normalisation to remove attenuation effects seen initially seen in Figure 11.

18

detectors to determine if the problem was down to any changes in these at the later stagesof the experiment. The results may have been improved by restoring the apparatus backto its original count rate. This could be achieved by testing each experimental componentto ensure that it is working correctly and receiving the correct amount of power. At timesthere may have been too many NIM modules in one power bin meaning that some modulesmay have suffered slight power losses. It may have also been more advantageous to use theTh-228 source for this part of the experiment since the states involved stay aligned for alonger period of time that in Am-241. This means it is easier to see discrepancies in thepeaks of the different angles measured.

5.3 Coincidence Measurement

Results for the coincidence measurements produced energy spectra with unresolved peaksand a large amount of noise. As such, results were deemed inconclusive due to a reductionin the energy resolution of the alpha detector. The most likely source of this is radiationdamage (Section 3.1). By the time that this part of the experiment was undertaken, theapparatus had been used for an extensive amount of time. Ideally, the detector would bereplaced between experiments to ensure that the resolution remains as high as possible,particularly given that it involves the comparison of energy spectra.

6 Conclusions

Timing measurements were taken to measure the lifetime of the intermediate state of acorrelated alpha-gamma decay, as well as the angular correlation between the two andthe observation of energy spectra in coincidence conditions. The lifetime measured wascomparable to the actual value, but the remaining two parts of the experiment producedinconclusive results. To improve on this, the equipment should be optimised to allow fora higher count rate by testing the equipment used. Also, the detector should be replacedwhen it becomes heavily radiation damaged, and a source whose intermediate states remainaligned longer, specifically for the angular correlation measurements.

19

References

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11L.M. Simms, Hybrid CMOS SiPIN Detectors as Astronomical Imagers, Stanford Uni-versity (2009), pp.24-25

12D.R. Kirkby, A Picosecond Optoelectronic Cross Correlator using a Gain ModulatedAvalanche Photodiode for Measuring the Impulse Response of Tissue, University of London(1999), p.90.

13W.R. Leo, Techniques for Nuclear and Particle Physics Experiments: A How-To Ap-proach, Springer (1994), p.226.

14Leo, p.237.

15Leo, p.156.

16Leo, p.157

17Leo, pp.163-164.

18Leo, p. 169.

19G.F. Knoll, Radiation Detection and Measurement, Wiley (2010), p.274.

20

20Knoll, p.246.

21Leo, p.194.

22Leo, p.236.

23Knoll, p.594.

24Knoll, p.571

25Hoagland, p.2.

26Ortec: Fast-Timing Discriminator, AMETEK Corporation, p.3.

27Fast-Timing Discriminator, p.4

28Gamma-Gamma Coincidence, GSI Helmholtzzentrum fur Schwerionenforschung, p.11.

29Knoll, p.600.

30622 Quad 2 Input Logic Input Manual, LeCroy.

31J.P. Omtvedt, User Manual for NIM Gate and Delay Generator, University of Oslo(2010), p.1.

32Knoll, p.713.

21

IntroductionTheoryAlpha-Gamma CorrelationLifetimeAngular CorrelationSpin Relaxation

EquipmentSurface Barrier DetectorPlastic Scintillation DetectorCharge Sensitive PreamplifierFast Timing AmplifierSlow Spectroscopy AmplifierDiscriminators: Leading Edge and Constant FractionTime-to-Amplitude Convertor (TAC)Coincidence UnitGate and Delay GeneratorMultichannel Analyser (MCA)Arrangement

MethodResults and DiscussionLifetime MeasurementAngular Correlation MeasurementsCoincidence Measurement

Conclusions