Measurements of Photonuclear Reactions Induced with Linearly Polarized Gamma Rays. By Stephen Yates

Transcription

1 Measurements of Photonuclear Reactions Induced with Linearly Polarized Gamma Rays By Stephen Yates Duke University and Triangle Universities Nuclear Laboratory (TUNL) Second Edition Originally Submitted May 6, 2016 Abstract: This thesis reports the first measurements of cross sections and asymmetries for gamma ray induced emission of neutrons from 80 Se. These measurements are part of a broader project to obtain transition widths relevant to determining the weak-magnetism corrections to the standard Fermi function for the energy spectrum of electrons emitted in beta decay of radioactive nuclei. The measurements were performed using the linearly polarized and nearly mono-energetic gamma ray beam at the High Intensity Gamma ray Source (HIGS). The beam energies were selected to scan the excitation energies in 80 Se where the 1 + isobaric analog state to the ground state of 80 As is predicted. Candidate states at excitation energies below and above the neutron separation energy have been explored. In this work we report the measurements carried at excitation energies above the neutron separation energy. The experimental technique is described, and the results for the cross sections and asymmetries are presented for the emitted neutrons at several angles. Nuclear structure implications are discussed. 1

2 Committee Members: Calvin Howell, Supervisor Glenn Edwards Mohammad Ahmed This thesis is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science with departmental distinction in the Duke University Department of Physics. May 6, 2016 Contents: 2

3 I. Introduction and Motivation for Research, pg. 5 II. The Search for Isobaric Analog States, pg. 7 III. The (γ, n) Reaction, pg. 15 IV. Experimental Setup and Measurement Technique, pg. 22 V. Data Analysis, pg. 28 VI. Results, pg. 56 VII. Conclusion, pg. 65 VIII. References, pg. 68 Acknowledgements 3

4 The author would like to acknowledge the work of Brent Fallin, Duke Physics PhD candidate and TUNL researcher, who set up the experimental apparatus and took the data used in my analysis. Brent was consistently available to answer questions that came up in the course of my research. He helped to me to calculate the paddle efficiency, and also taught me how to replay and analyze the data in SpecTcl. The author would also like to thank TUNL researcher Alex Crowell for running the Monte Carlo simulations that provided the efficiency curves for the neutron detectors and paddle calibration. TUNL researcher Ron Mallone gave me multiple tutorials in analyzing data using Root. Ron taught me everything that I currently know about coding in C++ and was willing to help troubleshoot my program on numerous occasions. None of this would have been possible without Ron s help. An extra special thanks to Profs. Glenn Edwards and Mohammed Ahmed, who agreed to serve on the author s thesis committee. Their feedback, suggestions, and criticism showed me how to focus the written portion of the thesis toward its intended readership. Profs. Edwards and Ahmed also attended my thesis defense talk, asking many thought-provoking questions. Finally, the biggest thanks of all goes to Prof. Calvin Howell, who spent countless hours and late nights working with the author at all stages of this project. Thank you for agreeing to be my thesis advisor, and thank you for all the support and encouragement you have shown me since my freshman year at Duke. I. Introduction and Motivation for Research 4

5 The nucleus is a quantum system consisting of nucleons that interact in a self-generated mean field, mediated by the strong nuclear force. The many-body quantum nature of nuclei produces complicated structure features and rich dynamical phenomena, e.g., collective excitations. Spectroscopic techniques based on a variety of reaction mechanisms are used to acquire structure and reaction dynamics information for the purpose of identifying patterns that contribute to advancing understanding and modeling of nuclear structure features and dynamical responses of nuclei to stimuli. Also, nuclear structure and reactions data are needed for applications in energy and security. The well-established theoretical treatment of electromagnetic interactions and the angular momentum selectivity of gamma rays make them a highly effective probe of nuclear structure and dynamical responses of nuclei to energy absorption. The experiment and data analysis reported in this thesis is part of a project that uses gamma ray beams to search for and measure the electromagnetic decay widths of 1 + states in nuclei for applications in correcting calculations of the energy spectrum of the electrons emitted in beta decay. The interest in developing high-precision calculations of the beta-particle energy spectrum in nuclear decay is to reduce the error in predicting the energy spectrum of neutrinos from nuclear reactors. The correction that motivated this work is referred to as weak magnetism [1-3]. A brief description of the weak magnetism correction is given in Section II. Initially, the experiment searched for the 1 + state in 80 Se at high excitation energies that is the isobaric analog state (IAS) of the ground state of 80 As. However, the 1 + IAS is not believed to have been observed in the data. Nevertheless, our measurements yielded original cross section and asymmetry data for the 80 Se(γ,n) reaction. The experiment method, data analysis 5

6 and results for the 80 Se(γ,n) reaction are described in this thesis. The following sections contain description and discussion of: (II) the background and motivation for measuring gamma ray (γray) decay widths of IAS; (III) nuclear structure insights gained from (γ, n) reaction data; (IV) the experiment setup and measurements; (V) the data analysis method; and (VI) results. II. The Search for Isobaric Analog States 6

