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«STUDENT RESEARCH PAPERS SUMMER 2011 VOLUME 22 REU DIRECTOR UMESH GARG, PH.D. REU Student Research Papers – Summer 2011 University of Notre Dame – ...»

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In this way, there is no possibility for over-etching through long cut-o times in the rapid coarse etching step. Tip shaping is nished in the ne etching stage, where the voltage is much lower, the control ner, and there is more inuence on the nal tip shape. Additionally, the progress of the tip shaping can be seen easily under the microscope, unlike the coarse etching setup. The disadvantage of this method is that it is dicult to stop the etching late enough so that enough of a neck is formed to be easily etched away (if the thinned sections not suciently small compared to the tip shank, the etching will not progress correctly and will lead to a blunt tip) but early enough so that the end does not drop o or become so thin that the end section bends and deforms during cleaning or micropolishing. With practice, it is not dicult to tell when etching should be stopped. Our group relied on sound (the zzing of the reaction will taper o just before it is done) and monitoring the current. When the current dropped to 10-20% of its initial value, the etching was almost complete and the power was shut o.4 There is one problem that will be explored in the future and that was the issue of the neck of the tip bending when pulled through the wire loop in the ne etching step. This bending is believed to be caused by the surface tension of the solution in the loop. This could be solved by dabbing some of the solution in the loop away with a piece of paper towel, leaving a lm instead of a droplet in the loop, or with a slightly larger loop. The tips produced by this method were the sharpest our group has produced (despite the bend in the tip apex) and show great promise as STM tips if a better method of preventing the strain on the neck of the wire in the last step could be found.

4 It should be noted that the current does not decrease uniformly to zero as the reaction nishes. Our group found that it reached a nite value at about 10% of the initial value and then discontinuously fell to zero when the end of the tip dropped.

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2.1 Procedure

1. The experimental method follows the same steps 1-4 as the Argonne method outlined in section 1.1.

2. Set the power supply to 35 V and start the timer. The time table for this step is the same as step 5 in section 2.1, with the important exception of cutting the reaction short just before the end of the wire breaks o. 5

3. Clean and dry the tip as in step 6 in section 1.1, being careful when handling the tip, as the end of the tip is quite prone to bending.

4. Insert the tip into the optical microscope micropolishing setup and dip the loop in the 1.5M calcium chloride solution. Dab o some solution with a Kimwipe such that a thin lm is left in the loop instead of a droplet.

5. Move the loop onto the wire behind the thinned section.

6. Draw the loop o of the wire while holding the switch button. It is not necessary to draw the entire loop past the neck of the wire each time, as the strain from the wicking between the wire and solution bends the thinned section to the side at late stages in micropolishing.

7. Refresh the solution as necessary and cease etching once the thinned section is removed.

8. Clean and dry the tip using the same method as in step 3.

5 Details on determining when the reaction is about to nish and what a tip should look like after this step can be found in the introduction to section 2.

–  –  –

As exemplied in the optical pictures for tips #2 and #3, this method does produce signicant bending at the tip apex. This makes it very dicult to align the tip properly with respect to the sample in order for tunneling to occur. Tips #1 and #3 produced fairly decent image resolution at 200nm scales, but it was dicult to get any more detail and all three images show signicant smearing and noise. This method is still incomplete and not reliable in its current form. However, it does show promise as part of a dierent procedure as a way to control more of the etching in the micropolishing step instead of the dicult coarse etching step. Tips #1 and #2 had the thinned sections broken o and then etched a few times to sharpen.

#3 had the thinned section broken o and then etching immidiately ceased. #6 had the thinned section fold completely over during micropolishing and produced the worst image.

3 Electron Microscope Images Our group took three tip samples mounted on carbon tape to the Notre Dame Integrated Imaging Facility and used a Leo SEM (scanning electron microscope) under Dr. Alexander Mukasyan in order to produce a series of images at x10,000 and x50,000 of three tip-making methods; the Argonne method, the experimental method, and the Geneva method used primarily by our group up to this point.

–  –  –

As one can see, though the electron microscope we used was not able to resolve much below 1µm, the Argonne method produces much sharper tips (less than 100nm) than the currently used Geneva method (about 300nm). The experimental method also produced sharper tips than the Geneva method, however the bend at the apex is obvious and must be rened before useable tips are produced. A more detailed measurement of the tips' radii of curvature could be made in a higher resolution electron microscope, if additional accuracy or more information about the last few nanometers of the tip are desired.





4 Conclusions and Suggestions The recommendation for the method at this time is the Argonne procedure. It produced atomic-resolution images, was not dicult to implement, and showed resilience to errors in the etching stages. The experimental method explored dierent ways to avoid run away etching at the end of the coarse etching step, but suered from the problem of producing a delicate tip that deformed in the last stages of ne etching and produced tips with bent ends. Various other tip production techniques were not explored, but would be interesting to study in the future. These include tip annealing with a Bunsen burner in order to smooth out the tip apexs and eliminate multi-tips, using various other solutions (including hydrochloric acid, sulfuric acid, and acetone), and building a cut-o circuit to further minimize cut-o time.

–  –  –

Previous experimental studies of 12C + 12C fusion at sub-barrier energies using gamma spectroscopy have been limited by the use of a single detector. Use of the Gammasphere at the Argonne National Laboratory, however, allows for an array of germanium detectors to pick up the characteristic gamma rays, greatly increasing the information received. These decay products do not give us the total cross section for the fusion reaction though; we rely on statistical models that relate them to how the excited states are originally populated and decay. Using a combination of gamma spectroscopy based on data from the Gammasphere and proton spectroscopy from a recent 12C + 12C fusion experiment at Notre Dame, we tested these statistical models. The initial population of excited states for 23Na predicted by Empire, a standard statistical model for the decay of different Mg spins, was compared with the population determined from the gamma and proton spectroscopy. This comparison will potentially help us more accurately predict the spin population of 24Mg, further constraining the fusion reaction theory.

