Polarization Correlation in the Gamma- Gamma Decay of Positronium
|
|
- Nancy Henderson
- 6 years ago
- Views:
Transcription
1 Polarization Correlation in the Gamma- Gamma Decay of Positronium Bin LI Department of Physics & Astronomy, University of Pittsburgh, PA 56, U.S.A April 5, Introduction Positronium is an unstable bound state of a positron and an electron. It is very like hydrogen atom, except that a positron replaces the proton. The ground state of positronium can be either a singlet S or triplet state 3 S, where the angular momentum number L=, and these two states are corresponding to spin zero and spin one respectively. Due to the conservation principles of linear momentum, angular momentum, parity and charge conjugation, we know the singlet decays through annihilation into a pair of gamma particles, and the triplet decays into three gamma particles. Theoretical calculation shows that the decay rate of singlet is three orders of magnitude fasters than that of triplet state. So most of the decaying gamma rays come from singlet state annihilation and they will exist as two back-back gamma particles with same magnitude but vice-visa momentums. Now, we begin to discuss about the polarizations of the two gamma particles. In order to satisfy the conservation laws mentioned previously, both of the two back-back gamma particles must be RHC (right hand circulated) or LHC (left hand circulated). Meanwhile, we know the parity of singlet state of positronium is (-) L+ =(-) + =-, so the two-photon state should also be negative parity, we can write it as following: ψ = R R > L L >, where R R > is the uncoupled states of R > and R > ; same with L L >. We are supposed to set up a counter that only accepts the lights with x-polarization on one side of our source X >, and another counter that only accepts the lights with y-polarization on the other side Y >. So we can calculation the amplitude that ψ will be in the state of X Y > since we know the RHC gamma is X > + i Y > X > + i Y > R > = or R > =, and the LHC gamma is L >= X > i Y > or = L > X > i Y >.
2 So from < X Y ψ > = < > < > i i X Y RR X Y L L = ( ) =i, we get the possibility to obtain one photon with x-polarization on one side and another photon with y-polarization on the other side is unit ( i =). Similarly, we can also get the possibility to obtain both of these two photons with x-polarizations ( or both with y-polarizations) is < X X ψ > =. Since the directions of x-axis and y-axis are arbitrary, the only constraint is that they are perpendicular, so more generally, we get that the polarizations of the two detectable correlated back-back gamma particles should be orthogonal. Method In our experiment, we use Na as irradiation source. As Na decays into Ne, a positron will be emitted. And this positron forms positronium when it becomes bound to an electron. Most of positroniums are in singlet state, and they will decay into two backback gamma rays. Now we use Compton Scattering to measure the relative polarizations of the two photons since the signal rate is proportional to the scattering cross section, which is strongly dependent on the polarizations of incident gamma particle and outgoing gamma particle. From reference, we have the formula of deferential cross section for Compton Scattering: d e = ( dω mc k' ) ( ) k ε ε, If we consider =, k and ε are the momentum and polarization of the incident h gamma ray, k' and ε are the momentum and polarization of the scattering gamma ray. From the point of classical electrodynamics, we can estimate the differential scattering cross section as the following: (omit) k n In this diagram, and are the propagation directions of the incident wave and scattering wave respectively, so these two vectors build up a plane called scattering plane. ε and ε are two special choices for the possible polarization of the two outgoing ε k wave after the scattering, where is in the plane containing and (scattering plane), ε is perpendicular to it. Since both cases ε and ε are perpendicular to, in term of unit vectors parallel to the coordinate axes, we have: ε = cosθ ( e cosφ + e sinφ) e x y z sinθ n n
3 ε = e x sinφ + e y cosφ If we assume that the out-going wave is unpolarized (this might be a reasonable assumption for circular polarized wave), we will get: () For an incident linearly polarized wave with polarization parallel to x-axis, the angular distribution summed over final polarizations is: cos θ cos φ + sin φ. () For the incident wave with polarization on the y-direction, the over all angular distribution for final polarization is: cos θ sin φ + cos φ In order to see the apparent difference due to the variation of the polarizations of the gamma particles, we choose θ = 9. That is to say, the propagation direction of incident momentum and that of the scattering momentum are perpendicular. So we will put our detector for the out-going gamma particle at some place perpendicular to the incident direction with some azimuthal orientation. The following figure shows how our detecting system works. We use the combination of two detectors. () Parallel Configuration ()Diagonal Configuration
4 Everything is the same with the previous configure for parallel case except that the relative orientations of the two detectors are not parallel but perpendicular and they are still kept orthogonal to the incident directions respectively. Now we know, for both of these two cases, θ = 9. Using Compton Scattering formula: = ( cosθ ) and the energy conservation for Positronium k k mec annihilated to two back-back gamma particles with same magnitude momentum: k kc = mec, we can easily get d e =. So we have = ( ) sinφ for the incident k dω mc d e wave with x-polarization; while = ( ) cosφ for the incident wave with y- dω mc polarization. If assuming that spherical angle of the surface area of detector due to the scattering center is small, we can calculate d at an approximate constant θ 9. So dω π e we obtain the scattering cross section at that orientation is = d φ( ) sinφ, or mc π φ( e = d ) cos mc φ. So the signal rate (due to cross section) is totally depended on the polarizations of the incident gamma rays. (Since here these two correlated gamma particles are circular polarized, we can only change the conformation of our detectors to see this effect.) Now we are going to estimate the expected counting rates of the two different detectors configurations. From the discussion in Introduction, we know the polarizations of the two correlated back-back gamma particles should be perpendicular with each other. So for the case parallel configuration: If the polarization of one incident gamma particle is along the x-direction, the polarization of the other one must be the y-direction (or just exchange their polarizations). For the other case orthogonal detecting configuration: If the polarization of one incident gamma particle is along x-direction, in order to satisfy the condition that the polarizations of these two particles are perpendicular, the polarization of the other one must be also the its x-direction, or both of them are on their own y-directions. So for the first case parallel configuration, we have: π e () = α * dϕ[sin ϕ * cos ϕ*], where α = ( mc For the second case perpendicular configuration, we have: π ϕ () = α * dϕ[sin ϕ *sin ] ), it s a constant.