7 The detection of neutrinos emitted by nuclear reactors is the basis for many of the major experiments that investigate the fundamental properties of neutrinos. Both basic science research and applications require high precision calculations of the neutrino energy spectrum. The neutrinos from a nuclear reactor are emitted from the beta (β) decay of the radioactive nuclei resulting from the energy-producing nuclear fission reactions in the reactor core. Lepton number conservation requires that for each emitted β - particle an associated electron antineutrino be emitted. For example, As Se + β +ν e The energy of the electron antineutrino is related to that of the associated β - particle by conservation of energy and momentum. Achieving calculated neutrino energy spectra with accuracies better than about 5% requires corrections to the standard Fermi function for the β - emission from the radioactive fission fragments in reactors. The weak-magnetism correction is one of the three main corrections that must be applied to the Fermi function [2]. The weak-magnetism correction accounts for the interaction of the weak currents that mediate the β-decay process with the transition magnetic moment of the nucleons involved in the decay. The name weakmagnetism was created by Murray Gell-Mann as a label for the term in the Hamiltonian for the nuclear weak interaction that was analogous to the magnetic effects that induce the emission of M1 photons in electromagnetic nuclear de-excitations [4]. The weak-magnetism correction to the β- energy spectrum can be calculated with the equation: 7

8 δ WM = 4 2µ 3 m A M GT m e (1) M GT is the Gamow-Teller matrix element for the transition from the initial to final nuclear states; m A and m e are the masses of the nucleus and β -, respectively; and µ is the magnitude of the transition magnetic moment. The value of µ can be determined by measuring the magnetic dipole M1 γ-ray decay width (Γ M1 ) of the corresponding isovector transition of the IAS in the residual nucleus [1]: " µ = 3Γ m 2 % M1 A $ 3 # αe ' γ & 1/2 (2) α is the fine structure constant and E γ is the energy of the γ-ray emitted in the M1 transition. There is very little data that can be used to extract the values of Γ M1 needed to compute δ WM for nuclei heavier than A = 32. The objective of the overarching project, to which this thesis contributes, is to search for the IAS in nuclei for which a neighbor nucleus in the isospin chain β decays. Once the IAS is identified, the next step is to measure Γ M1. There are various techniques that can be used to determine the values Γ M1 needed to compute δ WM. We elected to use nuclear resonance fluorescence because of the high sensitivity of γ-rays for probing dipole nuclear excitations. The initial focus is on nuclei with the spin and parity of the ground state equal to 0 +. This choice is made to simplify the identification of M1 γ-ray transitions from excited states to the ground state. Exploratory measurements were performed at the High Intensity Gamma ray Source (HIGS) during spring In these measurements a linearly polarized and nearly mono-energetic gamma ray beam bombarded a sample. The beam 8

9 energies were selected to scan the excitation energies where 1 + IAS states are predicted. We explored candidate states that were below and above the neutron separation energy, i.e., the excitation energy was sufficient for the nucleus to decay by neutron emission. Both gamma rays and neutrons emitted from the sample were detected in these measurements. The nuclear resonance fluorescence, i.e., (γ, γ ), measurements were used to search for discrete 1 + states that could possibly be the IAS for the 80 As ground state. No discrete peaks were observed in the energy spectra of the detected gamma rays, indicating the absence of a strong 1 + state in the range of excitation energies scanned. We concluded that this search had a null result for identifying a candidate 1 + state. The focus then turned to analyzing the (γ, n) data, which was the first measured for this nucleus. The main goal of this thesis project is to carry out the analysis of the (γ, n) data collected on 80 Se. The deliverables of the analysis work are cross section and asymmetry data for the neutron channel of the reaction. Before discussing the (γ, n) reaction, a short overview of IAS states will be presented. Isobaric Analogue States 9

10 Any two nuclear states with the same spin and parity are Isobaric Analogue States (IAS) if they have the same total isospin number. The concept of isospin was first introduced by Werner Heisenberg in 1932 to explain the symmetry relationship that the newly discovered neutron had with the proton [5]. The application of isospin to nuclear structure theory is derived from the approximate charge-independence of nuclear interactions, allowing us to treat protons and neutrons as two forms of the same particle. Isospin derives its name from its mathematical similarity to intrinsic angular momentum. Every individual nucleon has an isospin vector with a magnitude of ½. However, this vector can have a z-projection in isopsin space of either +1/2 or -1/2. It is this projection that differentiates the proton and the neutron the proton has an isospin projection of -1/2, while the neutron s projection is +1/2. The isospin projection for a complex nucleus is simply the sum of the z component of all the individual nucleons, given by the equation: T! =!!!! (3) Examples of isospin multiplets are shown in Fig The 1 + state in 12 C at excitation energy Ex = 15.1 MeV is the Isobaric Analog State of the 1 + ground states of 12 B and 12 N. That is, these three states form an isobar triplet. The 0 + excited state in 12 C at Ex = MeV is the IAS of the 0 + excited states in 12 B (Ex = MeV) and 12 N (Ex = MeV). These three states are members of an isobar quintet. 10

11 Figure 2.1: Isobar diagram for A = 12. This figure is taken from the paper by Antony, et al. The isospin projection T z and the potential energy (mc 2 ) of each state are on the horizontal and vertical axes of the diagram, respectively. The three tiers, starting from the bottom of the diagram, correspond to isospin values T of 0, 1, and 2. The main differences in the energy levels of the isobaric analog states are due to the Coulomb energy and the mass difference of the proton and neutron. We now apply this scheme for identifying IAS to Selenium-80 ( 80 Se). The 80 Se nucleus has 34 protons and 46 neutrons (N = 46, Z = 34). It therefore has an isospin projection of 6. The value of T Z is conserved over gamma-induced nuclear transitions, so all excited states of the 80 Se nucleus also have isospin projections of 6. For the vast majority of ground-state nuclei, the total isospin T is equal to Tz. The 0 + ground state of 80 Se therefore has T = 6 and Tz = 6. But total isospin is also affected by the spin and parity of the nucleus. The 1 + ground state of 80 As beta-decays to the 0 + ground state of 80 Se. In order to find the weak-magnetism correction for this decay, we must find the M1 γ-ray transition width of Arsenic-80 s IAS in 80 Se. 80 As has 33 protons and 47 neutrons (N = 47, Z = 33). Its isospin 11