1 INTRODUCTION

Carbon burning is the third step in the evolution of a star, preceded by Hydrogen and Helium burning as the first two steps. Studying these primary processes can help us understand not only stellar evolution, but also the nucleosynthesis of heavier elements. After fusing, two 12Cs form Mg, which quickly evaporates to one of three channels: an alpha particle and 20Ne, a proton and Na, or a neutron and 23Mg. In this report, we concentrate on the second channel. These evaporation products are in an excited state and decay to their ground state, releasing gamma rays [1]. This paper will focus on gamma spectroscopy from a 12C fusion experiment using the Gammasphere at Argonne National Laboratory [2] and proton spectroscopy from a recent experiment at Notre Dame. While previous experiments used only one germanium detector [3, 4], the Argonne experiment is unique in that it collects data from an array of 110 germanium detectors, allowing us to gather many more gamma rays. We can in fact collect almost the full gamma decay information from the 24Mg decay from which the decay feeding intensities for various channels are then determined. Such work was not possible in previous experiments, in which much of the information was lost by the simple detection system. Since experiments at the low energies most relevant to astrophysics are not feasible, these accurate measurements at higher energies are especially important to test the statistical models crucial to the determination of the total cross section at low energies.

In this paper, the analysis of the gamma ray data includes determining the efficiency corrected initial population of the 23Na prior to its decay and checking this with the initial populations

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predicted by Becker’s data [3] and the proton channel of the Notre Dame experiment. We then compared the Gammasphere’s initial population to the prediction by Empire, allowing us to predict the spin population of 24Mg and test the statistical model [5]. Analyzing and understanding the new information obtained from this experiment will provide us with a new possibility to predict the spin population, which is essential for the understanding of the reaction mechanism of the formation of the 12C + 12C resonances.

2 EXPERIMENTAL METHOD

Na and 20Ne Decay Scheme 2.1 Using the data analysis program ROOT, I made a gamma-gamma graph of the Gammasphere data with the Doppler shift correction applied displaying two gamma ray energies that were detected in coincidence, which indicates they came from the same decay. Theoretically, this would be a matrix of points, as we know all of the expected energies from the decay, and due to quantization we should get only those energies. The graph, however, appears as a grid of lines because of background and Compton scattering events. Points appear at the crossing of lines where we would expect to see points on a theoretical graph.

–  –  –

By gating on a specific energy line and projecting the data onto one axis, we can find which gammas are emitted in coincidence with the first gamma energy by locating peaks. These peaks

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can be identified using a level scheme, and we can determine the levels of 23Na that were populated before the decay. We miss some of the decays because of their weak relative intensity, but this still provides an accurate picture. Gating on the 440 keV line, the strongest line in the spectrum, I found up to the 9th excited state populated for the 23Na. There were two peaks not associated with 23Na decay: one at around 900 keV which was identified as 88Y contamination, probably left over from a previous Gammasphere experiment, and the standard 511 keV peak, which is the annihilation energy from pair production.

Figure 2: Left: Projection onto the y-axis of the gating at 440 keV. Right: 23Na level scheme, ground to 9th excited

2.2 Efficiency Calibration The germanium detectors pick up high energies with less efficiency, so before the data can be analyzed further, an efficiency curve must be calculated to correct this effect. To do this, we use gamma ray data from a source placed in the Gammasphere and allowed to decay. Since the source is known, its decay pattern is known including relative intensities of the gamma ray energies. We used 152Eu and 56Co as our calibration sources. With the measured intensity for each of the peaks, we can then use the equation,

–  –  –

with εr as the relative efficiency ( = ), A through G as variable parameters that were adjusted to fit the efficiency curve, and x and y given by,

–  –  –

with E1 = 100 keV, E2 = 1000 keV, and Eγ also in keV [6]. The curve was first fitted separately to the two different sources, then an eighth parameter, H, was calculated to relate the two curves.

The efficiency curves are displayed in Figure 3. Since these values are relative instead of absolute, to use the curve, we must pick a point as 100% efficient, determine the relative efficiency of the surrounding points, then apply this to the data.

–  –  –

To determine the initial population of 23Na, we first assumed there were no levels populated above the 9th excited state, as the gamma ray energies that decay through 440 keV from above the 9th are too high for us to detect. According to Becker’s data, decays from the 10th to 16th states would account for less than a tenth of the total decays, so this is a reasonable assumption, though a potential source of error. As discussed in section 2.1, by gating on the 440 keV line, we have all of the lower energy strong decays that pass through 1st to ground, but are lacking both the decays that go straight to ground and the smaller relative intensity decays. Since the relative intensities for all the decays are well known, however, we can correct for these unknowns.

Starting with the 9th excited state, we observed decays from 9th  2nd and 9th  1st, and we expect to correct for 9th  ground, 9th  3rd, and 9th  6th. We must also correct the 9th  2nd yield to account for those which decay directly to the ground state from 2nd instead of to the 1st excited state. Once we know the total decay to the 2nd and 1st levels, we then use the known relative

intensities to calculate all of the decays. This procedure is followed for all of the excited states:

correct the experimental yields for any decays that go straight to ground then use the known relative intensities to calculate the decays that went undetected. For some of the lower levels, the cascading from above must be taken into account (e.g. 9th  6th when calculating 6th); this is not part of the original population of that level.



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