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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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We are limited in which levels we can calculate: anything that starts in the ground state will not give off gamma rays, so we are unable to determine the population of the ground state. The fourth state decays immediately to ground, and we gated on the energy from 1st to ground, so we lack the information to determine the initial population of the 4th and 1st excited states as well.

2.3.2 Comparison with Proton Channel and Becker

We next cross-checked the Gammasphere data with the proton channel from a recent Notre Dame experiment and the data from Becker’s paper. Becker’s data was displayed graphically; the graphs were printed out and the points found by hand. From the Notre Dame experiment, the energy versus angle of the emitted proton were recorded and are displayed in Figure 4, in which each horizontal line corresponds to the population of a particular state in the 23Na. The 4th and 5th

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To compare the data, ratios of the channels were made (e.g. 7th/6th), combining levels 9 and 8 since they are inseparable for the proton channel and ignoring the ground, 1st, and 4th excited states, as we do not have that information from the Gammasphere data.

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2.4 Mg Spin Population Empire is a standard statistical model code developed by NNDC. It predicts the population of Na using Hauser-Feshbach theory for a specific spin of 24Mg: 0+, 2+, or 4+. We took that initial population and used it as input in another code, written by Professor Xiao-Dong Tang, which uses the known level scheme to simulate the gamma decay for a given 23Na initial population and track the gamma rays emitted. It then displays these in the same format as the Gammasphere data, gating on the 440 keV line to produce a graph similar to Figure 2.

Taking these graphs, we get three different sets of peaks: one for each spin. We can set three undetermined constants, A, B, and C, to represent the percentage of each spin in the original spin population. To determine the values, I used Excel’s Solver function to minimize the difference between the gamma yields from the Gammasphere and from the combination of 24Mg spins as given by the statistical model. This gave a 24Mg spin population with 7.33% spin 0+, 92.67% spin 2+, and 0% spin 4+.

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## 3 RESULTS AND DISCUSSION

The Gammasphere data does not match up entirely with the proton channel data from ND or the Becker data, however with an increase in the yield of the 6th and 7th excited states from the Gammasphere data, they would match within uncertainty. There could be states above the 9th excited level that cascade down to these which could be investigated by gating on other lines.

The statistical model and the Gammasphere data match with the 2+ spin assignment for the resonance at ECM = 5MeV, however there is a large discrepancy for the 3237 keV line, corresponding to the transition from 7th  1st (see Figure 6). We can conclude that the statistical model is not perfect. With comparisons to data from the other channels of the Gammasphere experiment and the rest of the data from the Notre Dame experiment, we can hope to one day quantitatively understand how much the statistical model goes wrong and fix it for a better estimation of the fusion cross section at low energies.

## 4 ACKNOWLEDGMENTS

Support for this research comes from NSF Grants PHY-1068192 and PHY-0822648. A special thanks to Professor Xiao-Dong Tang, Brian Bucher, and Xiao Fang for their patience and many long hours of explanation, and to the Notre Dame Physics REU for a wonderful summer research experience.

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[2] Gammasphere – Argonne National Laboratory:

http://www.phy.anl.gov/gammasphere/index.html/ [3] Becker, Hans-Werner. “Teilchenspektroskopische Untersuchungen Zur Absorption Unter Der Barbiere Bei Der 12C+12C Reacktion.” Ph.D. diss., Institut für Kernphysik Munster.

[4] Kettner, K.U., “The 12C+12C Reaction at Subcoulomb Energies.” In Zeitschrift für Physik A Hadrons and Nuclei, 65-75. Springer Berlin / Heidelberg, 1980.

[5] Empire code: http://www.nndc.bnl.gov/empire219/ [6] Wang, Xiaofeng. “Exotic Collective Excitations at High Spin: Triaxial Rotation and Octupole Condensation.” Ph.D. diss., University of Notre Dame.

[7] Evaluated Nuclear Structure Data File (ENSDF) – National Nuclear Data Center:

http://www.nndc.bnl.gov/ensdf/

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## Abstract

The Double Chooz experiment is designed to measure sin2 (2θ13 ), which is a parameter of neutrino oscillations. The Chooz Nuclear Power Station produces anti-neutrinos as part of the decay of ssion products with short half lives, and those anti-neutrinos react with protons in our detector, which in turn produce neutrons and positrons. Gadolinium captures these neutrons with a characteristic energy that we can use to eliminate much background. This is important because only about 1 in every 144,000 triggers recorded signies the reaction of a neutrino. We can use the coincidence of neutron capture on Gadolinium and look back to nd the energy o`f the annihilation of positron and electron to signify a neutrino. Given the known rate of neutrino production from the Chooz Nuclear Power Plant, the known squared mass dierence of neutrino eigenstates, and the distance between the Power Station and our detector, theory gives us the rate at which we should receive neutrinos of the same avor. In approximately three months of data taking we have found about 1,700 neutrino candidates.

1 Introduction According to the standard model, neutrinos are mass-less leptons, traveling at the speed of light, each associated with a massive lepton and given a lepton family number, which is conserved.

Unfortunately, in one of the biggest errors of the standard model so far, none of these statements are true. Neutrinos are seen to oscillate, or change avor, which indicates that they have mass.

Knowledge of this phenomenon began when it was noticed that only a third to a half of the neutrinos that were supposed to be coming from the sun due to H-He fusion (electron neutrinos) were observed. Some responses were to question the current solar model, but there was thought among the physics community that neutrinos might be able to oscillate. Further experiments were performed until from Super-Kamiokande, in Japan around 1998, we were given suciently convincing evidence that neutrinos oscillate. This experiment specically tested the oscillation between muon and tau neutrinos, but later experiments conrmed neutrino oscillation for all avors and also conrmed the ratios which neutrino oscillation would produce coming from the sun. Ever since the quest has been to discover the precise mixing angles of the neutrinos and

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a mixing angle involving electron neutrinos.