12 projection Tz therefore is 7, and the total isospin of the 1 + ground state is T = 7. We search for a 1 + excited state in 80 Se that has T = 7 and T Z = 6, which would be the IAS of the 1 + ground state of 80 As. Figure 2.2: Energy-Level Diagram, beta-decay of 80 As and (g,n) reaction of 80 Se IAS. This figure demonstrates how the theoretical excitation energy of the IAS was calculated from the differences in coulomb and mass energy We employ a multi-step process to calculate the energy level of 80 Se that corresponds to the Isobaric Analog State of 80 As. To begin with, we define the ground-state energy level of 80 Se to be 0 MeV. According to data from Brookhaven National Institute s National Nuclear Data 12

13 Center, the beta-decay of 80 As to 80 Se releases 5.54 MeV of energy. We therefore define the energy level of the 1+ ground state of 80 As to be 5.54 MeV. Next, we calculate the increase in energy required to replace one of the neutrons in the 80-Arsenic nucleus with a proton, thereby transmuting it to 80-Selenium. This will involve a large increase in electromagnetic potential energy, to account for the coulomb repulsion of the additional proton against the other protons in the nucleus, as well as a slight decrease in mass-energy to account for the slightly smaller mass of the proton as compared to the neutron. To calculate the increase in nuclear binding energy needed to accommodate the electrostatic repulsion of the additional proton, we use the Semi-Empirical Mass Formula, which simplifies our calculation by modeling the nucleus as a sphere of uniform charge distribution. For the purposes of estimating the energy of the Isobaric Analog State, this approximation holds. The formula models the repulsion between protons as proportional to the square of the number of protons Z and inversely proportional to the atomic radius further approximated as proportional to the cube root of the total number of nucleons A: E! =!!!!/! a! (4) The constant A C is the Electrostatic Coulomb Constant, which internalizes all of the constants used in this approximation: a! =!!!!"!!!!! (5) 13

14 e is the charge of the proton, ε 0 is the permittivity of free space, and r 0 is the empirical radius of the proton. a c works out to be.691 MeV, a value which can be empirically verified. This equation simplifies our calculation by modeling the nucleus as a sphere of uniform charge distribution. But for the purposes of estimating the energy of the Isobaric Analog State, the approximation holds. This formula yields a value of MeV for the 80 Se nucleus and MeV for the 80 As nucleus. Subtracting the two values yields an energy difference of MeV. But we must still account for the slightly smaller mass of the proton. By massenergy equivalence, this works out to be an energy reduction of approximately 0.78 MeV. The 1 + excited state of 80 Se should therefore have energy approximately 9.96 MeV greater than the 1 + ground state of 80 As. We defined the ground state of 80 As as having energy 5.54 MeV greater than the 0 + ground state of 80 Se, which we arbitrarily declared to be 0 MeV. The 1 + excited state of 80 Se should therefore have energy of MeV above the ground state. We will therefore probe the 80 Se nucleus in search of 1 + states with incident gamma ray energies around MeV. 14

15 III. The (γ,n) Reaction The cross section of an atomic nucleus is a measure of the probability that an incoming particle will produce a reaction with that nucleus. For example, when an incoming photon is absorbed by an atomic nucleus, it can induce that nucleus to expel a neutron in order to obtain a lower energy configuration. The differential cross section for the (γ,n) reaction therefore measures the probability that the interaction of a photon with the nucleus will cause a neutron of a particular energy to be emitted in a specified direction. Classically, the nuclear cross section is analogous to the two-dimensional area over which a particle will collide with an object. It is measured in units of area per solid angle per energy (nb/sr/kev, nanobarns per steradian per kilo-electronvolt), where the energy is of the emitted neutron. Accurate cross section data is critical in nuclear physics research. It yields information about the size of nuclei, nuclear structure, reaction processes, and spins and parities. The goal of our analysis is to determine cross sections and asymmetries for the neutron channel of the gamma ray induced nuclear reaction. We specifically investigate Selenium-80 because of its high atomic mass number and the low amount of published data on this nucleus for γ-ray induced reactions. This thesis will explain the experimental methodology by which we obtained neutron spectra using the High Intensity Gamma Source (HIGS) at Duke University. It will detail the computation and data analysis techniques developed for converting the measured neutron time-of-flight spectra into cross sections and asymmetries. It will present our experimental findings and discuss sources of error. In conclusion, we will discuss the interpretation of the data to obtain nuclear structure information. 15

16 The nuclear reaction being investigated in this experiment is the interaction of a Selenium-80 nucleus with an incident photon to produce a Selenium-79 nucleus and a free neutron: 80Se + γ 79Se + n (6) In expelling a neutron and decaying to 79 Se, total angular momentum must be conserved. We can therefore expect the following relationship to hold:!!"!" =!!"!" +!! +!! (7) The symbols are: J 80Se = Total Angular Momentum of the excited state in the 80 Se Nucleus J 79Se = Total Angular Momentum of the state in the 79 Se Nucleus S n = Intrinsic Angular Momentum ( Spin ) of Neutron L n = Orbital Angular Momentum of Neutron The neutron is a spin-1/2 particle. When a neutron is expelled from the Selenium-80 nucleus, it always carries away intrinsic angular momentum equal to ħ/2. The value of S n will therefore be 1/2 in all cases. Whether the neutron also carries away orbital angular momentum depends on the energy of the neutron in relation to the allowed energy levels of the 80 Se and 79 Se nuclei. In our interpretation of the data, the value of L n was limited to be either 1 or 0. The total angular momentum J n carried away by the neutron is the vector sum of L n and S n. For L n = 1, two values for J n are possible either 1/2 or 3/2. 16

