Measurement of the lifetimeof positronium in matterIlja Homm und Thorsten BitschBetreuer: Angel Givechev25.06.2012

Fortgeschrittenen-PraktikumAbteilung C

Content

1 Introduction 2

2 Theory 22.1 The origin of positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Positronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 22Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Experimental part 33.1 Pulse spectra of the source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Lifetime of positronium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Results 54.1 Pulse spectrum of 22Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2 Time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.3 Lifetime of ortho- and parapositronium . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Discussion 11

6 Literature 12

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1 Introduction

The aim of the experiment is the investigation of matter and anti-matter objects (in this casepositronium in aluminium (conductor) and teflon (isolator)). The challenge is the measure-ment of lifetime scales in ranges of a few nanoseconds. We do this with a special experimentalsetup, that will be explained later. In matter a positron can interact with an electron and createpositronium. This bound state annihilates in two or more photons after a certain lifetime. Butin conductors this lifetime is much smaller than in isolators, because conductors have a higherelectron density and that’s why the probability for a positron to annihilate with an electron ismuch higher. In the following measurement a radioactive source 22Na is used.

2 Theory

2.1 The origin of positrons

The positron is the antiparticle of the electron and similar to it. The difference between themis that the positron has a positive electric charge. The formation of positron is given by the β+

decay. A proton turns into a neutron by emitting a positron and a neutrino (p→ n+ e++ ν).

2.2 Positronium

When a positron interacts with an electron both particles annihilate each other. Then twogamma quanta of 511 keV each are emitted. For a very short time before such an annihilationbetween electron and positron there is the possibility of reaching an unstable bound state called"positronium". This state is similar to the hydrogen atom, but instead of a proton in the core thepositronium has one positron. The two types of positronium are observed: parapositronium -where the spins of the two particles are antiparallel and orthopositronium - the spins are paral-lel. The parapositronium emits two γ-quanta with opposite directions while orthopositroniumcan decay in three or more gammas. However the probability for a decay of orthopositroniumin more then three gamma quanta is highly low.

2.3 22Na

The 22Na is a β+ emitter with a half life of 2.6 years. With a probabylity of 90.5% it decaysby emitting a positron and 9.5% by electron capture. After a decay the isotope turns into anexcited state of 22Ne and reaches the ground state by emission of a gamma ray with an energyof 1275 keV. The second transition happens only 5 ps after the first decay.

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Figure 1: Decay scheme of 22Na

3 Experimental part

In order to obtain the lifetime of positronium we will measure the time difference between twoγ-quanta. The first γ-quant has an energy of 1275 keV and comes from the transition from the22Ne excited state to the ground state. The second one comes from the annihilation of a positronfrom the β+-decay of 22Na with an electron and has an energy of 511 keV.

3.1 Pulse spectra of the source

At first we will get familiar with the pulse spectrum of 22Na. We want to measure the pulsespetrum of the source to select the compton edges to fix the start (1275 keV) and stop (511 keV)signals for the later lifetime measurement. The following image shows the setup for this part ofthe experiment.

Figure 2: The setup for the measurement of the pulse spectrum

The detector is a combination of a plastic scintillator and a photomultiplier. A γ-quantumcan excite the scintillator, that emitts light flashes. These light flashes can unstack electrons ofthe photomultiplier’s anode. The photomultiplier multiplies these photoelectrons by using ofan electrical field applied between its dynodes. This is the signal, which we amplify with the

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amplifier. The amplifier is necessary, because the signals from the photomultiplier are too smallto get a clear pulse spectrum. The analog to digital converter (ADC) converts the analog signalpeak to a digital signal and sends it to the multi-channel-analyzer (MCA). The MCA counts thedetected decays.To measure the pulse spectrum we place the 22Na source close to the detector and start themeasurement.

3.2 Lifetime of positronium

On figure 3 is shown the experimental setup for the lifetime measurement of positronium.

Figure 3: The setup for the lifetime measurement

A radioactive source (22Na) is placed in front of two scintillation detectors. The signals ofthe detectors are passed through two constant fraction discriminators (CFD). With these CFDs atreshold can be set to select detector signals of a chosen amplitude. The output signal becomesindependent from the amplitude of the input signal. This is done by splitting the incoming signalin two signals. After that, one of them is inverted and attenuated. A small decay is applied andthen the signal is added to the other one. The resulting signal has a transition through groundzero. The first signal starts the time to amplitude converter (TAC), the other one stops it. TheTAC creates a signal with an amplitude proportional to the time interval between start andstop signal. After that, we can record this signal with an ADC and a multi channel analyzer.In the first step of the measurement we have to calibrate the time scale of the multi-channel-analyzer. This is done by using different delays. After the time calibration we can start thelifetime measurement. For our time calibration we use the formula:

t(channel) = m · channel + b (1)

The fitting exponential function is:

f (t) = C · e(−t−t0τ) (2)

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4 Results

4.1 Pulse spectrum of 22Na

The following pulse spectrum shows two compton edges. The first one around channel 200belongs to the 511 keV 22Ne annihilation of the positrons and the second around channel 700to the 1275 keV γ. There is a linear correlation expected between channel number and energy.The errorbars were estimated by the square root of the number of counts.

