Measurement of the Breakup Cross Section of the D(d, n) Reaction at 6.94 MeV for the. Active Interrogation of Hidden Fissile Materials

Transcription

1 Measurement of the Breakup Cross Section of the D(d, n) Reaction at 6.94 MeV for the Active Interrogation of Hidden Fissile Materials A thesis presented to the faculty of the College of Arts and Sciences of Ohio University In partial fulfillment of the requirements for the degree Master of Science Andrea L. Richard May Andrea L. Richard. All Rights Reserved.

2 2 This thesis titled Measurement of the Breakup Cross Section of the D(d, n) Reaction at 6.94 MeV for the Active Interrogation of Hidden Fissile Materials by ANDREA L. RICHARD has been approved for the Department of Physics and Astronomy and the College of Arts and Sciences by David Ingram Professor of Physics and Astronomy Carl Brune Professor of Physics and Astronomy Robert Frank Dean, College of Arts and Sciences

3 Abstract 3 RICHARD, ANDREA L., M.S., May 2014, Physics and Astronomy Measurement of the Breakup Cross Section of the D(d, n) Reaction at 6.94 MeV for the Active Interrogation of Hidden Fissile Materials (83 pp.) Directors of Thesis: David Ingram and Carl Brune The D-D reactions are well known and widely used for a variety of purposes, mainly due to the mono-energetic neutron peak from the D(d, n) 3 He reaction. The least studied of the D-D reactions is the D(d, np)d reaction known as the deuteron breakup reaction. The D(d, np)d reaction produces a continuum of neutrons at energies lower than that of the mono-energetic peak. In this work, the D(d,np)D reaction has been studied for the purpose of use as a neutron source for the active interrogation of hidden fissile materials. The d neutron energy distribution as a function of angle for the cross section, 2 σ, of the dωde D(d,np)D reaction has been measured using a 6.94-MeV pulsed deuteron beam incident upon a D 2 gas target. The time-of-flight technique was used to determine the energy of the neutrons detected in the array of two lithium glass scintillators and one NE-213 scintillator. The breakup cross section was determined as low as 225-keV neutron energy in the lithium glass detectors.

4 Dedication 4 I would like to dedicate this thesis to my father, David Alan Richard who passed away on July 27, He never stopped believing in me and that made me the person I am today.

5 Acknowledgments 5 I would like to begin by expressing my sincere gratitude to my advisors, Dr. David Ingram and Dr. Carl Brune. I cannot fully express my appreciation for their knowledge, dedication, and kindness. The things I have learned and experience gained from working with them will never be forgotten. I would like to give special recognition to Devon Jacobs and Don Carter for teaching me how to operate the accelerator and for keeping things running. I would also like to thank John O Donnell for helping me get my gas cell ready for this experiment and for operating the accelerator when I was in class. I am extremely grateful for the help and guidance given to me from Dr. Tom Massey. I had no idea what I was getting myself into when I started running my experiment and he helped me take baby steps until I understood what was going on. These are some of the most dependable people that I have ever known and without them, I would certainly be lost. I would like to express my appreciation for the members of my committee, Dr. Arthur Smith, Dr. Justin Frantz, and Dr. Julie Roche. Though they were busy and had many other things to focus on, they took time out of their schedule to play a role in my MS thesis. I also want to thank my fellow graduate students, Cody Parker, Alina Karki, and Sushil Dhakal who operated the accelerator during my experiment. I want to extend my gratitude to Kevin Cooper for the many conversations we have had about the accelerator, active interrogation, and other things that are too numerable to write here. I would like to thank all of my friends who have consistently shown me patience and kindness even at the worst of times. Lastly, I want to thank my mom for all of her love and support. She keeps me smiling and reminds me daily of who I am and all that I can be.

6 Table of Contents 6 Page Abstract Dedication Acknowledgments List of Tables List of Figures Introduction The D(d,n) Reactions Past Work Present Work Experimental Methods Facility Overview Cs Sputter Source and Pulsed Beam Swinger and Tunnel Targets D 2 Gas Cell Aluminum Beam Stop Detectors NE-213 Detector Lithium Glass Detectors Stillbene Detector Electronics and Data Acquisition Electronic Modules and Settings Data Acquisition Data and Analysis Analysis Procedure Channel to Time Conversion Time of Flight to Neutron Energy Conversion Background Subtraction The Al(d,n) Reaction

7 7 4 Results Neutron Yield D(d,n) 3 He Neutron Yield D(d,np)D Neutron Yield Cross Section D(d, n) 3 He Cross Section D(d,np)D Cross Section Fitting Conclusions and Future Work Discussion of Results Background Subtraction Lithium Glass Detector Response Error Analysis Future Work Additional Angles, Deuteron Energies, and Binning Schemes Active Interrogation Conclusion References

8 List of Tables 8 Table Page 3.1 Experiment data collection summary for angles with D 2 gas Swinger angle D 2 disks and corresponding background disks Neutron Yield for the D(d, n) 3 He peak from the NE-213. The error is measured in terms of the number of neutrons/(mev µc sr) Neutron Yield for the D(d, np)d region from the NE-213 and Li glass detectors. The error is in terms of the number of neutrons/(mev µc sr) Angular Distribution of the Cross Section the D(d, n) 3 He reaction for the NE Differential Cross Section for the D(d, np)d region from the NE-213 and Li glass detectors. The region of integration for the NE-213 was from 1 MeV up to approximately 3.5 MeV and was from 225 kev up to approximately 3.5 MeV for the lithium glass detector Definitions of fitting parameters defined in Equations Definitions of fitting parameters defined in Equations Summary of Systematic Errors

9 List of Figures 9 Figure Page 1.1 Differential Cross Section Obtained for D(d, n) 3 He calculated from the drosg code Differential Cross Section Obtained in Edwards Accelerator Lab for D(d, np)d Photograph of the Edwards Accelerator Tank Photograph of the Swinger and tunnel entrance Photograph of the 3.14cm gas cell Photograph of the 3.14cm gas cell attached to the Swinger Photograph of Aluminum beam stop which was used for detector efficiency Photograph of the main detector array Photograph of the monitor detector Electronics Diagram for the Li Glass Detectors Electronics Diagram for the NE Graph of the time calibration using a 60 Co source Graph of the raw data for the NE-213 at Graph of the time channels for the NE-213 at Graph of the neutron energy spectrum at 0 for NE Graph of the background subtracted neutron energy spectrum at 0 for NE Graph of the standard neutron spectra for Al(d, n) Graph of the neutron spectra for Al(d, n) from the NE Graph of the neutron spectra for Al(d, n) from the Lithium Glass detector Graph of the neutron efficiency for the NE Graph of the neutron efficiency for the Lithium Glass detector Graph of the neutron yield for the D(d, n) 3 He reaction Graph of the neutron yield for the D(d, np)d reaction for angles 0 to Graph of the angular dependence of the differential cross section for the D(d,n) 3 He reaction Graph of the double differential cross section of the D(d, np)d reaction for Graph of the double differential cross section of the D(d, np)d reaction for Graph of the double differential cross section of the D(d, np)d reaction for Graph of the double differential cross section of the D(d, np)d reaction for 0-20 for the NE Graph of the double differential cross section of the D(d, np)d reaction for for the NE

10 4.9 Graph of the double differential cross section of the D(d, np)d reaction for for the NE Plot of the χ 2 minimization fits for the breakup region Graphical comparison of Drosg angular distribution and current work Graph of Drosg angular distribution and current work ratios Graphical comparison of previous work from [Dha13] and current work

11 1 Introduction The D(d,n) Reactions The D-D reactions are well known and widely used for producing neutrons of varying energies. Use of the D-D reaction for production of neutrons is desirable because deuterium is readily available and not radioactive. Moreover, the D-D reaction has a large cross section that makes it ideal as a neutron source. The D-D reaction produces neutrons through the D(d,n) 3 He reaction, the D(d, np)d reaction known as the deuteron breakup reaction, and through the D(d, np)np reaction known as the double deuteron breakup reaction. The D(d,n) 3 He reaction produces mono-energetic neutrons which can be used in a variety of applications including those in the medical field and those for nuclear security. The D-D reaction yields mono-energetic neutrons ranging from 2.45 MeV to MeV based upon the incident deuteron energy and yields breakup neutrons at even lower energies [Dro99]. Other mono-energetic neutron sources are available, such as the D-T reaction or the p-t reaction. The D-T reaction has the capability to produce mono-energetic neutrons well above the D-D reaction. These D-T mono-energetic neutrons extend up to 14 MeV [Dro99]. The p-t reaction, on the other hand, covers the entire mono-energetic neutron energy range of the D-D reaction in addition to lower neutron energies that the D-D reaction cannot produce. While the D-T and p-t reactions seem more attractive, reactions involving tritium are less desirable because tritium is radioactive and requires special licenses for use. For this reason, the D(d,n) 3 He reaction is the safest and most widely used reaction for production of mono-energetic neutrons. The breakup reactions are three and four-body events which produce a continuum of neutrons at energies lower than the mono-energetic neutrons. These breakup reactions have often been viewed as a source of contamination and studies have been done to quantify the amount of breakup that occurs.