17 The Selenium-80 nucleus has 34 protons and 46 neutrons. In situations in which the number of nucleons is odd, the parity of the nuclear ground state is determined by the L-value of the unpaired proton or neutron. But for the case of Selenium-80, there are no unpaired nucleons. This allows us to assume that the J = 0 ground state of Selenium-80 has positive parity. There are two possible J = 1 excited states: the E1 giant electric dipole resonance and the M1 magnetic dipole resonance. The parities of electric and magnetic multipole resonances are respectively given by the equations: P! = ( 1)! (8) P! = ( 1)! (9) L = Multipolarity of resonance (1 = dipole, 2 = quadrupole, etc.) The E1 excited state of Selenium-80 therefore has spin and parity of 1 -, with J 80Se = 1 and negative parity. Likewise, the M1 excited state has spin and parity of 1 +. Based on data obtained for the (g, g ) channel of the reaction, we believe that our experiment is primarily probing the E1 Giant Dipole Resonance, with the cross-section of the M1 excitation hidden underneath that of the much stronger E1 excitation. Parity is conserved by the strong nuclear and electromagnetic interactions. Parity-shifts between the intermediate excited state in 80 Se and the resultant state in 79 Se must therefore be compensated for by odd values in the orbital angular momentum of the expelled neutron. This is related to the fact that even values of L n are associated with spherically-symmetric solutions of the Schrödinger Equation, while odd values of L n lack this kind of symmetry. If the neutron 17

18 carries away orbital angular momentum (L n = 1), it will induce a parity-shift between the intermediate state in 80 Se and the final state in the residual 79 Se nucleus. If the neutron carries away only intrinsic spin (L n = 0), no parity-shift occurs. Parity-shifts produce an angular asymmetry in the differential cross section. Neutrons carrying away orbital angular momentum will be emitted with an angular dependence in relation to the polarization axis of the incident gamma-particles. The explanation of our experimental setup will detail how we detect this phenomenon by setting up multiple detectors and comparing the cross sections at three different angles. We now possess all the necessary information to solve Equation 3.2 for J 79Se : J 80Se = 1 - S n = ½ L n = 0 or 1 By the rules of vector addition: J 79Se = 3/2 - or ½ - for L n = 0 J 79Se = 5/2 +, 3/2 +, or 1/2 + for L n = 1 The residual Selenium-79 nuclei produced by this reaction will all be in one of these five states. The differential cross section that we observe for this reaction will be a superposition of the neutrons emitted in the transitions to each of these five residual states. By the laws of energy conservation, residual states with lower excitation energies will therefore correspond with higher-energy neutrons and states with higher excitation energies will correspond with 18

19 lower-energy neutrons. The detected neutron yields are used to determine the (γ,n) cross section as a function of the energy of the emitted neutrons. The emitted neutron energy can then be related to the excitation energy of the residual state by the equation: E! = E! Q E! (10) E x = Excitation energy of residual nucleus Q = Neutron separation energy of reaction (Q-value) E N = Energy of the emitted neutron The 80 Se(γ,n) reaction has a neutron separation energy of MeV. This means that the highest-energy neutrons that can be produced with an incident gamma-energy of MeV will have a kinetic energy of MeV ( MeV MeV, neglecting the kinetic energy transferred to the residual nucleus). The transition from the 1 - intermediate state to the 3/2 - and 1/2 - residual states feature no accompanying parity-shifts. If our asymmetry plots show an asymmetry of zero for a spectrum of energy levels, this is indicative that these excitations correspond with one or both of these two states. However, we must be cautious. The parity of the states in 79 Se are reversed for the case in which J 80Se = 1 +, i.e., a magnetic dipole excitation. If our assumption is wrong, and our gamma beam is indeed exciting the 1 + state of 80Se, then transitions to 3/2 - and 1/2 - will produce asymmetries. The cross sections of emitted neutrons at the three detector angles, coupled with the cross-sectional asymmetries, allow us to constrain the spins and parities of the residual nucleus. The immediate contribution that this research will make to nuclear physics databases 19

20 will be to improve the assignment of spins and parities to high excitation energies of the Selenium-79 nucleus. Figure 3.1: Theoretical representation of constraining spins and parities from cross section To assign spins and parities, we must fit our experimental data to theory. [6] The theoretical equation describing the differential cross section for the (γ,n) reaction induced with a linearly polarized γ-ray beam is: σ θ, φ = ƛ2!! [(B!!!!!!!!! +! B!!!!"!! )R! R!!!P!!(cos θ)! cos 2φ B!!!!!! R! R!!!P!!! ] (11) ƛ = Angular wavelength of incident gamma beam t = {p L b l s} p = Mode of resonance (E =1, M = 0) 20