5 After calculation, we get = 3, so the ratio of the expected coincident counting rate of the second configuration to the first configuration is about 3. But this is only true for the ideal case: A). Solid angles from the detector surface to the scattering centers on both sides of the source are small and exactly same so θ 9 for all the detected outgoing scattering gamma rays. This requires the surface of our detector is small, and is pretty far from the scattering center, but it couldn t be too far away since that will reduce the counting rate greatly! B). The solid angles for the two configurations are same. It requires that when we change the detecting configuration from one to the other, we should keep the distances from the scattering center to the detectors are identical with the previous case. C). The Compton Scattering here is single scattering (just scatters from free electron once). This is pretty true if the thickness of our scattering material (here is aluminum) is not two big. D). The detecting system and the electronic instruments can work consistently. For point D), it is very hard to say for our experiment set-up. For point C), it is approximately true. And we try our best to satisfy the requirement B), but we still need to consider the correction for A). This is due to that the count rate is partially contributed by the signals scattering at an angle not equal to 9, it will make the experimental result of less than 3. The precise calculation requires us to measure the surface of the PMT detector and the distance away from scattering center, then do integral for both θ and φ. From previous experiment record, we can estimate. Experiment Set-Up and Procedures The following are all the instruments involved in our experiment. G: Sample Holder with irradiation source inside. Na P, P : Photo Multiplier Tubes as detectors for outgoing gamma particles.
6 H, H: High voltage for the Photo multipliers P and P respectively. S, S: Aluminum Pieces as Compton Scattering center for gamma rays. A: Model 776, Sixteen Channel Amplifier. Q: Model 74, QUAD Linear. D: Model 7, Six Channel Discriminator. C: Model 465, Coincidence Unit. C`: Digital Counter. O: Oscilloscope. H HHH S S H P G P A Q D C C O ch ch In this experiment, our goal is to measure the coincidence counting rates when the two photo multipliers P, P are in parallel configuration and in perpendicular configuration. So we have to figure out the best working conditions of our system and meanwhile find out a method to estimate and get the background for our measurements. Here, I want to give a summary of our set up. The high voltage is about 9 Volts, which is the suggested value from the manual. P, P can change the scattering light
7 signal into electronic signal, and then send it to amplifier. The amplifications for the signals coming out from both tubes are same approximate. The Instrument Q was used to adjust the offset of the signals, we made it very closed to zero. Discriminator can transform the incoming signals into the square wave fronts with width at some magnitude if the amplitudes of the incoming signals are beyond the threshold value. A good threshold value can differentiate the signals from the huge amount of noises. Our threshold voltages for both of the two channels are about 5 mv. We can also adjust the width of the Discriminator and use oscilloscope to watch the change of shape of the square wave front and measure it. Here, our widths are. us and.5 us for the two different channels. Coincidence Module has several different options, it can read the signals from channel one, signals from channel two and coincidence signals of channel A and channel B. The counter here is used to count the number of invents in some finite time scale. After successful setting-up and adjustment, we can begin to do measurement. Experimental Data As we know, backgrounds are very important in this experiment since our signal rate is very low. And the background rates come from cosmology irradiation, the rate of randomly overlapping coincidences, the fluctuation and inconsistence of our electronic instruments, etc. First, we try to check the consistence of our instruments for measurement. So, we removed the source Na away from our detectors and measured bare-counting-rates. We got the following results: Channel : 564/5mins 48/min Channel : 46/5mins 844/min Coincidence: 7/5mins 4/min So, we can see even there is no source at all, the coincidence rate is still very high, beyond /min. Knowing this information, then we can measure the backgrounds (keeping the irradiation source but removing the aluminum scattering targets) and the coincidence rates for the two configurations parallel and diagonal. In order to reduce the accidental deviations and measure our data as precisely as possible, we extended our measurement time to one day (4 Hrs). But before doing that, we can measure the single channel rates for both two cases in short time scale since the high rate of single channel will reduce the accidental fluctuation greatly. Parallel Configuration:
8 Channel : 53636/5mins Channel : 39/5mins 377/min 645/min Background: 64/8.5Hrs Coincidence: 4388/4.43Hrs 3.46/min 8.3/min Diagonal Configuration: Channel : 83755/6mins Channel : 455/6mins 366/min 379/min Background: 3477/.75Hrs Coincidence: 4766/4.83Hrs 6.6/min 3./min The width values that we set in the two channels of our discriminator are: Channel : T =. us Channel : T =.3 us We can use it to evaluate the background rates due to the randomly overlapping coincidence by referring to the formula R= ν ν T + ). ( T Configuration Expectation Background Due to randomly overlapping Experimental Background Rates Coincidence Rates Refined Coincidence Rates (Real correlated signal) Parallel 4.3/min 3.46/min 8.3/min 4.77/min Diagonal 7.83/min 6.6/min 3./min 5.4/min Discussion and Conclusion
9 From the Data table, we see either for the parallel configuration or the diagonal configuration, the experimental background rates are very close to the calculated background rates due to random overlapping signals. So we know the main part of background of gamma-gamma coincident signals is the random overlapping signals. But unfortunately, our experimental value of is far from expected value, (here it is only.3), this is because here the background rate is very high, it almost accounts for 7% of the total signals, so how could we estimate it will give us reasonable results at this condition. We have two possible ways to improve our experimental result: () Use a much stronger decaying source, which will give us higher coincidence rate. () Improve the electronic detecting circuit, and make the ratio of signal to noise increasing.
Positron-Electron Annihilation
Positron-Electron Annihilation Carl Akerlof September 13, 008 1. Introduction This experiment attempts to explore several features of positron-electron annihilation. One of the attractive aspects of e
More informationThe Compton Effect. Martha Buckley MIT Department of Physics, Cambridge, MA (Dated: November 26, 2002)
The Compton Effect Martha Buckley MIT Department of Physics, Cambridge, MA 02139 marthab@mit.edu (Dated: November 26, 2002) We measured the angular dependence of the energies of 661.6 kev photons scattered
More informationApplied Nuclear Physics (Fall 2006) Lecture 19 (11/22/06) Gamma Interactions: Compton Scattering
.101 Applied Nuclear Physics (Fall 006) Lecture 19 (11//06) Gamma Interactions: Compton Scattering References: R. D. Evans, Atomic Nucleus (McGraw-Hill New York, 1955), Chaps 3 5.. W. E. Meyerhof, Elements
More informationORTEC AN34 Experiment 10 Compton Scattering
EQUIPMENT NEEDED FROM ORTEC 113 Preamplifier (2 ea.) TRUMP-PCI-2K MCA System including suitable PC operating Windows 98/2000/XP (other ORTEC MCAs may be used) 266 Photomultiplier Tube Base (2 ea.) 4001A/4002D
More informationhν' Φ e - Gamma spectroscopy - Prelab questions 1. What characteristics distinguish x-rays from gamma rays? Is either more intrinsically dangerous?
Gamma spectroscopy - Prelab questions 1. What characteristics distinguish x-rays from gamma rays? Is either more intrinsically dangerous? 2. Briefly discuss dead time in a detector. What factors are important
More informationTHE COMPTON EFFECT Last Revised: January 5, 2007
B2-1 THE COMPTON EFFECT Last Revised: January 5, 2007 QUESTION TO BE INVESTIGATED: How does the energy of a scattered photon change after an interaction with an electron? INTRODUCTION: When a photon is
More informationPhys 622 Problems Chapter 6
1 Problem 1 Elastic scattering Phys 622 Problems Chapter 6 A heavy scatterer interacts with a fast electron with a potential V (r) = V e r/r. (a) Find the differential cross section dσ dω = f(θ) 2 in the
More informationMeasurements of liquid xenon s response to low-energy particle interactions
Measurements of liquid xenon s response to low-energy particle interactions Payam Pakarha Supervised by: Prof. L. Baudis May 5, 2013 1 / 37 Outline introduction Direct Dark Matter searches XENON experiment
More informationEEE4106Z Radiation Interactions & Detection
EEE4106Z Radiation Interactions & Detection 2. Radiation Detection Dr. Steve Peterson 5.14 RW James Department of Physics University of Cape Town steve.peterson@uct.ac.za May 06, 2015 EEE4106Z :: Radiation
More informationCopyright 2008, University of Chicago, Department of Physics. Experiment VI. Gamma Ray Spectroscopy
Experiment VI Gamma Ray Spectroscopy 1. GAMMA RAY INTERACTIONS WITH MATTER In order for gammas to be detected, they must lose energy in the detector. Since gammas are electromagnetic radiation, we must
More informationLAB 4: Gamma-ray coincidence spectrometry (2018)
LAB 4: Gamma-ray coincidence spectrometry (2018) As you have seen, in several of the radioactive sources we encountered so far, they typically emit more than one gamma photon per decay or even more than
More informationPHYS 3650L - Modern Physics Laboratory
PHYS 3650L - Modern Physics Laboratory Laboratory Advanced Sheet Photon Attenuation 1. Objectives. The objectives of this laboratory exercise are: a. To measure the mass attenuation coefficient at a gamma
More informationChapter 12: Phenomena
Chapter 12: Phenomena K Fe Phenomena: Different wavelengths of electromagnetic radiation were directed onto two different metal sample (see picture). Scientists then recorded if any particles were ejected
More informationStudy of the Scintillation Detector Efficiency and Muon Flux
Study of the Scintillation Detector Efficiency and Muon Flux Ali Al-dulaimi 1, Areeg Al-hamadany 1, Mohammed Al-Gherairy 1, Rafid Al-Zuhairi 1 and Amar Al-timimi 1 Department of Physics, College of Science/University
More informationAnti Compton effect (1). A.M.shehada. Division of physics, Sciences college, Damascus university, Syria