12 12 The motivation of this thesis is to study the D(d, np)d reaction for possible applications in the realm of nuclear security. Mono-energetic neutrons from the D(d,n) 3 He reaction are currently being used as a neutron source for the active interrogation of hidden fissile materials. During active interrogation, these mono-energetic neutrons bombard a cargo container, vehicle, or package in order to induce fission and detect concealed fissile materials. When the incident deuteron energy increases to above 4.45 MeV, another reaction is kinematically possible. The breakup reaction, D(d,np)D, produces a continuum of neutrons at a energies lower than that of the mono-energetic peak when the incident beam energy is above the threshold of 4.45 MeV. In this case, the deuteron breaks up into its constituent particles, the neutron and the proton. Therefore, use of the D-D reaction as a mono-energetic neutron source for deuteron energies greater than 5 MeV is complicated by the presence of break-up neutrons lower in energy than the mono-energetic neutrons from the D(d,n) 3 He reaction. Because the neutron yield from deuteron breakup increases rapidly with incident deuteron energy, the D-D reaction is not particularly well described as a mono-energetic neutron source at higher deuteron energies. Concerning active interrogation, measurement of the breakup reaction has a two-fold purpose. The first purpose is that the continuum of neutrons from the D(d,np)D reaction cause a significant background for the current D-D neutron sources used during active interrogation and the second being that utilizing the breakup reaction as an additional component of the neutron source for active interrogation is desirable. Deeper understanding of the breakup reaction will help to quantify these backgrounds and how the breakup varies with angle, energy, and other parameters. At higher energies, the yield from these breakup neutrons surpasses that of the mono-energetic neutrons. This makes it an ideal candidate to study as an additional component to the current D-D neutron source. Because the D(d,np)D reaction has a Q-value of MeV, it is known as self-collimating.

13 13 Self-collimated reactions require a threshold kinetic energy before neutrons can be produced. The reactants will have a forward momentum due to overcoming the threshold kinetic energy and will therefore self-collimate. These self-collimated neutrons can then be directed onto a target. These neutrons, along with the mono-energetic neutrons coming from the reaction, can be used as a directed neutron source for active interrogation of hidden fissile materials. Quantification of the cross section of the breakup reaction allows for better understanding of the range of neutrons from the D-D reaction thus making it possible to better interpret spectra from active interrogation. Furthermore, determination of the cross section of the breakup reaction will provide quantitative knowledge about this additional, directed component of the neutron source for active interrogation. The cross section of the D(d,np)D reaction has been studied in the past but has not been fully quantified below neutron energies of 1 MeV due to threshold limits and the efficiency of the detectors used. The region below 1 MeV is significant because the breakup region extends substantially below 1 MeV especially when the reaction takes place at 0. In the future, it may be possible to predict the breakup cross section using theoretical calculations, but thus far no one has attempted to use theory to calculate the D(d, np)d cross section. Calculations of the deuteron breakup reaction will soon be possible due to the state of the art theoretical cross section calculations shown in [Ara11, Hof08, Nav10, Del12], which are concerned with three- and four-nucleon breakup and scattering. Measurement of the breakup cross section will contribute to basic low energy nuclear physics by determining fully the cross section below 1 MeV. The purpose of this thesis is to determine the cross section of the D(d,np)D reaction for applications in the use of active interrogation and in order to add to basic scientific knowledge of low energy nuclear physics.

14 Past Work Initial study of the D(d,np)D reaction was done because the D(d, n) 3 He reaction produces mono-energetic neutrons which are polluted by breakup neutrons from D(d,np)D. These breakup neutrons from D(d,np)D were viewed as a contamination that needed to be quantified. However, the extent of the breakup neutrons from the D(d,np)D reaction was not known. The cross section needed to be experimentally determined in order to quantify the amount of deuteron breakup that was occurring. Work began on the D(d,np)D reaction in 1955 with Henkel et al. [Hen55] who were studying the breakup of deuterons on H, T, 3 He, and 4 He. Upon studying the D-D reaction, Henkel et al. reported that no low energy neutrons were observed for deuteron energies up to 7 MeV due to an error of 5-10 mb/sr in the differential cross section and because the high neutron yield of the D(d, n) 3 He reaction smeared into the breakup region. Work continued in 1956 with Cranberg, Armstrong, and Henkel [Cra56]. The original motivation for Cranberg et al. was to study the D(d, n) 3 He reaction as a source of mono-energetic neutrons for neutron energies up to 2.5 MeV. However, seeing that a continuum of neutrons was possible above 4.45-MeV, they began work in quantifying the breakup neutrons. The experiment was done at the Los Alamos Van de Graaff accelerator with a pulsed beam and detector at a distance of 1.5 m for the time of flight (TOF) technique. The TOF technique relies on pulses of the deuteron beam arriving at the target at a particular frequency. Knowing this frequency and the distance of the detectors from the target allowed for a correlation between time of flight of the neutron and the energy of that neutron. The target for Cranberg et al. was a 6-cm-long gas cell with 11.6 psi of D 2 gas and an entrance window which had a 1.5-µm-thick nickel foil. Data were taken at 6.3-MeV incident deuteron energy at ten degree angular intervals up to 40. Cranberg et al. reported breakup neutrons which extended from 3 MeV to as low as 670 kev.

15 15 Determining the breakup cross section below 670 kev became the goal of the following experiments. In 1958, Anderson et al. studied the D(d,np)D reaction at MeV at laboratory angles between 0 and 30 [Mar60] with a breakup neutron region starting at 9-MeV and extending down to 2 MeV. Continuing in 1961, experiments with breakup of deuterons on deuterons began at 18.8 MeV with Rybakov, Sidorov, and Vlasov [Ryb61] who reported breakup neutrons starting at 6 MeV and going as low as 600 kev. Then, in 1962, Lefevre et al. studied the D(d,np)D reaction at deuteron energies of 9.94 MeV for 0 to 30 and 9.75 MeV for angles from 30 to 70 [Lef62]. Work was done with a tandem electrostatic accelerator and a proton-recoil plastic scintillation counter coupled to a photo-multiplier tube. The target was a gas cell with a gold beam stop and a 1-µm thick Ni foil. The cell was filled with 12 psi of D 2 gas. The breakup neutron region was found to be from 1 MeV to 7 MeV. A decade passed before further studies were published, but in 1972 both Pope et al. and Valkovic et al. published results concerning the breakup reaction. Pope et al. [Pop72] used 11.3-MeV deuterons in conjunction with an NE-213 scintillator but was only able to detect neutrons down to 1 MeV. Similarly, Valkovic et al. [Val72], used 10-MeV deuterons and an NE-218 scintillator but could not extend the detection below 1 MeV. In 1978, significant work was done by Drosg [Dro72] using the Van de Graaff accelerator at Los Alamos Scientific Laboratory with deuteron energies of 6 to 17-MeV. A 3-cm long gas cell was used and filled with 25-psi D 2 gas. The NE-213 detectors were used at a flight path of 2.56 m. Drosg determined the absolute cross section of the D(d, n) 3 He reaction and determined the D(d,np)D cross sections at 0 for energies from 6 to 17 MeV. However, the cross section of the D(d, np)d was not determined below 1 MeV. Several cross section evaluation papers have been published for the D(d, n) 3 He reaction, including one from Drosg [Dro99] and another from Liskien and Paulsen

16 16 [Lis73]. These evaluation papers compiled data from previous experiments in order to interpolate the data and calculate the cross section at any energy. Drosg wrote a code known as Drosg-2000 which calculates the cross section based upon evaluations of data from previous experiments. Figure 1.1 shows the angular dependence of the differential cross section for the D(d, n) 3 He reaction as evaluated by the Drosg-2000 code [Dro05]. The cross section was calculated at 6.94 MeV, the exact energy determined for the current work. Later authors have used cross section evaluations from [Dro99] and [Lis73] as a consistency check for the analysis of the differential cross section of the breakup reaction dσ/dω [mb/sr] Θ L [deg.] Figure 1.1: The angular dependence of the differential cross section for D(d, n) 3 He calculated from the drosg-2000 code at a deuteron energy of 6.94 MeV.

17 17 In 1982 at Edwards Accelerator Laboratory of Ohio University, Grimes et al. began work on quantifying backgrounds caused by breakup neutrons from the D(d, n) reactions [Gri82]. They determined that the background caused by deuteron breakup was more significant than those backgrounds caused by reactions upon contaminants within gas cells during the experiments. An 8.03-MeV deuteron beam was used to determine the cross section of the D(d, np)d reaction in conjunction with an NE-213 detector. NE-213 thresholds only allowed for detection down to 1 MeV. In order to determine a method for subtraction of the background caused by deuteron breakup, the 3 He(d, n) reaction was also produced at a slightly lower energy. A dual gas cell assembly was designed which allowed for cycling between the two gases (D 2 and 3 He) to simulate the deuteron breakup background. The dual gas cell ultimately was not feasible for simulating deuteron breakup below 1 MeV due to the expense of 3 He. Furthermore, the 3 He breakup yield would not be the same as the deuteron breakup yield and thus represented some uncertainty in the estimation of backgrounds caused by breakup neutrons. In 1986, Kornilov et al. [Kor86] studied the angular dependence of the D(d, np)d cross section at 11-MeV and noted that deuteron breakup limited the use of the D-D reaction as a neutron source. Furthermore, Kornilov et al. made significant advancements in producing a fitting function of the deuteron breakup region. Angular dependence was not determined below 1-MeV until 1989 when Cabral et al. studied the angular dependence of the D(d, np)d cross section [Cab89]. Deuterons between 5.34-MeV and MeV were used in conjunction with NE-213 detectors and a 3-cm gas cell with 26.7-psi of D 2 gas. Emission angles of 0 to 15 were studied and the lowest neutron energy detected was 800-keV. Recent work in Edwards Accelerator Laboratory in Ohio University by Dhakal and Brune [Dha13] studied the D+D neutrons at 5 and 6.94 MeV using NE-213 detectors. The breakup cross section was not determined below 1.5 MeV due to the efficiency cutoff of the NE-213 detectors in that region. Figure 1.2 shows the