21 L = Multipolarity of resonance b = Total angular momentum of the system l = Orbital angular momentum of outgoing channel s = Channel spin The R parameters represent the reduced matrix elements for transitions to states with specific quantum numbers in the 79 Se residual nucleus. A high R-value indicates a high cross section for producing the state with the specified quantum numbers in 79 Se. This equation gives us theoretical predictions for the angular dependence of the cross section, as well as the cross section s overall size. When we fit this equation to our experimental findings, the asymmetry data constrains the relative sizes of the nuclear matrix elements, while the cross section determines the absolute magnitudes of those elements. 21

22 IV. Experiment Setup and Measurement Technique We bombard an isotopic enriched 80Se target with a collimated, linearly polarized gamma ray (γ-ray) beam. The polarization of the beam is in the horizontal plane. Measurements were performed at three incident γ-ray beam energies: , , and MeV. Schematic diagrams of the experimental setup are shown in Figures 4.1 (top view) and 4.2 (end view). The γ-ray beam originates about 60 meters upstream of the target in the straight section of the electron storage ring, where light pulses inside the optical cavity of a free electron laser collide with electron bunches circulating in the ring to produce γ-rays by Compton backscattering. This gamma ray source is referred to as the High Intensity Gamma Source (HIGS) [7]. The γ-ray beam passes through a collimator before reaching the target. The diameter of the collimator determines the energy spread in the γ-ray beam that is incident on the target. The collimator is made of lead, with a circular opening of 12.5 mm diameter. The energy spread of the γ-ray beam incident on the target was about 2.5% FWHM. A thin plastic scintillator paddle just after the exit of the collimator is used to monitor the beam flux before striking the target. The absolute detection efficiency of the paddle is calibrated relative to an HpGe detector that could be moved in and out of the γ-ray beam path. The Selenium target consists of 2.99 g of 99.45% isotopic enriched 80 Se metallic powder, encased in a shallow plastic cylinder. The front and back ends of the plastic cylinder are about 1 mm thick each, and the surrounding circular wall is about 5 mm thick. The volume containing the 80Se powder is 20 mm diameter x 5 mm thick, measured to +/-.5 mm. The target is placed in the beam path, with the cylinder coaxial to the beam. Data is collected for the target sample, as well as for an 22

23 empty sample holder. This allows us to subtract out counts that are purely due to the interaction of the γ-beam with the holder. Figure 4.1: Experimental Setup, Top View. This figure is a schematic diagram of the experimental setup, as seen looking from above. The γ-ray beam path enters from the left. Only the neutron detectors located in the horizontal plane are shown. The scattering and azimuthal angles of the detectors are labeled in the drawing. The drawing is not to scale. 23

24 Figure 4.2: Experimental Setup, Front View. This figure shows the experimental setup as seen by an observer facing toward the target and looking along the beam path, facing toward the sample. The scattering and azimuthal angles of the detectors are labeled in this drawing. Three liquid-scintillation detectors are placed around the target. The incident beam axis, directly following the target sample, is defined to be a scattering angle of 0 degrees. Detectors 1 and 3 are placed at scattering angles of 90 degrees relative to the incident beam axis, and Detector 4 is placed at a scattering angle of 135 degrees. Detector 3 is positioned at an azimuthal angle of 270 degrees, locating it directly under the target sample. Detectors 1 and 24

25 4 are positioned in the horizontal plane (same as the beam polarization), on opposite sides of the beam axis. The angles of the detectors were selected to provide information about the angle correlations of the emitted neutrons, relative to the polarization axis of the incident γ-ray beam. The angle correlations can be used to constrain the possible values of angular momentum carried by the neutrons. The hardware pulse-height thresholds on the neutron detectors are set to about 30 kevee. Each detector is cylindrical, with dimensions 2 dia. X 2 thick. The exact placement of the three detectors is summarized in the following Table 5.1: Table 5.1: Placement of the centers of the neutron detectors Detector Distance from Target θ-angle (scattering) φ-angle (azimuthal) Detector cm Detector cm Detector cm The quantity Distance from Target measures the distance from the central axis of the target cylinder to the midpoint of the detector. Detector distances are measured to about +/- 2 mm. The θ and φ define the direction from the center of the target to the center of the detector, with θ denoting the scattering angle measured from the beam axis, and φ denoting the azimuthal angle above the horizontal plane. In this coordinate system, a θ-angle of 0 and a φ-angle of 0 indicates an object in the beam axis, on the opposite side of the target from the beam source. 25

26 When gamma rays from the incident beam interact with the electrons and nuclei in the target material, both neutrons and gammas are emitted. The liquid-scintillation detectors are sensitive to both gamma rays and neutrons. The time structure of the incident beam enables measurement of the time of flight of the neutrons emitted from the sample following a (γ, n) reaction. The γ-ray beam at HIGS is pulsed with a beam bunch width of about 300 ps FWHM and a period of 180 ns between pulses. Our data-taking hardware records the number of detector counts that occur during each.1029 ns time bin between beam pulses and produces a histogram of counts versus time-of-flight channel. The resulting plot we refer to as our Timeof-Flight (TOF) spectrum. Detector counts generally have statistical uncertainties less than about +/- 1%. Gamma rays travel at the speed of light; the gammas produced in the reaction therefore simultaneously arrive at the detectors at a time earlier than the neutrons. This produces a sharp peak on the TOF spectrum that is referred to as the gamma flash. Neutrons, however, have mass. The velocity of an individual neutron is therefore determined by its energy, and our neutrons arrive at the detectors over a broad stretch of time after the initial gamma flash. The γ-ray beam flux is monitored with the thin plastic scintillation paddle detector placed directly in the beam path between the collimator and the target sample. It measures the total number of gammas that are incident on the target. The paddle interacts with only a very small fraction of the gamma rays incident on it. We therefore need to determine its detection efficiency. We do this by placing a series of attenuators in the beam path between the collimator and the paddle, and by placing an HPGe gamma detector at the end of the beam path. We can determine the efficiency of the paddle by adding up the counts recorded by the 26