Anti Compton effect (1). A.M.shehada. E-mail : abdullahsh137@yahoo.com Division of physics, Sciences college, Damascus university, Syria Introduction : In the usual Compton effect, coming photon ( have
More informationAbsolute activity measurement
Absolute activity measurement Gábor Veres, Sándor Lökös Eötvös University, Department of Atomic Physics January 12, 2016 Financed from the financial support ELTE won from the Higher Education Restructuring
More informationCopyright 2008, University of Chicago, Department of Physics. Gamma Cross-sections. NaI crystal (~2" dia) mounted on photo-multiplier tube
Gamma Cross-sections 1. Goal We wish to measure absorption cross-sections for γ-rays for a range of gamma energies and absorber atomic number. 2. Equipment Pulse height analyzer Oscilloscope NaI crystal
More informationInelastic scattering
Inelastic scattering When the scattering is not elastic (new particles are produced) the energy and direction of the scattered electron are independent variables, unlike the elastic scattering situation.
More informationDetection and measurement of gamma-radiation by gammaspectroscopy
Detection and measurement of gamma-radiation by gammaspectroscopy Gamma-radiation is electromagnetic radiation having speed equal to the light in vacuum. As reaching a matter it interact with the different
More informationExperiment 6 1. The Compton Effect Physics 2150 Experiment No. 6 University of Colorado
Experiment 6 1 Introduction The Compton Effect Physics 2150 Experiment No. 6 University of Colorado In some situations, electromagnetic waves can act like particles, carrying energy and momentum, which
More informationElectromagnetic Radiation. Chapter 12: Phenomena. Chapter 12: Quantum Mechanics and Atomic Theory. Quantum Theory. Electromagnetic Radiation
Chapter 12: Phenomena Phenomena: Different wavelengths of electromagnetic radiation were directed onto two different metal sample (see picture). Scientists then recorded if any particles were ejected and
More information17. Jones Matrices & Mueller Matrices
7. Jones Matrices & Mueller Matrices Jones Matrices Rotation of coordinates - the rotation matrix Stokes Parameters and unpolarized light Mueller Matrices R. Clark Jones (96-24) Sir George G. Stokes (89-93)
More informationFlux Studies: Muons & Gamma Rays. By: Akkshay Khoslaa & Duncan Wilmot
Flux Studies: Muons & Gamma Rays By: Akkshay Khoslaa & Duncan Wilmot Calibration Graphs 50 45 40 35 30 25 20 15 10 5 0 0.5 0.6 0.7 0.8 0.9 25 20 15 10 5 0 0.55 0.65 0.75 0.85 0.95 1.05 A & B Coincident
More informationIonization Energy Loss of Charged Projectiles in Matter. Steve Ahlen Boston University
Ionization Energy Loss of Charged Projectiles in Matter Steve Ahlen Boston University Almost all particle detection and measurement techniques in high energy physics are based on the energy deposited by
More informationNotes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015)
Notes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015) Interaction of x-ray with matter: - Photoelectric absorption - Elastic (coherent) scattering (Thomson Scattering) - Inelastic (incoherent) scattering
More informationSpace-Time Symmetries
Space-Time Symmetries Outline Translation and rotation Parity Charge Conjugation Positronium T violation J. Brau Physics 661, Space-Time Symmetries 1 Conservation Rules Interaction Conserved quantity strong
More informationAngular Distribution of Neutrons from. by Frank Genevese Physical Review Vol.76, # 9 (Nov 1, 1949) A paper on experiment Paper Club, 22, Feb, 2011
Angular Distribution of Neutrons from the Photo-Disintegration of Deuteron by Frank Genevese Physical Review Vol.76, # 9 (Nov 1, 1949) A paper on experiment Paper Club, 22, Feb, 2011 The Outline of the
More informationNuclear Physics and Astrophysics
Nuclear Physics and Astrophysics PHY-30 Dr. E. Rizvi Lecture 4 - Detectors Binding Energy Nuclear mass MN less than sum of nucleon masses Shows nucleus is a bound (lower energy) state for this configuration
More informationCherenkov Detector. Cosmic Rays Cherenkov Detector. Lodovico Lappetito. CherenkovDetector_ENG - 28/04/2016 Pag. 1
Cherenkov Detector Cosmic Rays Cherenkov Detector Lodovico Lappetito CherenkovDetector_ENG - 28/04/2016 Pag. 1 Table of Contents Introduction on Cherenkov Effect... 4 Super - Kamiokande... 6 Construction
More informationMEASURING THE LIFETIME OF THE MUON
B6-1 MEASURING THE LIFETIME OF THE MUON Last Revised September 19, 2006 QUESTION TO BE INVESTIGATED What is the lifetime τ of a muon? INTRODUCTION AND THEORY Muons are a member of a group of particles
More informationAnalysis of γ spectrum
IFM The Department of Physics, Chemistry and Biology LAB 26 Analysis of γ spectrum NAME PERSONAL NUMBER DATE APPROVED I. OBJECTIVES - To understand features of gamma spectrum and recall basic knowledge
More informationMITOCW watch?v=wr88_vzfcx4
MITOCW watch?v=wr88_vzfcx4 PROFESSOR: So we're building this story. We had the photoelectric effect. But at this moment, Einstein, in the same year that he was talking about general relativity, he came
More informationCOMPTON SCATTERING OF GAMMA RAYS
COMPTON SCATTERING OF GAMMA RAYS v2.7 Last revised: R. A. Schumacher, January 2017 I. INTRODUCTION Compton scattering is the name given to the scattering of high-energy gamma rays from electrons. The gamma
More information(10%) (c) What other peaks can appear in the pulse-height spectrum if the detector were not small? Give a sketch and explain briefly.