18 18 preliminary differential cross section results obtained by Dhakal and Brune at a deuteron energy of 6.94 MeV. The differential cross section of D(d, np)d shown in the Figure has not been determined below 1.5 MeV. 20 d 2 σ/dω L de L (mb/sr-mev) θ L = 0 0 θ L = 5 0 θ L = 10 0 θ L = 15 0 θ L = 20 0 d 2 σ/dω L de L (mb/sr-mev) θ L = 25 0 θ L = 30 0 θ L = E L (MeV) Figure 1.2: The preliminary differential cross section results obtained by Dhakal and Brune at deuteron energy of 6.94 MeV. The horizontal axis represents the neutron energy in the laboratory frame. Figure taken from [Dha13]. 1.3 Present Work This thesis presents results of work done to determine the differential cross section of the breakup reaction using a tandem Van de Graaff accelerator and a 6.94-MeV pulsed and bunched deuteron beam. A 3.14-cm-long gas cell filled with 30 psi of D 2 gas served as the

19 19 target to simulate the D-D reaction. An NE-213 scintillator was used to detect high energy neutrons from the D(d, n) 3 He reaction and two lithium glass scintillators were used to detect low energy neutrons from the D(d, np)d reaction. The differential cross section of the D(d, np)d reaction was determined for laboratory angles at 5 increments between 0 and 60. While similar in design to previous experiments by use of a pulsed beam and gas cell target, this experiment made several key improvements. This approach differs from past work mainly by the use of lithium glass detectors which have non-zero efficiency below 1 MeV. This was done in order to extend knowledge of the breakup cross section and neutron yield below the lower limits from past work. Thresholds on the NE-213 were taken as low as possible in order to give the best possible estimation of the breakup cross section. Furthermore, lithium glass detectors were utilized below 1 MeV in order to improve upon the lower limit of the breakup cross section set by past work such as work shown in Figure 1.2. In this thesis, the next chapter will focus on the experimental overview. This section will include the facility overview, targets, detectors, and electronics used. The third chapter will focus on the data analysis, including the detector calibration and efficiency as well as the method used to determine the cross sections. The fourth chapter will focus upon the cross section results obtained from the experiment as well as fitting results for the breakup region. The fifth and final chapter will present discussion concerning the results and possibilities for future work.

20 2 Experimental Methods Facility Overview Figure 2.1: The 4.5-MV Tandem Van de Graaff Accelerator at Ohio University. The experiment was conducted at the 4.5-MV Tandem Van de Graaff Accelerator located in the John E. Edwards Accelerator Laboratory of Ohio University. A Cesium sputter source produced the deuteron beam for the experiment. Before transport through the accelerator shown in Figure 2.1, the beam was tuned with electrostatic steerers and lenses. Prior to reaching the main acceleration phase, the beam underwent pulsing and bunching, which allowed the beam to be divided into discrete pulses. During the main acceleration phase, the negatively charged ions produced at the Cs source passed though a carbon-foil stripper. This carbon-foil stripping removed two electrons causing the beam to be positively charged. Because the accelerator is likewise positively charged, there was a secondary acceleration. After this acceleration, the beam was focused with a quadrupole

21 21 magnet. Energy of the deuteron beam was determined by passing the beam through the Analyzing Magnet which used nuclear magnetic resonance to determine the magnetic field of the magnet. The magnetic field was proportional to the momentum of the particle and thus was used to determine the energy of the beam as it passed through the Analyzing Magnet [Sar95]. Three detectors, housed in the time of flight tunnel, observed the γ-rays and neutrons which resulted. This chapter will focus on the different components of the experimental layout including the Cs sputter source and pulsed beam, Swinger and tunnel, targets, detectors, electronics and data acquisition Cs Sputter Source and Pulsed Beam A major component and key aspect of the experiment was the pulsed and bunched deuteron beam. A continuous deuteron beam was produced in the sputter source and injected into the low energy end of the beam line. Once 2 µa of the ion beam was produced in the sputter source, it was sent through the pulsing and bunching system. The pulsing and bunching system divided the deuteron beam into discrete pulses. In order to measure the timing for the pulses, either the oscillator or beam pick off (BPO) on the control panel could be used. Initially the oscillator was used in order to obtain proper timing but once the beam was transported down the beam line, the BPO was used. The BPO was used for the final timing determination because it was physically located closer to the target and could provide more accurate timing information. Timing obtained from the oscillator would not be as accurate as timing from the BPO. The frequency of the pulses was f /16 where f corresponded to the fundamental repetition rate of 5 MHz. The significance of f /16 was that only one of every sixteen pulses continued down the beamline and the remaining fifteen were discarded. The advantage to using the f/16 setting was that in conjunction with the flight path chosen, there was a clear separation between the γ-rays and neutrons from the D(d, np)d and D(d, n) 3 He regions. The timing

22 22 between the start signal of one pulse to the start signal of the next was 3.2 µs. If this rate had been smaller, there would have been interference between the neutrons of one pulse and the γ rays from a subsequent pulse. Throughout the experiment, the BPO trigger would occasionally fluctuate such that the proper start times for the beam pulses were missed. The number of events lost from failure to trigger the start pulses was less than or equal to 1%. The significance of the pulsed and bunched beam and repetition rate was that they allowed for the use of the time of flight (TOF) technique to distinguish between particles and to determine the neutron energy. Packets of deuteron beam were accelerated down the beam line and on to the target. The products of the D(d, n) reactions were detected at different times based upon their energy. Thus, γ-rays resulting from background and interactions with the walls of the gas cell and the beam stop arrived to the detector first because of their higher energy. The neutrons arrived at later, differing times based upon their energy. Because the beam was pulsed and bunched, the discrete packets arrived at a specific time and reacted with the target to yield neutrons and γ-rays. Pulsing and bunching the beam in conjunction with timing from the BPO allowed for good time-separation between the incoming particles. This time-separation between detection of different particles allowed for good neutron energy resolution and separation between the D(d, np)d and D(d, n) 3 He regions.

23 Swinger and Tunnel Figure 2.2: The Swinger positioned at 90 with collimated opening for the tunnel in the background. The pulsed deuteron beam was transported down the beamline onto the Swinger shown in Figure 2.2. The Swinger consists of two magnets, which deflected the beam so that it emerged from the Swinger perpendicular to the original beam path [Fin82]. The Swinger has the unique feature that it is rotatable to forward and backward angles between -4 and 150. The target for the experiment was attached to the end of the Swinger. Because of this, the target and incoming beam remained at the same angle relative to each other. The Swinger rotation changed the angle between the reaction center and the fixed detectors within the tunnel. To determine the angular distribution of the breakup cross section, the Swinger was rotated between angles of 0 and 60 in 5 increments. The

24 24 resulting neutrons from the D(d, n) reaction and γ-rays from background entered into the time-of-flight tunnel. Use of the time-of-flight tunnel allowed for high resolution and low background measurements of neutron-scattering. The time-of-flight tunnel is a concrete shielded, 30 meter-long tunnel that was necessary for time of flight measurements to be taken. Due to the 1 m thick concrete walls surrounding the tunnel, measurements taken were at low background. The tunnel was located behind the silver collimated opening behind the Swinger in Figure 2.2. The collimated opening focused the resultant particles to eliminate background neutrons. Within the tunnel, three detectors were fixed at a distance of 6.283±0.001 m from the target to the front face of the detectors in the array. 2.2 Targets Two targets were used for this experiment. A 3.14±0.01-cm-long gas cell filled with diatomic deuterium gas was used for the main part of this experiment to produce the D-D reaction. Additionally, an Aluminum beam stop was used for the standard calibration reaction 27 Al(d, n).

25 25 Figure 2.3: The gas cell was filled with D 2 gas maintained at 30.0±0.1 psi throughout the experiment D 2 Gas Cell The deuterium gas cell, shown in Figure 2.3, was filled with diatomic deuterium gas throughout the experiment. Interactions of the beam with different components of the gas cell caused a beam-induced background. However, this beam-induced background was subtracted from the final result by removing D 2 gas from the cell and obtaining the spectra for each angle. The ability to subtract most of the background at every angle was the reason a gas cell was used instead of a solid deuterium target [Gri82]. The gas cell was maintained at an absolute pressure of 30.0±0.1 psi of D 2 gas throughout the experiment. The cell had a 5.1±0.1-µm thick tungsten window and a 0.040±0.001-inch gold foil beam stop at the end. The gold beam stop was used to reduce the amount of background neutrons from reactions upon contaminants within the gas cell [Wen12]. The incident deuteron beam was tuned to be 7.34 MeV, however the deuteron beam lost energy as it traveled through the W foil and D 2 gas. By using the SRIM (Stopping

26 26 Range of Ions in Matter) program [Zie04], the deuteron energy was determined to be 6.940±0.012 MeV at the center of the gas cell, the effective reaction center. Energy loss through the W foil was determined to be 336±12 kev while the energy loss through the gas to the center of the gas cell was found to be 67.0±2.4 kev. Therefore, at the center of the gas cell, the energy of the deuteron beam was determined to be 6.940±0.012 MeV. The gas cell was maintained at 30 psi throughout the experiment in order to regulate the number of target atoms/cm 2 as well as the energy loss of the deuteron beam as it traveled through the gas in the cell. The gas cell pressure was monitored during the experiment but the gas pressure sensor was not sensitive enough to determine more than a 0.1-psi fluctuation. The pressure, length of the gas cell, and the total number of deuterons hitting the gas cell were used to determine the number of target atoms per cm 2. This areal density was calculated by use of the ideal gas law. The uncertainty in the the areal density was estimated to be 3% coming from uncertainty in the pressure measurement as well as uncertainty in the number of deuterons hitting the target. Additional uncertainty came from the beam heating effect. As the beam current increased, the gas within the cell underwent beam heating which caused the temperature of the gas inside the cell to increase. Beam heating causes the density of the gas to change. This changing density, in turn, can cause the changes in the cross section. The systematic uncertainty in the areal density after considering the beam heating effect was estimated to be 5%.