27 HPGe detector during the paddle calibration run and comparing it to the number of counts recorded by the paddle in the same period of time, subtracting for background. This method of paddle calibration is subject to high numbers of erroneous counts due to Compton scattering, and efforts to decouple genuine HPGe counts from erroneous ones through computer extrapolation introduces large uncertainties into the paddle calibration. We performed two paddle calibration runs, one with a beam centroid energy at MeV and one at an energy of MeV. The individual results that we obtained from these runs following Compton decoupling were more widely divergent than we anticipated, so we elected to average the two together in order to give us the closest possible approximation of the actual paddle efficiency. We therefore report a paddle efficiency of.0009, but with a +/- 35% systematic uncertainty. 27

28 V. Data Analysis When an incoming neutron or gamma ray interacts with the liquid-scintillation detectors, it disturbs the organic molecules in the fluid. Neutrons interact directly with the protons in the atomic nuclei of the molecules, producing a recoiling proton that excites atomic and molecular states. These states relax through fluorescence, generating light. Gamma rays interact primarily with atomic electrons through Compton scattering, thereby ionizing atoms or leaving them in excited states. These also relax by fluorescence, and in both cases the light generated is picked up by a photomultiplier tube (PMT). Whether the excitations are created by recoiling protons from neutron interactions or by recoiling electrons from Compton-scattering of gamma rays, the onset of the light flash from the relaxation process is fast, i.e., the rise time of the light signal is short (less than 5 ns for most liquid scintillators). However, the decay time of the fluorescence depends on how the material was excited. The more massive recoiling protons from neutron scattering tend to excite molecular states with longer life times than electrons from gamma ray interactions. Therefore, the characteristic decay time of the light flash caused by neutron interactions in the detector is longer than that created by gamma ray interactions. This dependence of the fluorescence decay time on the particle creating the light enables us to use signal pulse-shape discrimination (PSD) to distinguish neutron and gamma ray interactions in the detector. Each detector signal that our data-taking software reports therefore has a fast rise time that is followed by a particle-dependent decay-time, as shown in Figure

29 Figure 5.1: Schematic drawing of PMT anode signal for a liquid scintillator, produced by detection of gamma rays (dashed signal) and neutrons (solid signal). The signal amplitude is on the vertical axis, and time is on the horizontal axis. The time-to-digital converter (TDC) records the start time of the PMT signal, relative to the arrival of the gamma ray beam bunch on the target sample. TDC channels are calibrated to a value of nanoseconds/channel. The analog-to-digital converter (ADC) analyzes the shape of the PMT signal and records the integrated charge (i.e. pulse height) and the decay time (PSD) of the signal. These values are recorded in ADC converter channels. We can therefore construct two-dimensional (2D) histograms that bin detector counts into plots of Time of Flight vs. Pulse Height (TOF vs. PH, Figure 5.2), Time of Flight vs. Pulse Shape (TOF vs. PSD, Figure 5.3), and Pulse Height vs. Pulse Shape (Figure 5.4). These histograms are shown for counts accumulated at incident γ-ray beam energy Eγ = kev. 29

30 Figure 5.2: Two-dimensional histogram of TOF (x axis) versus pulse height (y axis). The neutron spectrum is washed out by the gamma flash in this representation. This histogram was acquired for E γ = kev by Detector 1, positioned at (θ = 90, φ = 180 ) 30

31 Figure 5.3: Two-dimensional histogram of pulse decay time (x axis) versus neutron TOF (y axis). This histogram was acquired for E γ = kev by Detector 1, positioned at (θ = 90, φ = 180 ) 31

32 Figure 5.4: 2-dimensional histogram of pulse shape (x-axis) vs. pulse Height (y-axis) for incident beam energy E γ = kev. This data was collected from Detector 1, positioned at θ = 90 and φ =

33 Our detectors register a very large number of counts from the initial gamma flash, as well as from other sources of noise. If we collapse our raw data into a 1-dimensional histogram of counts vs. TOF, our graph will contain so many gamma counts that our neutron spectrum will be washed out. We therefore wish to impose pulse shape discrimination (PSD) to differentiate between neutrons and gammas. We first construct a histogram of pulse shape vs. pulse height, as shown in Figure 5.4. This figure records the decay time of a particular count in time channels on the horizontal axis and the height of that count in ADC channels on the vertical axis. When the data is presented in this way, we see a clear separation between the detected gamma rays on the left and the neutrons on the right. Gamma particles appear to generate a symmetrical distribution of decay times, centered around channel 700. Neutrons generate signals with longer decay times the vast majority having decay times longer than 1170 time-channels. Lower pulse-heights appear to be correlated with longer decay-times. We impose a PSD cut at channel 1050 on our data, filtering out counts that have a PSD value lower than This value is intended to be conservative, so that there is no risk of losing neutrons at the low end of the PSD spectrum. As demonstrated in Figures 5.5 and 5.6, the result is a massive reduction in the number of counts in the gamma-peak, revealing the spectrum of counts that are produced by neutrons later in the time spectrum. 33