Sample questions for Quiz 3, 22.101 (Fall 2006) Following questions were taken from quizzes given in previous years by S. Yip. They are meant to give you an idea of the kind of questions (what was expected
More informationGamma Spectroscopy. References: Objectives:
Gamma Spectroscopy References: G.F. Knoll, Radiation Detection and Measurement (John Wiley & Sons, New York, 2000) W. R. Leo, Techniques for Nuclear and Particle Physics Experiments: A How-to Approach,
More informationMaxwell s equations. electric field charge density. current density
Maxwell s equations based on S-54 Our next task is to find a quantum field theory description of spin-1 particles, e.g. photons. Classical electrodynamics is governed by Maxwell s equations: electric field
More informationGamma Spectroscopy. Calligaris Luca Massironi Andrea Presotto Luca. Academic Year 2006/2007
Gamma Spectroscopy Calligaris Luca Massironi Andrea Presotto Luca Academic Year 2006/2007 Abstract Here we propose the results of a number of experiments with gamma rays. In the first part we concentrated
More information1.1.1 Bell Inequality - Spin correlation
January 8, 015 Lecture IV 1.1.1 Bell Inequality - Spin correlation Consider the final spin singlet state of the decay η 0 µ + µ We suppose that the η 0 decays and the muon and µ + travel in opposite directions,
More informationRutherford Backscattering Spectrometry
Rutherford Backscattering Spectrometry EMSE-515 Fall 2005 F. Ernst 1 Bohr s Model of an Atom existence of central core established by single collision, large-angle scattering of alpha particles ( 4 He
More information1.2 Spin Dependent Scattering - II
.2. SPIN DEPENDENT SCATTERING - II March 4, 205 Lecture XVI.2 Spin Dependent Scattering - II.2. Spin density matrix If the initial spin state is ν n with probability p i,n, then the probability to scatter
More informationQuality Assurance. Purity control. Polycrystalline Ingots
Quality Assurance Purity control Polycrystalline Ingots 1 Gamma Spectrometry Nuclide Identification Detection of Impurity Traces 1.1 Nuclides Notation: Atomic Mass Atomic Number Element Neutron Atomic
More informationGAMMA RAY SPECTROSCOPY
GAMMA RAY SPECTROSCOPY Gamma Ray Spectroscopy 1 In this experiment you will use a sodium iodide (NaI) detector along with a multichannel analyzer (MCA) to measure gamma ray energies from energy level transitions
More informationDETECTORS. I. Charged Particle Detectors
DETECTORS I. Charged Particle Detectors A. Scintillators B. Gas Detectors 1. Ionization Chambers 2. Proportional Counters 3. Avalanche detectors 4. Geiger-Muller counters 5. Spark detectors C. Solid State
More informationScintillation Detector
Scintillation Detector Introduction The detection of ionizing radiation by the scintillation light produced in certain materials is one of the oldest techniques on record. In Geiger and Marsden s famous
More information129 Lecture Notes More on Dirac Equation
19 Lecture Notes More on Dirac Equation 1 Ultra-relativistic Limit We have solved the Diraction in the Lecture Notes on Relativistic Quantum Mechanics, and saw that the upper lower two components are large
More informationLecture 3 - Compton Scattering
Lecture 3 - Compton Scattering E. Daw March 0, 01 1 Review of Lecture Last time we recalled that in special relativity, as in pre-relativistic dynamics, the total energy in an interaction or collision
More informationWarsaw University of Technology, Faculty of Physics. Laboratory of Nuclear Physics & Technology. Compton effect
Warsaw University of Technology, Faculty of Physics Laboratory of Nuclear Physics & Technology Compton effect Author: MSc. Eng. Dariusz Aksamit, Dariusz.Aksamit@pw.edu.pl, Faculty of Physics on the basis
More informationPHY 192 Compton Effect Spring
PHY 192 Compton Effect Spring 2010 1 The Compton Effect Introduction In this experiment we will study two aspects of the interaction of photons with electrons. The first of these is the Compton effect
More informationPARTICLES AND WAVES CHAPTER 29 CONCEPTUAL QUESTIONS
CHAPTER 29 PARTICLES AND WAVES CONCEPTUAL QUESTIONS 1. REASONING AND SOLUTION A monochromatic light source emits photons of a single frequency. According to Equation 29.2, the energy, E, of a single photon
More informationFigure 1. Decay Scheme for 60Co
Department of Physics The University of Hong Kong PHYS3851 Atomic and Nuclear Physics PHYS3851- Laboratory Manual A. AIMS 1. To learn the coincidence technique to study the gamma decay of 60 Co by using
More informationWorkout Examples No.of nucleons Binding energy
Workout Examples 1. Find (i) mass defect (ii) binding energy (iii) binding energy per nucleon for a helium nucleus. Given the mass of helium nucleus= 4.001509 a.m.u., mass of proton= 1.00777 a.m.u. and
More informationScattering is perhaps the most important experimental technique for exploring the structure of matter.