27 27 Figure 2.4: The gas cell was attached to the end of the Swinger arm and equipped with water and air cooling. The gas cell was attached to the end of the Swinger arm shown in Figure 2.4. A 0.25-inch diameter collimator was attached between the end of the Swinger arm and the start of the gas cell apparatus. After the first collimator was an inch diameter collimator which served as the final collimation of the deuteron beam before it reached the deuterium gas in the cell. Collimation was necessary to focus and direct the beam onto the target. All of the beam energy went to the W foil, the D 2 gas, and the Au beam stop. To reduce beam heating, the gas cell was fitted with water and air cooling which are visible in the above Figure. The water cooling consisted of de-ionized water which was circulated from a small pump beside the Swinger through two tubes and on to the two metal prongs protruding from the gas cell. The metal pieces which were fitted with small tubes for water cooling are visible in Figure 2.3.

28 Aluminum Beam Stop Figure 2.5: The Al beam stop was attached to the end of the Swinger arm and used for determining the detector efficiency. The aluminum beam stop seen in Figure 2.5 was used to produce the 27 Al(d, n) reaction. This reaction was used as a calibration for the current experiment. Previous work from [Mas98] showed that the 27 Al(d, n) reaction was a standard reaction for determination of the efficiency of neutron detectors. Comparison of current data to that of [Mas98] allowed for calibration of the detectors and determination of detector efficiency. Similar to the D 2 gas cell, the Al beam stop was fitted with a 0.25-inch diameter collimator and air cooling.

29 Detectors There were three main detectors and a monitor detector used in this experiment. The monitor detector was a Stillbene detector that was attached to the Swinger. The main detector array was housed in the time-of-flight tunnel and consisted of a NE-213 scintillator detector and two lithium glass scintillating detectors. These detectors were located at a distance of 6.283±0.001 m from the target to the front face of the detectors and were enclosed in a lead house. The lead house was built to shield the detectors from background γ-rays. The NE-213 and Stillbene detectors were equipped with pulse shape discrimination (PSD) which was used to discriminate between incoming γ rays and neutrons. The Li glass detectors were not equipped with PSD. However, with use of the TOF technique determination of neutron energy was still done. Figure 2.6: The main detector array was located in the tunnel and encased in a lead house to shield from background gamma rays. The top detector was the NE-213 and the bottom two were the lithium glass detectors.

30 NE-213 Detector The commonly used NE-213 detector, the top detector displayed in Figure 2.6, is an organic liquid scintillator which is used for detection of fast neutrons. The NE-213 used in this experiment was 12.5 cm in diameter and the scintillating disk was 5 cm in thickness. The NE-213 had the characteristic of emitting different pulse shapes in response to different types of particles[leo94]. In the NE-213, incoming neutrons had a longer pulse shape than incoming γ-rays. For this reason, the NE-213 was able to discriminate between incoming neutrons and γ-rays. The NE-213 detector is a standard detector used for neutron spectroscopy. This detector is widely used for neutron scattering experiments because of its large size and its efficiency. The NE-213 had an efficiency of approximately 25% above 5 MeV but dropped precipitously below about 1 MeV [Dro78]. Because the region of interest for this experiment was in the low neutron energies, other detectors were required for full determination of the breakup cross section Lithium Glass Detectors The low-energy neutron detectors were the Lithium Glass scintillating detectors. These are the bottom two detectors in the array of Figure 2.6. Studies of kev range neutrons have commonly involved cerium-activated Lithium glass scintillators due to their non-zero efficiency below 1-MeV [Nei70]. Incoming neutrons underwent the 6 Li(n, α) reaction in which the 6 Li captures a neutron and the resulting 7 Li decays into an alpha particle and a triton [Wal12]. The Q-value for this reaction is positive and the reaction produces charged particles with substantial energy even for low energy neutrons. This is critical for detection of the low energy neutrons from the breakup reaction because the resulting efficiency is non-zero. The alpha particle and the triton interact with the glass to cause ionization and transfer energy to the cerium ions causing them to enter an excited

31 31 state. Emission of a photon allows the cerium ions to return to their ground state. These photons pass through a photo-cathode and electrons are emitted due to the photoelectric effect. These electrons are multiplied within the PMT to produce a signal which is then detected. [Nei70]. The Lithium Glass detectors used in this experiment were 5-inches in diameter and had 8mm thick scintillating disks. The scintillating disk was composed of a 6 Li substrate which was coupled to a PMT. These detectors were formulated to have low backgrounds, a feature required for low energy studies. Lithium Glass scintillators are most efficient in the low energy range of approximately 1-MeV down to 100-keV [Wal12]. The efficiency in this region is approximately 1%, which is higher than that of the NE-213. Use of the NE-213 detector above 1-MeV allowed for determination of the D(d, n) 3 He cross section while use of the Lithium Glass detector allowed for calculation of the breakup cross-section. While two lithium glass detectors were used throughout the experiment, only data from one lithium glass detector was used. Data from the other lithium glass detector was collected and analyzed, but the resulting peaks had long tails which made accurate determination of the cross section to be impossible. Analysis of data from both lithium glass detectors, in fact, revealed long tails and the extent of the tail as well as the detector response function are still under investigation as discussed in subsection

32 32 Figure 2.7: The monitor detector was attached to the Swinger at a 45 angle with respect to the target Stillbene Detector The monitor detector, displayed in Figure 2.7, was known as the Stillbene detector. This detector was used as a reference for the data obtained because it was attached to the Swinger. The Stillbene detector was made of organic scintillating crystals composed of C 14 H 12 and was also equipped with PSD. The Stillbene detector was attached to the Swinger arm and aligned at an angle of 45 with respect to the target. Because the Stillbene detector never changed angle with respect to the target, at each Swinger angle the data from the Stillbene was exactly the same. This served as a consistency check in order to determine if any parameters changed throughout the experiment.

33 Electronics and Data Acquisition Electronic Modules and Settings All electronics for the detectors were run through the Edwards 8 ADC data acquisition system located in the control room. Use of this system allowed for monitoring of the detectors and data acquisition in real time. To reach the 8 ADC system, electronics started in the tunnel where the detectors were located. Figure 2.8 shows the electronics schematic for the lithium glass detectors. Both lithium glass detectors had the same electronics and were set at a high voltage (HV) of V. Single vertical lines in the schematic depict the end of the tunnel. All electronics beyond these lines were located in the control room. The NE-213 electronic schematic is displayed in Figure 2.9.

34 34 High Voltage 2200 Bottom of Tunnel electronics Detector numbering as seen facing front of detectors. Tennelec TC 454 Unit #3 Tunnel Control Room #6 100 Ohm #6 100 Ohm Gate & Delay Unit #3 1 Route #5 2 Li Glass 2 "Magic" 50 ohm Tee Mesytech Unit #1 E PSD E Sum PSD SUM Li Glass 1 Tennelec TC 454 Unit #4 Tunnel Control Room #7 100 Ohm #7 100 Ohm Gate & Delay Unit #3 Route #5 "Magic" 50 ohm Tee Mesytech Unit #2 E PSD E Sum PSD SUM Figure 2.8: The electronics diagram shows the different modules that were connected to the Li glass detectors. The numbers on the cables represent places where the cable went from the tunnel and into the control room. Diagram courtesy of Dr. Thomas Massey.

35 35 Fine Gain 8.40 Course Gain microsecond shaping time High Voltage 2700 V Dynode Out Preamp 113 Ortec 572 X100 Gain 100 ohm #8 Controroom Patch 50 ohm C ADC #1 NE213 5"Diameter PMT 2" Thick Amp. Summer Amplitude #3 100 ohms Scatter detector (See Scatter Detector Electronics) #9 lower 100 Ohm ADC #3 ADC #2 Magic 50 ohm T Mesytec #2 PSD Summer PSD #4 100 Ohm 50 Ohms "D" ADC0 Fast Add Fast 50 ohm #1 50 ohm A Channel Descriminator Ortec 9309 Ortec Ω Preamp 100 ohm #4 (Top bank) Section 2 #4 50 Ohm Router #3 To Router Gate and Delay True Start Start Stop Beam Pickoff TAC Gate and Delay Strobe ADC 4 Figure 2.9: The electronics diagram shows the different modules that were connected to the NE-213 detector. Diagram courtesy of Dr. Thomas Massey. The D-D reaction produced neutrons whose time of flight was measured based upon start signals from when the neutron was detected and stop signals from the BPO. The scintillating material was connected to a PMT so that when a neutron or γ-ray interacted with the the material, a photon would be produced. Photons entering the PMT produce electrons via the photo-electric effect. Within the PMT are many dynodes and an anode. Upon reaching the last dynode, a positive pulse is produced which is proportional to the energy deposited in the detector. The signal from the anode was used to determine the