Figure 4: Pulse spetrum of 22Na

4.2 Time calibration

There were taken three spectra each with a different delay. The delays were 32 ns, 40 ns and48 ns. The following figure shows the three peaks with their fitted Gaussian curves.

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Figure 5: Correlation between counts and delays

Table 1: Data points for linear calibrationpeak center time/ns FWHM

298.77± 0.037 32 18.93398.72± 0.037 40 18.62501.62± 0.034 48 18.82

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Figure 6: Linear fit for the time calibration

Using equation (1) we fit the data points from table (1).

m (ns/channel) b (ns)(0.0789± 0.0007) 8.4752± 0.2703

Table 2: Result of the fitting function for the time calibration

The uncertainty of the time resolution is given by the full width at half maximum (FWHM).The mean of the three FWHMs is 18.79 channels and thus 1.4825 ns.

4.3 Lifetime of ortho- and parapositronium

To determine the lifetime of ortho- and parapositronium, we used 22Na as source that was cov-ered by an aluminium and a teflon jacket. Aluminium has a much higher electron density, sothere we expect a shorter lifetime than in teflon. The following figures show the measurementsof 22Na in the aluminium and teflon jacket.

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4 2 4 4 4 6 4 8 5 0 5 2 5 41 0

1 0 0

1 0 0 0

1 0 0 0 0

Coun

ts

T i m e ( n s )

Figure 7: Time spectrum obtained with 22Na in aluminium (∆N =p

N )

4 2 4 4 4 6 4 8 5 0 5 2 5 41 0

1 0 0

1 0 0 0

1 0 0 0 0

Coun

ts

T i m e ( n s )

Figure 8: Time spectrum obtained with 22Na in aluminium including fits

Figure 7 shows the time spectrum of 22Na in aluminium with the errorbars. In figure 8 isshown the same plot, but it includes a Gaussian fit (red line) and a fit of an exponential decay(blue line). Using equation (2) we fit the time spectrum of 22Na in aluminium where t0 is thecenter of the Gaussian peak and τ is the lifetime of orthopositronium.

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Table 3: Result of the exponential fitting function for aluminiumt0 (ns) τ (ns)

blue line 47.93 0.41± 0.02

We repeat the steps above for the teflon measurement.

4 2 4 4 4 6 4 8 5 0 5 2 5 4 5 6 5 8 6 0

1 0 0

1 0 0 0

1 0 0 0 0

Coun

ts

T i m e ( n s )

Figure 9: Time spectrum obtained with 22Na in teflon (∆N =p

N )

4 2 4 4 4 6 4 8 5 0 5 2 5 4 5 6 5 8 6 0

1 0 0

1 0 0 0

1 0 0 0 0

Coun

ts

T i m e ( n s )

Figure 10: Time spectrum obtained with 22Na in teflon including fits

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For teflon we can fit two exponential functions. The blue line belongs to parapositroniumand the green one to orthopositronium. τ is their lifetime. For the blue line t0 is the cen-ter of the Gaussian peak and for the green line it is the starting point of the second decay(orthopositronium).

Table 4: Result of the exponential fitting functions for teflont0 (ns) τ (ns)

blue line 48.64 0.67± 0.03green line 51.45 2.93± 0.21

4 2 4 4 4 6 4 8 5 0 5 2 5 4 5 6 5 8 6 01 0

1 0 0

1 0 0 0

1 0 0 0 0

A l T f

Coun

ts

T i m e

Figure 11: Comparison between the aluminium and teflon spectra

A comparison between the aluminium and the normalized teflon spectrum shows that inaluminium we are not able to fit a second exponential curve to see the decay of parapositroniumlike in teflon.

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5 Discussion

The experiment showed, that it was not possible to prove the existence of parapositronium inaluminium. Due to the high electron density of aluminium we can’t fit two exponential curvesto see the decay of parapositronium. We assume that it’s only possible to identify orthopositro-nium. The literature says that the lifetime of orthopositronium is τlit,alu,ortho = 0.29 ns[2]. Ourmeasured value is τalu,ortho = (0, 41± 0, 02) ns. This value doesn’t fit to the literature but it’sin the same range. Probably we would be able to see a decay of parapositronium by picking alonger measuring time for the experiment.For teflon we can see both decays. Parapositronium has in our case a lifetime of τtef,para =(0.67±0.21) ns. The literature value is for parapositronium τlit,tf,para = (0.96...1.03) ns and fororthopositronium τlit,tf,ortho = (3.69...3.95) ns[2]. For our measurement of orthopositroniumwe have a value of τtf,ortho = (2.93± 0.21) ns. As well as for aluminium we have here slightdeviant values, but they are also in the same scale.The time resolution of the electronic tools isn’t sufficient. With a better time resolution maybewe could reach better results due to higher data quality.

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6 Literature

[1] Versuchsanleitung Versuch 2.8-A, Abteilung C, TU Darmstadt

[2] Literaturmappe Versuch 2.8-A, Abteilung C, TU Darmstadt

[3] www.wikipedia.org

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