.2. SCATTERING February 4, 205 Lecture VII.2 Scattering Scattering is perhaps the most important experimental technique for exploring the structure of matter. From Rutherford s measurement that informed
More informationUGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM PHYSICAL SCIENCE TEST SERIES # 4. Atomic, Solid State & Nuclear + Particle
UGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM BOOKLET CODE PH PHYSICAL SCIENCE TEST SERIES # 4 Atomic, Solid State & Nuclear + Particle SUBJECT CODE 05 Timing: 3: H M.M: 200 Instructions 1.
More informationCompton Storage Rings
Compton Polarimetry @ Storage Rings Wolfgang Hillert ELectron Stretcher Accelerator Physics Institute of Bonn University Møller-Polarimeter Compton-Polarimeter Mott-Polarimeter Compton Scattering Differential
More informationBeyond Bohr Model. Wave-particle duality, Probabilistic formulation of quantum physics Chap. 28
Lecture 22-1 Beyond Bohr Model Unfortunately, the classical visualization of the orbiting electron turns out to be wrong even though it still gives us a simple way to think of the atom. Quantum Mechanics
More informationGLOSSARY OF BASIC RADIATION PROTECTION TERMINOLOGY
GLOSSARY OF BASIC RADIATION PROTECTION TERMINOLOGY ABSORBED DOSE: The amount of energy absorbed, as a result of radiation passing through a material, per unit mass of material. Measured in rads (1 rad
More informationPropagation in the Galaxy 2: electrons, positrons, antiprotons
Propagation in the Galaxy 2: electrons, positrons, antiprotons As we mentioned in the previous lecture the results of the propagation in the Galaxy depend on the particle interaction cross section. If
More informationRadiation Signals and Signatures in a Detector (Gamma spectroscopy) Sangkyu Lee
Radiation Signals and Signatures in a Detector (Gamma spectroscopy) Sangkyu Lee Photon interactions Photoelectric effect Compton scatter Pair production μ= τ + σ + κ μ = Total cross section τ = Photoelectric
More informationMulti Channel Analyzer (MCA) Analyzing a Gamma spectrum
Multi Channel Analyzer (MCA) Analyzing a Gamma spectrum Objective: Using the MCA to acquire spectrums for different gamma sources and to identify an unknown source from its spectrum, furthermore to investigate
More informationPHYS 3313 Section 001 Lecture #7
PHYS 3313 Section 001 Lecture #7 Photoelectric Effect Compton Effect Pair production/pair annihilation PHYS 3313-001, Fall 1 Reading assignments: CH3.9 Announcements Homework #2 CH3 end of the chapter
More informationApplication of positrons in materials research
Application of positrons in materials research Trapping of positrons at vacancy defects Using positrons, one can get defect information. R. Krause-Rehberg and H. S. Leipner, Positron annihilation in Semiconductors,
More informationINTRODUCTION TO MEDICAL PHYSICS 1 Quiz #1 Solutions October 6, 2017
INTRODUCTION TO MEDICAL PHYSICS 1 Quiz #1 Solutions October 6, 2017 This is a closed book examination. Adequate information is provided you to solve all problems. Be sure to show all work, as partial credit
More informationThe reaction p(e,e'p)π 0 to calibrate the Forward and the Large Angle Electromagnetic Shower Calorimeters
The reaction p(e,e'p)π 0 to calibrate the Forward and the Large Angle Electromagnetic Shower Calorimeters M.Battaglieri, M.Anghinolfi, P.Corvisiero, A.Longhi, M.Ripani, M.Taiuti Istituto Nazionale di Fisica
More informationPhysics 111 Homework Solutions Week #9 - Friday
Physics 111 Homework Solutions Week #9 - Friday Tuesday, March 1, 2011 Chapter 24 Questions 246 The Compton shift in wavelength for the proton and the electron are given by Δλ p = h ( 1 cosφ) and Δλ e
More informationRadiation Detection for the Beta- Delayed Alpha and Gamma Decay of 20 Na. Ellen Simmons
Radiation Detection for the Beta- Delayed Alpha and Gamma Decay of 20 Na Ellen Simmons 1 Contents Introduction Review of the Types of Radiation Charged Particle Radiation Detection Review of Semiconductor