36 36 time when the incoming particle arrived at the detector. From the PMT, information about timing and energy was obtained. The signal was split into a fast and slow component. The slow signal component was passed through to an Ortec 460 Delay Line Amplifier (DLA) with fine gain of 0.75 and coarse gain of 100. The DLA expanded the amplitude of the pulse from the detected particle. This was used for neutron-gamma separation [Leo94]. The signal was then passed into an Ortec 433 Sum Invert Amplifier and then to an Ortec 427A Delay Line Amplifier which delayed the signal and passed it to a four-channel sum amplifier. This entire process produced the energy data that was received and read in real-time via the DaqLinux system discussed in the next section. The fast signal coming from the anode was passed into an Ortec 934 Constant Fraction Discriminator (CFD) with a four nanosecond delay. The CFD allowed for timing measurements to be made such that each input signal was delayed and then subtracted from a fraction of the undelayed signal [Leo94]. Each signal was delayed by some constant fraction and passed to an Ortec 437A Time to Amplitude Converter (TAC). The TAC provided information about the time of flight of each detected particle by converting the time period between the start and stop signals into an output pulse that was proportional to the amount of charge deposited in the detector. The start pulse for the TAC timing was generated by the arrival of particles to the detector and the stop pulse was generated by the passage of the deuteron beam pulse through the BPO. Time of flight data was read in real-time via the DaqLinux system Data Acquisition Data was acquired through the data acquisition software, developed at the Edwards Accelerator Laboratory, known as DaqLinux [Car13]. The software was written in C and modification of an initial program load (IPL) allowed each experiment to be customized. Within the IPL code, parameters such as route numbers for the detectors, ADC settings,

37 37 gate settings, and description of histograms to be used were written. The histograms for each detector included e.dat.1, the pulse height spectra for detector 1, time.dat.1 and tofn.dat.1, the TOF spectra for detector 1, and psd.dat.1, the pulse shape discrimination for detector 1. The psd.dat.1 histogram was only used for the NE-213 because it was equipped with PSD and the Li glass detectors were not. Histograms were saved in these forms for each of the detectors initialized in the IPL code. Other histograms were BCI and dtime which corresponded to the beam current integration (BCI) and the dead time, respectively. The software collected the data in event mode, meaning that pulse height and time information were stored for each individual event. These events could be replayed later in order to analyze the data. Events were visible during each data run and were saved onto disk and event files. These files were assigned a number which was incremented each time a new run began. At the end of each run, the events were saved in the format evt0801 in order to be analyzed later, where 0801 was the disk number chosen.

38 3 Data and Analysis 38 Table 3.1: Experiment data collection summary for angles with D 2 gas. Data Set Beam Current Target Swinger Angle nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas nA D 2 gas 0 Data were taken for angles from 0 to 60 in 5 increments both when D 2 gas was present within the gas cell and when it was absent from the cell. Data acquired when D 2 gas was absent from the cell served as a background measurement for the reaction at each angle. The run time for measurements taken with D 2 gas were approximately one hour while measurements taken with no gas in the cell were approximately thirty minutes. The data sets were assigned a disk number by the experiment and were recorded within the

39 39 data acquisition system. Disk numbers were usually incremented by one at the start of each run. Table 3.1 shows the disk assignments for angles where D 2 gas was present in the target. Disks 801 through 816 were runs with D 2 gas within the gas cell. Disks 817 through 831 were background runs where no gas was present in the gas cell. Disk 833 was the efficiency run using the 27 Al(d, n) reaction. Table 3.2 shows the Swinger angle with corresponding gas in and gas out background disks. All measurements, with exception of the 27 Al(d, n) reaction, were taken at 6.94 MeV. The 27 Al(d, n) reaction, disk 833, was done with the Swinger set at 120 and incident deuteron energy of 7.44 MeV as determined in [Mas98]. Table 3.2: Swinger angle D 2 disks and corresponding background disks. Swinger Angle Disk Background Disk

40 Analysis Procedure FORTRAN programs provided by [Mas13] were used to replay the data saved in event mode. Once replayed, programs were used to convert the channels into time of flight spectra and then convert the time of flight spectra into neutron energy spectra. This method is known as the time-of-flight or TOF technique. In order to subtract the background obtained at each angle, a program was used which compared the ratio of the BCI. Another program was used to determine the efficiency of the detectors and to determine the neutron yield in terms of neutrons/(mev µc sr), where µc refers to the charge from the beam current integration (BCI) and sr refers to the solid angle unit of steradians. Once neutron yield spectra were obtained, the cross section of the D(d, n) 3 He peak and breakup region were determined. This section will focus on the initial analysis programs up to the determination of the efficiency. Neutron yield and cross section will be discussed in the Results chapter.

41 Counts Channels Figure 3.1: The time calibration was done using a 60 Co source. The peaks shown above are the γ peaks from the decay of 60 Co. Each peak has a 100-ns separation Channel to Time Conversion The program called chttof06.f was used to convert the data from channels along the x-axis into time of flight channels. Using a 60 Co source, a time calibration was completed. The time calibration set 100-ns separation between the γ peaks of the source used. Determination of the starting and stopping channel for each peak allowed for a connection between the channels and the time separations that were determined by a delay generator. Between each peak shown in Figure 3.1 was a 100-ns separation. Using this time calibration and a random spectrum, raw channels shown in Figure 3.2 were converted into time channels shown in Figure 3.3. The γ peak arrived at the earliest time, followed by the

42 42 mono-energetic peak, and finally the breakup neutrons arrived at the latest time. The γ region is doubled peaked due to the deuteron beam hitting a collimator and then hitting the Au beam stop located at the end of the gas cell. The Au beam stop peak was used for timing information and corresponds to the piece of the γ peak closest to the D(d, n) 3 He region. The first γ peak from the right corresponds to the collimator because the beam first hits the collimator and then the beam stop. That is, the γ peak resulting from the collimator would arrive earlier in time. D(d,n) 3 He Gamma Counts 1000 D(d,np)D Background Channels Figure 3.2: The raw data where time increases from right to left for the NE-213 detector at 0. The different regions of the plot are identified with arrows.

43 43 5e+05 4e+05 D(d,n) 3 He Counts 3e+05 2e+05 1e+05 Background D(d,np)D Time (ns) Figure 3.3: The time channels, measured in nanoseconds, for the NE-213 detector at 0. The different regions of the plot are identified with arrows Time of Flight to Neutron Energy Conversion Once the original channels were converted into time channels, a program called tofte2.f was used to convert the time of flight channels along the x-axis into neutron energy. Because the lower energy neutrons took a longer time to reach the detector, they corresponded to later events than the higher energy neutrons did. Figure 3.3 shows the time of flight spectrum for the NE-213 at a Swinger angle of 0 prior to being converted into neutron energy spectra. A gate was placed on the γ peak from Figure 3.2 such that all γ rays arriving within that time interval were not mistaken for the mono-energetic neutrons which arrived second in time to the detector. These γ-rays resulted from

44 44 background reactions and were not resultant from the D(d, n) reaction. Figure 3.4 shows a neutron energy spectrum at Swinger angle of 0 for the NE-213. Those neutrons having a larger energy were those that arrived sooner to the detector than those lower in neutron energy. The lowest neutron energy attained from the data was 225 kev. The breakup region extends below this, but due to limitations upon the efficiency calibration, the current measurement could not be extended lower. 4e+06 3e+06 D(d,n) 3 He neutrons Counts/MeV 2e+06 D(d,np)D neutrons 1e+06 Background E n [MeV] Figure 3.4: The neutron energy spectrum at 0 for the NE-213. Arrows indicate the different regions of interest for the plot.

45 Background Subtraction After determining the neutron energy for both angles with D 2 gas in the cell and no gas in the cell, a program known as combspectra.f was used for background subtraction. The backgrounds surfacing within the gas-out spectra were from interactions of the beam with different components of the gas cell such as the collimators, the gas cell walls, the beam stop, and others. The exact interactions cannot be precisely known without further study, but from past experiments [Dha13], some of the common impurities were likely from carbon and oxygen. 1.5e e+06 Final Original Background Counts/MeV 9e+05 6e+05 3e E n [MeV] Figure 3.5: The neutron energy spectrum at 0 for the NE-213 for the gas-in and gas-out run. Red represents the original data, green represents the background, and black represents the final neutron spectrum after background subtraction.

46 46 For each data set, the total charge was obtained from the beam current integrator (BCI). This BCI was different for each run. The deposited charge represented the number of deuterons incident upon the target. The program utilized the ratios of the BCI for the gas-in and gas-out angles in order to subtract those events that were only from background and not from the D(d, n) reaction. Figure 3.5 shows the background subtracted neutron energy spectrum at 0 for the NE-213. Because the D(d, n) 3 He peak had no background beneath it, the Figure focuses on the breakup region. The red line indicates the original data, the green indicates the background, and the black indicates the final, background subtracted spectrum. There is a small region which became negative during the background subtraction. This occurred for all angles, but when the efficiency was applied to each spectrum, the negative regions were corrected to be zero because a negative neutron yield and cross section were not possible. Because there were regions at each angle where the background was over-subtracted, there was an estimated uncertainty of 3%. 3.2 The Al(d,n) Reaction The 27 Al(d, n) reaction was done in order to determine the efficiency of the neutron detectors. Following [Mas98], the incident deuteron energy was tuned to be 7.44 MeV and the Swinger was set to 120. The standard measurements of continuous neutron spectra were measured with a fission chamber. Neutron spectra from the current experiment were compared to that of the standard measurement. The reported systematic error for this method from [Mas98] was 5%. However, uncertainty for the experiment was estimated to be 8% because the standard measurements from [Mas98] were taken for a longer period of time and were more precise due to use of the fission chamber. Figure 3.6 shows the standard neutron spectrum obtained from measurements using a fission chamber [Mas98]. Neutron spectra obtained from the 27 Al(d, n) measurement allowed for

47 47 similar plots to be made for the NE-213 detector and the lithium glass detector. Figures 3.7 and 3.8 show the neutron spectra obtained for the 27 Al(d, n) reaction for the NE-213 and the Li glass detectors. The counts/mev for both detectors were less than that of the standard neutron spectrum, but those for the Li glass detector were significantly lower than those for the NE e+07 6e+07 5e+07 Counts/MeV 4e+07 3e+07 2e+07 1e E n [MeV] Figure 3.6: The standard neutron spectrum was acquired through measurements made with a fission chamber. Current experimental results were compared to this standard to determine the neutron detector efficiency. Figure taken from [Mas98].