34 Figure 5.5: Time-of-Flight histograms for incident beam energy E γ = kev. The raw TOF spectrum (green) is overlaid with the TOF spectrum with a Channel 1050 PSD cut (blue). This data was collected with the detector positioned at θ = 90 and φ =

35 Figure 5.6: Two-dimensional histogram of neutron TOF (x axis) versus pulse height (y axis) w/ PSD cut at Channel The neutron spectrum is now clearly visible. This histogram was acquired for E γ = kev by Detector 1, positioned at (θ = 90, φ = 180 ) 35

36 Even with a PSD cut in place, we still face the issue that low-energy gamma particles, as well as other sources of noise, can still bleed into our Time of Flight spectrum. Of particular annoyance are slow gammas, which can be produced by delayed re-emission in the target sample or reflection and scattering off extemporaneous surfaces. Slow gammas cause the tail end of the gamma particle distribution to blend together with the high-energy neutrons at the leading edge of the neutron TOF spectrum. A pulse height (PH) cut enables us to ensure a near-complete separation between gamma particles and neutrons. This is a high-pass filter that disregards signals whose pulse heights correspond to energies less than 59 kev electron-equivalent (KeVee). We determine which PH channel is equivalent to 59 kev by calibrating with an americium target substance, known to generate a 59 kevee peak in the neutron counts vs. PH channel histogram. With both the PSD and PH cuts in place, we achieve a clear separation between gamma rays and neutrons in the TOF spectrum. This is shown in Figures 5.7 and

37 Figure 5.7: 1-dimensional Time-of-Flight histograms for incident beam energy E γ = kev, with channel 1050 PSD Cut (See fig. 5.5). The PSD-gated spectrum (blue) is overlaid with the PSD and 59 kevee PH-gated spectrum (black). This data was collected with the detector positioned at θ = 90 and φ =

38 Figure 5.8: Two-dimensional histogram of pulse decay time (x axis) versus neutron TOF (y axis) w/ 59 kevee PH cut. This histogram was acquired for E γ = kev by Detector 1, positioned at (θ = 90, φ = 180 ) 38

39 Our Selenium-80 target sample resides in a plastic holder. This holder produces its own associated spectra of neutrons and gamma particles. We therefore perform two separate runs at each energy, taking identical data both for the Selenium-80 target and for an empty plastic holder. The empty run must be scaled by the ratio of both runs respective paddle counts to ensure that they represent equal numbers of incident gamma rays. We subtract the counts for the two runs, resulting in the elimination of any erroneous features associated with carbon atoms in the plastic holder. The 1-dimensional neutron Time of Flight histogram for the kev incident beam energy is shown in Figure 5.9, with an overlay of the sample-in and sampleempty data collection runs. This data has been gated with both PSD and PH cuts. 39

40 Figure 5.9: 1 dimensional histogram of Time-of-Flight Channel vs. Detector Counts for sample-in (black) and sample-empty (red) runs at incident beam energy E γ = kev. A 59 kevee PH cut and a 1050 time channel PSD cut have been imposed (see Figure 5.3). These data were collected with the detector positioned at θ = 90 and φ = 180. The sample-in histogram was acquired in 67 minutes of data collection, and the sample-empty was acquired in 26 minutes. 40

41 The sharp peak around channel 1250 is the remnant of the gamma flash that has survived both the PSD and PH cuts. The second, shorter peak around channel 1300 is attributed to the plastic sample holder, and it disappears when the background run is subtracted. The neutron Time of Flight spectrum is the wider peak beginning around 1350 and trailing off by This spectrum appears to have two distinct distributions one sharp peak centered around 1400, and a wider one that reaches its apex at From an initial analysis of the TOF data, the sharper peak around 1400 appears to be more pronounced in Detector 1 than it is in Detectors 3 and 4. This provides compelling initial evidence that there is an anisotropy present in the higher-energy neutrons, possibly generated by neutrons carrying away odd-numbered orbital angular momentum. The subtracted TOF histograms for detectors 1, 3, and 4 for Eγ = kev are shown in Figures 5.10, 5.11, and 5.12, respectively. 41

42 Figure 5.10: Time-of-Flight Channel vs. Detector Counts for Detector 1 at incident beam energy E γ = kev. A 59 kevee PH cut and a 1050 time channel PSD cut have been imposed, and the empty run has been subtracted from the target run. These data were collected with the detector positioned at θ = 90 and φ =

43 Figure 5.11: Time-of-Flight Channel vs. Detector Counts for Detector 3 at incident beam energy E γ = kev. A 59 kevee PH cut and a 1050 time channel PSD cut have been imposed, and the empty run has been subtracted from the target run. These data were collected with the detector positioned at θ = 90 and φ =

44 Figure 5.12: Time-of-Flight Channel vs. Detector Counts for Detector 4 at incident beam energy E γ = kev. A 59 kevee PH cut and a 1050 time channel PSD cut have been imposed, and the empty run has been subtracted from the target run. These data were collected with the detector positioned at θ = 135 and φ = 0. 44

45 The time at which the gammas arrive at the detectors can be computed from the speed of light. The Time-of-Flight spectrum therefore tells us how much time has elapsed between when the reaction occurred in the target and the arrival of the emitted neutron at the detector. If we make the assumption that the neutron velocities are non-relativistic, we can use nonrelativistic kinematic equations to calculate the energies of the neutrons from their times of flight: E =!! m!(!!! )! (12) m n = mass of the neutron d = distance to the detector (cm) t = true time of flight (ns) Our value for true time of flight must be derived from the channel numbers recorded by the time-to-digital converter. The equation governing this relationship is: TOF! =!!!!!! + TOF! (13) TOF n = TOF channel of an incoming neutron TOF γ = TOF channel of gamma flash τ = Time-calibration constant for the TOF spectra (ns/channel) The gamma flash is the specific channel which we define as the arrival time of the gamma rays at the detector. The energy calculation is highly dependent on this value, so one of our principal challenges in the analysis of our data was to accurately determine which channel to define as the gamma channel. 45