More informationInteraction theory Photons. Eirik Malinen
Interaction theory Photons Eirik Malinen Introduction Interaction theory Dosimetry Radiation source Ionizing radiation Atoms Ionizing radiation Matter - Photons - Charged particles - Neutrons Ionizing
More informationAdvanced lab course for Bachelor s students
Advanced lab course for Bachelor s students Versuch T2 Gamma spectroscopy and Compton scattering February 2018 Prerequisites Interactions of photons and matter Working principle and usage of scintillation
More informationThe Kinematics and Electron Cross Sections of Compton Scattering
The Kinematics and Electron Cross Sections of Compton Scattering Edwin Ng MIT Department of Physics (Dated: December 7, 0) We scatter 66.6 kev gamma rays off NaI scintillators and use coincidence techniques
More informationLecture 6 Scattering theory Partial Wave Analysis. SS2011: Introduction to Nuclear and Particle Physics, Part 2 2
Lecture 6 Scattering theory Partial Wave Analysis SS2011: Introduction to Nuclear and Particle Physics, Part 2 2 1 The Born approximation for the differential cross section is valid if the interaction
More informationAngular Correlation Experiments
Angular Correlation Experiments John M. LoSecco April 2, 2007 Angular Correlation Experiments J. LoSecco Notre Dame du Lac Nuclear Spin In atoms one can use the Zeeman Effect to determine the spin state.
More informationLecture 3. Experimental Methods & Feynman Diagrams
Lecture 3 Experimental Methods & Feynman Diagrams Natural Units & the Planck Scale Review of Relativistic Kinematics Cross-Sections, Matrix Elements & Phase Space Decay Rates, Lifetimes & Branching Fractions
More informationSCINTILLATION DETECTORS & GAMMA SPECTROSCOPY: AN INTRODUCTION
SCINTILLATION DETECTORS & GAMMA SPECTROSCOPY: AN INTRODUCTION OBJECTIVE The primary objective of this experiment is to use an NaI(Tl) detector, photomultiplier tube and multichannel analyzer software system
More informationDevelopment of a Dedicated Hard X-Ray Polarimeter Mark L. McConnell, James R. Ledoux, John R. Macri, and James M. Ryan
Development of a Dedicated Hard X-Ray Polarimeter Mark L. McConnell, James R. Ledoux, John R. Macri, and James M. Ryan Space Science Center University of New Hampshire Durham, NH AAS-HEAD Mt. Tremblant,
More informationPARTICLES REVELATION THROUGH SCINTILLATION COUNTER
14-25 JUNE 2004 SUMMER STAGE PARTICLES REVELATION THROUGH SCINTILLATION COUNTER by Flavio Cavalli and Marcello De Vitis Liceo Scientifico Statale Farnesina Tutor: Marco Mirazita 1) COSMIC RAYS - The Muons
More information1 The Cathode Rays experiment is associated. with: Millikan A B. Thomson. Townsend. Plank Compton
1 The Cathode Rays experiment is associated with: A B C D E Millikan Thomson Townsend Plank Compton 1 2 The electron charge was measured the first time in: A B C D E Cathode ray experiment Photoelectric
More informationMIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova
MIDTERM 3 REVIEW SESSION Dr. Flera Rizatdinova Summary of Chapter 23 Index of refraction: Angle of reflection equals angle of incidence Plane mirror: image is virtual, upright, and the same size as the
More informationScience of Nuclear Energy and Radiation a Comprehensive Course for Science Teachers June 22-25, 1998 McMaster University
Science of Nuclear Energy and Radiation a Comprehensive Course for Science Teachers June 22-25, 1998 McMaster University Notes to accompany Lab demonstrations by Barry Diacon, Technician, Department of
More informationPHY-494: Applied Relativity Lecture 5 Relativistic Particle Kinematics
PHY-494: Applied Relativity ecture 5 Relativistic Particle Kinematics Richard J. Jacob February, 003. Relativistic Two-body Decay.. π 0 Decay ets return to the decay of an object into two daughter objects.