48 48 1e+06 8e+05 Counts/MeV 6e+05 4e+05 2e E n [MeV] Figure 3.7: Neutron spectra acquired for the NE-213 using the Al(d, n) reaction A program called efficiency.f from [Mas13] was used to determine the efficiency of the NE-213 and the Li Glass detector by comparison of Figure 3.6 to Figures 3.7 and 3.8. The final efficiency curves are depicted in Figures 3.9 and In Figure 3.10, around 225 kev there is a sharp peak in the efficiency curve. This was due to the fact that a smaller binning scheme could not be used. For this reason, the breakup cross section had a higher uncertainty around 225 kev.

49 49 2e e+05 Counts/MeV 1e E n [MeV] Figure 3.8: Neutron spectra acquired for the Li Glass detector using the Al(d, n) reaction The efficiency of the NE-213 fell to around 0% at 1 MeV, making it impossible to determine the breakup cross section for that region. However, the efficiency of the NE-213 was 10-15% for the mono-energetic neutron peak. The Li glass detector, on the other hand, had an efficiency of approximately 1% in the region of deuteron breakup down to 225-keV. After these preliminary data analysis procedures, the neutron yield and cross section were calculated for the regions of interest.

50 Efficiency E n (MeV) Figure 3.9: Efficiency curve for the NE-213.

51 51 Efficiency E n (MeV) Figure 3.10: Efficiency curve for the Li Glass detector.

52 4 Results Neutron Yield The original data was transformed into neutron energy spectra and the efficiency of the NE-213 and Li glass detector was calculated. Application of neuts.f from [Mas13] was used to calculate the number of neutrons/(mev µc sr), a neutron yield. From the neutron yield, the cross section was calculated for the D(d, n) 3 He and D(d, np)d reactions. For the D(d, n) 3 He reaction, the NE-213 was used for analysis because it was the more efficient detector. The break-up region was calculated using both the NE-213 and the Li glass detector, however only the Li glass detector was able to determine the neutron yield below 1 MeV.

53 D(d,n) 3 He Neutron Yield Neutrons/(MeV µc sr) 2.5e+08 2e e+08 1e+08 0 o 10 o 20 o 30 o 40 o 50 o 60 o 5e E n [MeV] Figure 4.1: The neutron yield from the D(d, n) 3 He reaction from the NE-213 detector. Angles displayed are 10 increments from 0 to 60.

54 Table 4.1: Neutron Yield for the D(d, n) 3 He peak from the NE-213. The error is measured in terms of the number of neutrons/(mev µc sr) Swinger Angle Neutron Yield Error 54 Neutrons/(MeV µc sr) Neutrons/(MeV µc sr) The neutron yield from the mono-energetic neutron peak is well known. The reason for determining the neutron yield, in this case, was to check the validity of the analysis being done on the breakup region. Validating results from the past work of [Dro05] served as a consistency check for results of the breakup reaction. Figure 4.1 shows the neutron yield for angles in 10 increments from 0 to 60. The remaining angles were not shown in order to show separation between the mono-energetic peaks at each angle. Numerical integration of the mono-energetic peak at each angle was done in order to determine the number of neutrons/(mev µc sr) in each peak. Table 4.1 shows the number of

55 55 neutrons/(mev µc sr) in each peak with the associated error in terms of the number of neutrons/(mev µc sr). The error was determined by taking the square root of the number of neutrons/(mev µc sr) in each peak D(d,np)D Neutron Yield The neutron yield from the D(d, np)d reaction was calculated for the NE-213 and for the Li glass detector. The neutron yield calculated from the Li glass detector can be seen in Figure 4.2. The angles shown are 0 to 20. The remaining angles were not shown here for the purpose of clarity in the Figure. Numerical integration of the continuum of neutrons yielded the number of neutrons/(mev µc sr). Table 4.2 depicts the number of neutrons/(mev µc sr) along with the associated error for both the NE-213 and the Li glass detector. The region of integration for the NE-213 was from 1 MeV up to approximately 3.5 MeV and was from 225 kev up to approximately 3.5 MeV for the lithium glass detector.

56 56 Neutrons/(MeV µc sr) 4e e+07 3e e+07 2e e+07 1e+07 0 o 5 o 10 o 15 o 20 o 5e E n [MeV] Figure 4.2: The neutron yield from the D(d, np)d reaction from the lithium glass detector for angles 0 to 20.

57 Table 4.2: Neutron Yield for the D(d, np)d region from the NE-213 and Li glass detectors. The error is in terms of the number of neutrons/(mev µc sr). Angle NE-213 Error Lithium Glass Error 57 Neutrons/(MeV µc sr) Neutrons/(MeV µc sr) The neutron yield of the D(d, np)d reaction decreases as the angle increases. The highest neutron yield corresponds to 0 and the lowest yield to 60. Determination of the neutron yield, both in number and in distribution, was used to determine the cross sections of the D(d, n) reactions.

58 Cross Section The cross section obtained in this section for the D(d, n) 3 He reaction were done by use of the NE-213. Both the Li glass and the NE-213 were used to calculate the cross section of the D(d, np)d reaction D(d, n) 3 He Cross Section The cross section of the D(d, n) 3 He mono-energetic neutron peak was calculated in order to determine the validity of the analysis done for the breakup region. The cross section was calculated using dσ dω = i N i δe i e, (4.1) n where N i is the number of neutrons/(mev µc sr), e is the elementary charge of C, δe i is the energy width of each bin, and n is the areal density of the target. The differential cross section, dσ had the units of mb/sr. The areal density was dω calculated from n = 2Pl kt, (4.2) where P refers to the pressure of 30.0 psi maintained in the gas cell, l refers to the length of the gas cell, k refers to Boltzmann s constant, and T refers to the room temperature during the experiment. The areal density yielded the number of target nuclei per square centimeter. The areal density was found to be (1.58 ± 0.09) atoms/cm 2. The factor of two in the equation accounts for the use of diatomic deuterium gas in the target. Use of Equations 4.1 and 4.2 yielded the differential cross section values shown in Table 4.3 along with the associated errors calculated by use of propagation of errors. Figure 4.3 shows the angular distribution of the differential cross section. All points have error bars, but after 25, they are no longer visible.

59 Table 4.3: Angular Distribution of the Cross Section the D(d, n) 3 He reaction for the NE Angle dσ ( mb) dω sr mb Error ( ) sr

60 This work 70 dσ/dω [mb/sr] Θ L [deg.] Figure 4.3: The differential cross section of the D(d, n) 3 He reaction with respect to laboratory angle for the NE D(d,np)D Cross Section Because the D(d, np)d reaction produces a continuum of low energy neutrons, the cross section is expressed in terms of a double differential cross section: d 2 σ dωde = N i e, (4.3) n where N i refers to the neutron/(mev µc sr) value at each neutron energy value and the remaining variables are the same as in Equation 4.1. Use of Equation 4.3 yields the double differential cross section distribution shown in Figures 4.4, 4.5, and 4.6 for the lithium

61 61 glass detector. The solid lines are chi-square minimization fits which are discussed in subsection 4.3. Errors on the points come from propagation of errors from the neutron statistics and from errors on the efficiency. d 2 σ/dωde [mb/sr-mev] o E n [MeV] 0 o 5 o 15 o Figure 4.4: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of 0-15 for the Li glass detector. The solid lines show a fit which is discussed in subsection 4.3.

62 d 2 σ/dωde [mb/sr-mev] o o o o E n [MeV] Figure 4.5: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of for the Li glass detector. The solid lines show a fit which is discussed in subsection 4.3.

63 d 2 σ/dω de [mb/sr-mev] E n [MeV] o 45 o 50 o 55 o 60 o 63 Figure 4.6: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of for the Li glass detector. The solid lines show a fit which is discussed in subsection 4.3. Analysis of the breakup region was done for both the NE-213 and the Li glass detector. Figures 4.7, 4.8, and 4.9 show the double differential cross section of the D(d, np)d reaction for the NE-213 detector. The statistical errors on each point for the NE-213 were less than those on the Li glass detector because the NE-213 had a better detection efficiency than the Li glass detector.

64 64 d 2 σ/dωde [mb/sr MeV] o 5 o 10 o 15 o 20 o E n [MeV] Figure 4.7: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of 0-20 for the NE-213. The solid lines show a fit which is discussed in subsection 4.3.

65 65 d 2 σ/dωde [mb/sr MeV] o 30 o 35 o 40 o E n [MeV] Figure 4.8: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of for the NE-213. The solid lines show a fit which is discussed in subsection 4.3.