46 For each detector and energy level, we define the gamma channel to be the leading edge of the gamma ray peak in the non-gated TOF spectrum. This is based on the reasoning that the earliest gammas arriving at the detectors represent the initial reaction, with later gammas being produced through delayed re-emission or Compton scattering. The specific channel that we define as the leading edge must be determined empirically, so we utilized two different methods to ensure that our choice of gamma channel produced neutron energy calculations that were consistent with theoretical predictions. The neutron separation energy, also known as the Q-value of the 80 Se(g,n) reaction, puts an upper limit on the energy of the neutrons that can be produced in the course of the reaction. This limit is clearly visible in in both the 1D and 2D neutron TOF distributions as a lower bound on the shortest times of flight. We used theoretical predictions of the Q-value, generated by computer kinematics simulation, to verify that our choice of gamma channel leads us to observe the correct neutron separation energy in the data. As an additional test, we verified that our relative gamma channels were consistent with the relative distances of the detectors. As expected, the gamma channel does not vary with incident beam energy. Another highly-sensitive value is τ, the time-calibration constant that converts TDC channels to real time units, e.g. ns. This represents the conversion factor between the TOF channel and real time. This value was determined by dividing the total length of the TDC spectrum by the number of individual TDC channels, yielding a τ-value of.1029 ns/channel. 46

47 Once we determine the constants, equations (12) and (13) are used to convert the timeof-flight spectrum to an energy histogram i.e. a plot of detector counts as a function of computed neutron energy. We group the counts into 200 kev size bins of energy. The transformation from TOF channel to energy bins is non-linear. Neutrons with short times of flight have very high energy, and high-energy bins correspond to very small ranges in TOF channel. Neutrons with longer times of flight have low energy, and low-energy bins will encompass large ranges in TOF. When we report cross sections, the result of this is that high energy features in the TOF spectrum become spread out in the cross section, while low-energy features are compressed. The peak observed around channel 1400 in the TOF graph in particular becomes washed out when we convert from TOF to cross section. As our hardware takes data, it bins detector counts into time channels corresponding to discrete times of flight. However, our actual detector event could have taken place at any time during this window. If we model all of our detector counts as taking place at the beginning of the channel, our resulting energy histogram will have gaps. We solve this problem by adding a random number to the time of flight value for every detector count. This number is drawn from a uniform distribution between zero and τ, and it effectively simulates the random distribution of particles that arrive at the detector over the duration of a particular TDC channel. 47

48 The differential cross section is a linear transformation of the neutron energy histogram. The formula used to compute the differential cross section from the measured neutron energy spectrum is:!"(!,,!)!"!" =!!!,,! /!! (!)!!"#!!"#!!!"!" (13) In this equation the parameters are: N D (θ,φ,e) = Number of detector counts for a particular neutron energy E, observed by a detector at angle (θ, φ) ε D (E) = Neutron detector efficiency for neutrons with energy E N pad = Number of gammas detected by paddle ε Pad = Paddle efficiency N T = Number density of Selinium-80 atoms per nb of cross-sectional area dω = Solid angle of detector de = Width of energy bin We compute N T, the areal number density of Selenium-80, using the mass density (ρ Se ), the molar mass (M Se ), thickness of the target (l Target ), and Avogadro s number (n a ): N! = ρ!"n! l!"#$%& M!" (14) The de and dω symbols represent the width of the neutron energy bin and the solid angle over which we measured the cross section. For the purposes of our calculation, dω is the solid angle in steradians that is subtended by a detector, calculated from the radius of the detector (r D ) and the distance of the detector (d): 48

49 dω = πr!! d! (15) The units of the differential cross section work out to be nb/sr/kev. The function ε D (E) is the detector efficiency curve for a 59 kevee hardware threshold. This function was obtained through Monte Carlo simulations and is assumed to be highly accurate for the purposes of error propagation in this experiment. Figure 5.10: Calculated neutron detector efficiency curve for the 2 dia. X 2 thick liquid scintillators used in the reported measurements. The calculations are made for a 59 kevee PH Threshold. The calculations are made using the PTB computer code. [8] 49

50 The limits over which we chose to report the data are dictated by the efficiency of our detectors and the Q-value for the 80 Se(γ,n) reaction. While we analyzed data for neutron enegies as low as 254 kev, we decided that cross section could be reliably determined at neutron energies greater than around 1000 kev, i.e., just beyond the rapid rise in the detection efficiency near the threshold energy. The Q-value for this particular reaction is MeV. For a MeV incident beam, this places the upper limit on the energy of the emitted neutrons at 5,775 kev. For a MeV beam, the maximum energy of the emitted neutrons is around 6,175 kev. By Equation 10, both of these neutron energies correspond to a final excitation energy of 0 kev in the residual nucleus. The constants that we used in the course of our calculations are summarized in the following tables. Constants can be energy dependent, detector dependent, or invariable across all detectors and energies. The cross sections for the three incident γ-ray beam energies for the three angles measured are shown in Figures 6.1, 6.4, and