2 Experiment The Double Chooz experiment is located in the Champagne-Ardeaux region of France. The Chooz Nuclear Power Station is located on a peninsula-type intrusion of France into Belgium at the northeast corner of France. The detector is located a little more than a kilometer away from the nuclear reactors, which from the decay of products of the ssion reaction produce electron anti-neutrinos. These anti-neutrinos react with protons in our detector, which produce neutrons and positrons.

The neutrons will capture on various atoms in the detector, but the two most common on which it captures are hydrogen and gadolinium. The detector is multiple layers of containers, only two of which contain photomultiplier tubes, the data-taking apparatuses of the experiment.

Each layer contains a liquid made of organic molecules, some layers contain scintillator, some are simply oil, but each serve an important purpose.

The outermost layer is called the inner veto, whose job is to lter out cosmic muons. Muons are detrimental to the experiment because they have enough energy to simulate events which look like neutrinos. Neutrinos are detected by a coincidence event of a neutron capture on gadolinium, which has a binding energy around 8.2MeV, and a preceding event with slightly more ambiguous criteria, but it is essentially the gamma rays which come from the positron electron annihilation after the neutrino-proton interaction. While we know almost exactly the energy that the gamma rays from the annihilation should have, we don't know how much energy the neutrino had when it entered the detector, we can only know upper and lower bounds.

Muons can strike the outer rock surrounding the inner veto, which can produce showers of

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is buried far enough underground that the muon rate is not so high, approximately 10Hz, as to make data taking impossible, but it does present signicant background. We have to exclude

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possible events we can look at. For example, given the proper cuts (no inner veto signal in the early or late event being one of them) we see about 1700 neutrino candidates from about 1291 hours of running. If the same cuts are made, but force there to be something in the inner veto then you get about 5800 events, some of which might actually be neutrinos that we have to ignore.

The next layer is called the buer. It is full of, quite simply, mineral oil. The job of this layer is to act as another layer of protection from any outside particles. There is no scintillating material, so it will not produce light when any particles move through, except for the very weak Cherenkov light. Another useful feature of the buer layer is that the tank is made of steel so the photomultiplier tubes (PMTs) can be attached to it. The two inner-most layers, to be discussed later, have acrylic walls, so photons will pass through them easily and be caught on the PMTs.

This makes the buer layer, quite possibly, the most important layer, because it is able to mount the data-taking portion of the experiment.

The gamma catcher is the next layer. It is full of scintillating liquid which is designed to scintillate when any gamma rays from positron annihilation or gadolinium neutron capture escape the target. This is an important function, since we need to make sure to capture all of these possible, as so few indicate neutrino events.

Finally, contained inside the gamma catcher is the target. The main thing that separates this from any other portion of the detector is that it is loaded with gadolinium. As already explained, this is an extremely eective neutron capture atom. Gd-157, which makes up approximately 20% of the gadolinium has the highest thermal neutron capture cross section of any atom, 259,000 barns. To compare this with the other eective neutron capture atom in the experiment, hydrogen has a cross section of 0.3321 barns. Granted, there are many thousand times more hydrogen atoms than gadolinium-157 atoms, but the other benet of gadolinium is that it has a very short

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far before it gets captured. It is so short that we can make a cut three time constants out before we get close to the capture times of hydrogen. This makes it very eective for isolating only the

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The experiment is then buried approximately 300 meters underground to protect it from background. As is obvious, the major challenge of the experiment is to reduce the background as much as possible, rst done in the design of the experiment, and then in the post processing of the data.

3 Data Analysis The brunt of my work this summer has been in data analysis. I came into the program only having a cursory knowledge of a couple programming languages and reasonably little knowledge of general terminal usage and scripting. As a result I had to spend much of my time learning ROOT, which is the data analysis program used by many high energy physicists, including those at CERN and Fermilab. I learned quite a few tricks about shell scripting and terminal usage, and improved my prociency in C++. Unfortunately, I did not come into this REU with any particle physics classes under my belt. I regret that I wasn't able to learn more physics, but the computer science I learned will be invaluable to my future career as a physicist.

Some of the analysis that I was able to do this summer started out as work trying to analyze the dead time of our detector. It is known that our detector has some limitations as to the amount of data that it can take. One principle of our detector is that it only releases data every 32ns, so in that period the PMTs will collect all the energy they can from any photons that make it in and integrate it to output the total light for that time period in the form of a charge, which relates to energy. (Unfortunately, the detector is not calibrated, so we have to make our best guess as to how charge relates to energy.) 32ns is essentially only enough time for light to travel through the detector and reach a PMT from an event, so there is a high correlation between a single event happening and recording only the data from that event. Nevertheless, it is possible that multiple events could happen, by coincidence, within nanoseconds of each other and be combined in the same trigger. That means that we might throw out a useful event because it has the added energy of another event with it, but this would be impossible to distinguish, so

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bit of true dead time is following a trigger there is always at least a 146ns period where no data is taken. Fortunately, the data down there is almost entirely junk (meaning there is no physics that it could signify, it is just noise in the detector), but it still means there's a period of time where an important event could happen as we miss it. It means that at the very least there is this amount of dead time multiplied by the number of events that occur, which amounts to only about 0.002% of our run time. If this is the only dead time, then there is little reason to worry about it because that percentage is extremely small and well within the range of general

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