66 66 d 2 σ/dωde [mb/sr MeV] o 50 o 55 o 60 o E n [MeV] Figure 4.9: The double differential cross section of the D(d, np)d reaction with respect to neutron energy for angles of for the NE-213. The solid lines show a fit which is discussed in subsection 4.3. As the angle increases, the neutron yield and cross section decrease. It is evident that there is an angular threshold, after which deuteron breakup will not be detected. At 60, the amount of breakup is approximately 20 times less than it is at 0. Table 4.4 shows the calculated differential cross sections for the NE-213 and the lithium glass detectors. Differences between the detectors for the calculated cross sections are due to the zero efficiency of the NE-213 below 1-MeV.

67 Table 4.4: Differential Cross Section for the D(d, np)d region from the NE-213 and Li glass detectors. The region of integration for the NE-213 was from 1 MeV up to approximately 3.5 MeV and was from 225 kev up to approximately 3.5 MeV for the lithium glass detector. Angle NE-213 Error Lithium Glass Error 67 dσ ( mb) dω sr ( mb sr ) dσ ( mb) dω sr ( mb sr )

68 Fitting d 2 σ/dω de [mb/sr-mev] d 2 σ/dω de [mb/sr-mev] o 5 o 10 o 15 o 20 o 25 o 30 o 35 o 40 o 45 o 50 o 55 o 60 o E n [MeV] Figure 4.10: The χ 2 minimization fits for angles 0 to 60. In order to show the consistency of the results for the angular distributions of the cross section for the D(d, np)d region, a χ 2 minimization fit was performed. The χ 2 of data: χ 2 (α) = n ( f (x i, α) e i ) 2 σ 2 i=1 i (4.4)

69 describes the deviation of the fit from the data and is displayed in Equation 4.4, where α represents the free parameters being fitted in the function f (x i, α) and σ i represents the uncertainties in the measurements represented by e i. A χ 2 value is a measure of how a fit deviates the data and therefore how well the fit describes the data. Minimizing the χ 2 value will provide the best fit to the data. This χ 2 minimization fit allows for interpolation of data points and extrapolation to those regions where the differential cross section was not accessible, particularly below 225-keV neutron energy. Furthermore, the χ 2 minimization fit to the data is based upon kinematic variables and therefore represents a physically meaningful interpretation of the data. Equation 4.5 describes the function which was used to fit the double differential cross section data, where the fitting function is in center-of-mass coordinates. Equation 4.5 and further polynomial definitions are shown in Equations 4.6-8: ( ) d 2 σ = P 0 (E 1 )P 0 (E 23 ) f (E, cos θ) f BW (E), (4.5) dωde c.m. 69 f (E, cos(θ)) = a + be + ce 2, (4.6) a = a 0 + a 2 P 2 (cos θ) + a 4 P 4 (cos θ), (4.7) f BW (E) = Γ 2 /4 (E E R ) 2 + Γ 2 /4. (4.8) The different fitting parameters are defined in Table 4.5. The penetration factors, P 0 (E 1 ) and P 0 (E 23 ), are calculated assuming l = 0 and a radius of 4 fm. The function f (E, cos θ) described in Equation 4.5 depends upon a, b, and c, polynomials as defined in Equation 4.6, which are truncated after second order. Each of the parameters a, b, and c have the same expansion from Equation 4.7, where P 2 (cos θ) and P 4 (cos θ) are even

70 70 Legendre polynomials. Even Legendre polynomials were chosen because the angular distribution must be symmetric about θ = 90 in the center-of-mass frame. Equation 4.8 describes a Breit-Wigner distribution which commonly used to describe resonances, but was just used for convenience in this case. Fitting was done in the center-of-mass frame and then transformed to the laboratory frame in order to fit the data. Table 4.5: Definitions of fitting parameters defined in Equations Parameter P 0 (E 1 ) P 0 (E 23 ) E 1 E 23 E θ P 2 (cos θ) P 4 (cos θ) f BW (E) Γ E R Definition Penetration Factor for n+(p+d) Penetration Factor for p+d Kinetic Energy of n relative to p+d Relative Kinetic Energy of p+d Center of Mass Energy Center of Mass Angle Second Order Legendre Polynomial Fourth Order Legendre Polynomial Breit Wigner Polynomial Full Width at Half Maximum Position of Maximum Energy Value Each parameter of the fit was allowed to be either constant or variable. In the case of the fit used for the breakup region, the fits to the data were shown in Figures The χ 2 value was over 915 data points. Of the 915 data points, 605 were from lithium glass data and 310 were from NE-213 data. The parameters of the fit are shown in Table 4.6. The fits for each angle are shown in Figure The fits provide a reasonable

71 description of the data, but are far from perfect. The difficulties in achieving a good fit for the data are most likely due to reasons discussed in subsections and Table 4.6: Definitions of fitting parameters defined in Equations Parameter Constant or Variable Value a 0 Variable a 2 Constant 0.0 a 4 Constant 0.0 b 0 Variable b 2 Constant 0.0 b 4 Constant 0.0 c 0 Variable c 2 Variable c 4 Variable A Variable E r Variable Γ Variable

72 5 Conclusions and Future Work Discussion of Results The original goal of this thesis was to measure the breakup cross section of the D(d, n) reaction at 6.94 MeV for use as an additional neutron source in the active interrogation of hidden fissile materials. Past work indicated that the commonly used neutron source, the D(d, n) 3 He reaction, was not purely mono-energetic when the deuteron energy rose above 4.45 MeV. Above 4.45 MeV the deuteron began to break up into its constituent particles. The issue with the breakup reaction was that the cross section had not been measured below 1 MeV. This caused significant uncertainty in the measurement of the breakup cross section because the breakup region extends substantially below 1 MeV especially at 0. Therefore, in order to understand the cross section of the D(d, np)d reaction, the lower limit needed to be extended. For consistency, the well known cross section of the mono-energetic neutron peak was measured. Figure 5.1 shows the evaluated cross section angular distribution from [Dro05] compared to the data acquired from this thesis.

73 Drosg, 1978 This work 70 dσ/dω [mb/sr] Θ L [deg.] Figure 5.1: The differential cross section of the D(d, n) 3 He reaction with respect to laboratory angle for the NE-213 detector. The solid line depicts the evaluated cross section result for 6.94 MeV from [Dro05].

74 (dσ/dω) expt. /(dσ/dω) Drosg Θ L [deg.] Figure 5.2: Ratios were formed between cross section values from the current work and from [Dro05] in order to check the consistency of the results. The results from the current work for the D(d, n) 3 He are in agreement with the evaluation from Drosg [Dro05]. In order to further check the validity of the current analysis, ratios were made between the accepted values and the current work. Figure 5.2 shows the ratio of the differential cross section of this thesis to that of Drosg at each angle. The ratios were between 0.9 and The analysis done is in good agreement with accepted work from Drosg. Because the same approach was used to calculate the D(d, np)d differential cross section, the measurement and analysis procedures are valid.

75 75 20 This Work - Lithium Glass This Work - NE213 Dha13 d 2 σ/dωde [mb/sr MeV] E n [MeV] Figure 5.3: The comparison between previous data from [Dha13] and the current work. Both the NE-213 and Lithium Glass detector show good agreement with measurements made in the Edwards Accelerator Laboratory previously. The neutron energy is extended well below 1.5 MeV. The state of past work concerning the breakup cross section was shown in Figure 1.2 where the cross section distribution below 1.5 MeV was not known. This thesis has measured the breakup cross section as low as 225 kev, far below the previous state. The breakup cross section distribution was found to decrease in magnitude as the angle increases. The highest breakup cross section and neutron yield were at 0 and the lowest at 60. Extension of the breakup cross section to 225 kev has not been achieved until now. Figure 5.3 shows the comparison between the current work and previous work done in the same laboratory by [Dha13]. Breakup data are in good agreement with previous work and

76 76 extend the measurement substantially below 1.5 MeV. Discrepancy between the NE-213 and lithium glass data below 1 MeV is currently under investigation as discussed in the following subsections Background Subtraction The background subtraction caused significant issue throughout the analysis of the experiment. The background subtraction is of particular interest at the maximum energy for each angle. The background on several angles, specifically 20-30, was over-subtracted. This caused the breakup region to shift position so that the maximum energy position for these angles was not correct. This is visible by the deviation of the data from the fit, shown very clearly in Figures For this reason, a better method of background subtraction is necessary so that data will neither be over-subtracted nor under-subtracted. Better background subtractions will lead to better fitting and will allow for more insight into the physics Lithium Glass Detector Response The detector response function of the lithium glass detector also caused significant issue throughout the analysis of the data. On both the mono-energetic peak and the breakup region for the lithium glass detectors, a long tail was present on the low energy end. Both lithium glass detectors from this work exhibited long tail-like behavior. Evidence of this behavior can be seen in Figure 5.3, where the lithium glass and NE-213 start to disagree. One of the lithium glass detectors was worse than the other and was excluded from the results due to the long tail which smeared out features of the spectra. The lithium glass data shown in this work also exhibited a tail on the low energy ends of the mono-energetic peak and the breakup region. The extent of that tail is unknown and is still under investigation to determine a detector response function and a way to quantify and understand the tail-like behavior. The measurement of the breakup cross section was

77 77 extended to 225-keV neutron energy, but the exact shape of the distribution is still unknown due to the tail-like behavior of the lithium glass detector. The detector response function for the lithium glass detector is especially important for neutron energies below 1 MeV. Quantification of the detector response function will give insight into this issue. 5.2 Error Analysis There were several sources of systematic error throughout the experiment. Statistical error was displayed with error bars on the data points. Table 5.1 shows the sources of systematic error throughout the experiment. As discussed in section 2.2.1, the areal density was estimated from the gas cell pressure. The uncertainty in the areal density was estimated to be 5%. The uncertainty in the BCI was estimated to be 1%. Uncertainty in the number of lost events due to instability in the repetition rate was determined to be 1% as discussed in section The reported uncertainty for the Al(d, n) method for calculating the efficiency from [Mas98] was reported as 5% but for this experiment, the estimated uncertainty was about 8% for each detector. As discussed in section and 5.1.1, there were regions where the background was over-subtracted. The estimated uncertainty for the background subtraction was estimated to be 3%. The total systematic error contribution when added in quadrature was determined to be 10%. It should be noted that there are larger error bars near the maximum energy of the breakup region for each angle and that data below 1 MeV for the lithium glass detector are under investigation as discussed in subsections and The 10% error estimation does not include contributions from these two sources.

78 78 Table 5.1: Summary of Systematic Errors Source of Error Contribution Areal density 5% Beam Current Integration 1% Lost Beam Pick Off Signals 1% Background Subtraction 3% NE-213 efficiency 8% Li glass efficiency 8% Total 10% 5.3 Future Work Additional Angles, Deuteron Energies, and Binning Schemes In this thesis, an angular threshold was visible on the breakup cross section. However, the exact nature of that threshold is not known. In order to determine when breakup will no longer occur, further angles would need to be tested. Angles that should be studied are 90, 120, and 150 at least. Testing these angles will better show the angular threshold for the breakup cross section. In addition, testing more deuteron energies will provide insight into the breakup cross section. Using the same electronics and experimental setup, a determination of the breakup cross section at deuteron energies above 6.94 MeV could be completed. Because the breakup cross section has a strong energy dependence, testing different deuteron energies would show how exactly the breakup cross section scales with energy. All work was done using a 50-keV binning scheme. If work could have been done with a smaller binning scheme, the lower limit of 225 kev could be extended down to 100

79 79 kev. Because of the sharp peak in the lithium glass detector efficiency curve as well as the limitations of the repetition rate and the detector efficiency, 225 kev was the lowest possible neutron energy. In the future, more angles and deuteron energies will be studied and a smaller binning scheme will be devised. The most significant of these future plans would be doing additional deuteron energies Active Interrogation Determination of the breakup cross section down to 225 kev provides useful insight into using the D(d, np)d reaction as an addition to the already usable D-D neutron source for active interrogation. In order to determine how the D(d, np)d reaction could be used, the breakup cross section would need to be studied for a wider range of deuteron energies above 4.45 MeV. Since 0 has the highest differential cross section and neutron yield, fixing the Swinger at that angle and changing the incident beam energy would give a better idea of the possibility of using D(d, np)d as an additional component of the D-D neutron source Conclusion With the use of a pulsed, 6.94-MeV deuteron beam, a D 2 gas target, two lithium glass detectors and an NE-213, the cross section measurement of D(d, np)d reaction was extended down to 225-keV. The best method for use in active interrogation can now be studied further due to better measurement of the cross section. Future work in this reaction will take into consideration the addition of different deuteron energies in order to attain further information about how the D(d, np)d reaction depends on the incident beam energy. Furthermore, investigation into the background subtraction and detector response function of the lithium glass detector will yield better fits to the data and will increase understanding of the region below 1-MeV neutron energy. With current and future work, a better determination of how to use the D(d, np)d reaction as a component of the D-D

80 80 neutron source can be made and better understanding of the breakup region will be obtained.

81 References 81 [Ara11] K. Arai, S. Aoyama, Y. Susuki, P. Descouvemont, and D. Baye, Tensor Force Manifestations in Ab Initio Study of the 2 H(d,n) 4 He, 2 H(d,p) 3 H, and 2 H(d,n) 3 He Reactions, Phys. Rev. Lett. 107 (2011), [Cra56] L. Cranberg, A. H. Armstrong, and R. L. Henkel, Neutrons from the D-D Reactions, Phys. Rev. 104 (1956), [Car13] D. E. Carter, Daqlinux, Accessed: [Cab89] S. Cabral, G. Borker, H. Klein, and W. Mannhart, Neutron Production from the Deuteron Breakup Reaction on Deuterium, Nucl. Sci. Eng. 106 (1989), 308. [Dha13] S. Dhakal and C. R. Brune, Measurement of D+D Neutrons and Neutron Transmission from Iron Sphere, private communication, [Del12] A. Deltuva and A. C. Fonseca, Neutron- 3 H scattering above the four-nucleon breakup threshold, Phys. Rev. C 86 (2012), [Dro72] M. Drosg, Accurate Measurement of the Counting Efficiency of a NE213 Neutron Detector Between 2 and 26 MeV, Nucl. Instr. Meth. 105 (1972), 573. [Dro78] M. Drosg, Unified absolute differential cross sections for neutron production by the hydrogen isotopes for charged-particle energies between 6 and 17 mev, Nucl. Sci. Eng. 67 (1978), 190. [Dro99] M. Drosg, Monoenergetic neutron production by the two-body reactions in the energy range from to 500 mev, [Dro05] M. Drosg, DROSG-2000, Codes and database for 59 neutron source reactions, documented in the IAEA report IAEA-NDS-87 Rev. 9, May 2005, received from the IAEA Nuclear Data Section. [Fin82] Roger W. Finlay, C E. Brient, Don E. Carter, and J Rapaport, The Ohio University Beam Swinger Facility, Nucl. Instr. Meth. 198 (1982), 197. [Gri82] Steve M. Grimes, P. Grabmayr, Robert W. Finlay, SL. Graham, G. Randers-Pehrson, and Jack Rapaport, Nucl. Instr. Meth. 203 (1982), 269. [Hof08] H. M. Hofmann and G. M. Hale, 4 He experiments can serve as a database for determining the three-nucleon force, Phys. Rev. C 77 (2008), [Hen55] R. L. Henkel, Jr. J. E. Perry, and R. K. Smith, Breakup of Deuterons on H, T, 3 He, and 4 He, Phys. Rev. 99 (1955), 1050.

82 [Kor86] N. V. Kornilov and A. B. Kagalenko, The Differential Neutron Production Cross-Sections in the D(d,np) Reaction, Properties of Neutron Sources, IAEA-TECDOC-410, IAEA, 1986, p [Lef62] H. W. Lefevre, R. R. Borchers, and C. H. Poppe, Neutrons from Deuteron Breakup on D, T, and 4 He, Phys. Rev. 128 (1962), 491. [Leo94] W. R. Leo, Techniques for Nuclear and Particle Physics Experiments, revised 2nd ed., [Lis73] H. Liskien and A. Paulsen, Neutron Production Cross Sections and Energies for the Reactions T(p,n) 3 He, D(d,n) 3 He, and T(d,n) 4 He, Nucl. Data Tables 11 (1973), 569. [Mas98] Thomas N. Massey, S. Al-Quraishi, C.E. Brient, J.F. Guillemetter, Steve M. Grimes, Devon K. Jacobs, John E. O Donnell, J. Oldendick, and R. Wheeler, A Measurement of the 27 Al(d,n) Spectrum for Use in Neutron Detector Calibration, Nucl. Sci. Eng. 129 (1998), 175. [Mas13] T. N. Massey, 2012, FORTRAN analysis programs. [Mar60] J. B. Marion and J. L. Fowler, Fast Neutron Physics Part I, [Nei70] J M. Neill, D. Huffman, C A. Preskitt, and J C. Young, Calibration and Use of a 5-inch Diameter Lithium Glass Detector, Nucl. Instr. Meth. 82 (1970), 162. [Nav10] Petr Navratil, Robert Roth, and Sofia Quaglioni, Ab initio many-body calculations of nucleon scattering on 4 He, 7 Li, 7 Be, 12 C, 16 O, Phys. Rev. C 82 (2010), [Pop72] C. Pope, N. Buget, C. O. Blyth, P. B. Dunscombe, and J. S. C. McKee, A Search for Spin Dependent Effects in the Three Body Final Ftate from the D(d,n)pd Reaction at 11.3MeV Incident Deuteron Energy, J. Phys. A. 5 (1972), L33. [Ryb61] B. V. Rybakov, V. A. Sidorov, and N. A. Vlasov, Breakup of Deuterons on H, D, 3 He, and 4 He, Nucl. Phys. 23 (1961), 491. [Sar95] A. Sarkar, S. Ghosh, R. Joshi, D. Kanjilal, A. Roy, and R.K. Bhowmik, Calibration of the energy analyzing magnet of the NSC Pelletron using a differential time of flight technique, Nucl. Instr. Meth. 371 (1995), 351. [Val72] V. Valkovic, I. Duck, W. E. Sweeney, and G. C. Phillips, Three-Body Break-up in the d+d d+p+n Reaction, Nucl. Phys. A183 (1972),

83 83 [Wal12] Adam Wallace, Lithium-Glass Neutron Detection, B.S. thesis, Brigham Young University, [Wen12] M. T. Wenner, A. Haghighat, J.M. Adams, A.D. Carlson, Steve M. Grimes, and Thomas N. Massey, Novel Investigation of Iron Cross Sections via Spherical Shell Transmission Measurements and Particle Transport Calculations for Material Embrittlement Studies, Nucl. Sci. Eng. 170 (2012), 207. [Zie04] J F Ziegler, SRIM-2003, Nucl. Ins. Meth (2004), 1027.

84 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Thesis and Dissertation Services!