More informationThursday, April 23, 15. Nuclear Physics
Nuclear Physics Some Properties of Nuclei! All nuclei are composed of protons and neutrons! Exception is ordinary hydrogen with just a proton! The atomic number, Z, equals the number of protons in the
More informationIntroduction to Elementary Particle Physics I
Physics 56400 Introduction to Elementary Particle Physics I Lecture 16 Fall 018 Semester Prof. Matthew Jones Review of Lecture 15 When we introduced a (classical) electromagnetic field, the Dirac equation
More informationTHEORETICAL COMPETITION
VI International Zhautykov Olympiad Theoretical Competition Page /5 THEORETICAL COMPETITION January 3 2 Please read this first: The time available for the theoretical competition is 4 hours There are three
More informationRandom Coincidence between two Independent Pulses
Random Coincidence between two Independent Pulses Sean O Brien June 16, 2006 1 Random Coincidence Rates In nuclear experimentation there are genuine coincident events, those that are detected by two or
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 1 (2/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications
.54 Neutron Interactions and Applications (Spring 004) Chapter 1 (/3/04) Overview -- Interactions, Distributions, Cross Sections, Applications There are many references in the vast literature on nuclear
More informationRadioactivity and Ionizing Radiation
Radioactivity and Ionizing Radiation QuarkNet summer workshop June 24-28, 2013 1 Recent History Most natural phenomena can be explained by a small number of simple rules. You can determine what these rules
More informationModern Physics. Laboratory Experiment. Compton Scattering. Boston University International Program. Technische Universität Dresden
Modern Physics Laboratory xperiment Compton Scattering Boston University International Program Technische Universität Dresden Spring/Summer 009 1 COMPTO SCATTRIG Determination of the nergy γ of Scattered
More informationX-Ray Physics. that N [the atomic number] is the same as the number of the place occupied by the element in the periodic system.
X-Ray Physics Evan Berkowitz Junior, MIT Department of Physics (Dated: October 25, 2006) We measure a variety of phenomena related to X-Ray absorption and production. We present data which conforms within
More informationThe ortho-positronium lifetime puzzle & new Physics
The ortho-positronium lifetime puzzle & new Physics P.Crivelli ETH, Zürich, Switzerland Under the supervision of Prof.Andre Rubbia Introduction The Positronium, the bound state of electron and positron,
More informationLecture 16 Light transmission and optical detectors
Lecture 6 Light transmission and optical detectors Charged particle traversing through a material can generate signal in form of light via electromagnetic interactions with orbital electrons of the atoms
More informationMeasurement of Muon Lifetime
Measurement of Muon Lifetime Noah Scandrette Physics and Astronomy Department, San Francisco State University, San Francisco, California (Dated: December 16, 2016) The average lifetime of the muon has
More informationNuclear Lifetimes. = (Eq. 1) (Eq. 2)
Nuclear Lifetimes Theory The measurement of the lifetimes of excited nuclear states constitutes an important experimental technique in nuclear physics. The lifetime of a nuclear state is related to its
More informationarxiv: v1 [physics.ins-det] 3 Feb 2011
Nuclear Instruments and Methods in Physics Research A 00 (2018) 1 5 Alogo.pdf Nuclear Instruments and Methods in Physics Research A Scintillation decay time and pulse shape discrimination in oxygenated
More informationPositron theoretical prediction
Positron theoretical prediction Schrödinger equation: ˆ 2 p x, t Vx, t x, t i 22 m tt non-relativistic equation of motion for electron Erwin Schrödinger 1933 Nobel prize Positron theoretical prediction
More informationNeutron emission asymmetries from linearly polarized γ rays on nat Cd, nat Sn, and 181 Ta
Neutron emission asymmetries from linearly polarized γ rays on nat Cd, nat Sn, and 8 Ta Clarke Smith, Gerald Feldman, and the HIγS Collaboration George Triangle C. Smith, G. Feldman (GWU) Washington University
More informationThe Building Blocks of Nature
The Building Blocks of Nature PCES 15.1 Schematic picture of constituents of an atom, & rough length scales. The size quoted for the nucleus here (10-14 m) is too large- a single nucleon has size 10-15
More informationMeasurements of photon scattering lengths in scintillator and a test of the linearity of light yield as a function of electron energy
Measurements of photon scattering lengths in scintillator and a test of the linearity of light yield as a function of electron energy Alexandra Huss August 31, 2013 Abstract The SNO+ experiment in Sudbury,
More informationMeasurement of ortho-positronium lifetime and 2γ to 3γ branching ratio of positronium
Measurement of ortho-positronium lifetime and 2γ to 3γ branching ratio of positronium Semester Thesis by Fukuda Yasutaka, Ikeda Tatsuya, Khaw Kim Siang Shimozawa Masaaki, Tanaka Shinichiro Science Faculty,
More informationGamma-ray spectroscopy with the scintillator/photomultiplierand with the high purity Ge detector: Compton scattering, photoeffect, and pair production
Experiment N2: Gamma-ray spectroscopy with the scintillator/photomultiplierand with the high purity Ge detector: Compton scattering, photoeffect, and pair production References: 1. Experiments in Nuclear
More informationChapter 2 Problem Solutions
Chapter Problem Solutions 1. If Planck's constant were smaller than it is, would quantum phenomena be more or less conspicuous than they are now? Planck s constant gives a measure of the energy at which
More informationRelativistic Behavior Detection through Electron Acceleration
Relativistic Behavior Detection through Electron Acceleration Henry Shackleton MIT Department of Physics (Dated: April 28, 2017) Classical and relativistic mechanics differ in their predictions of how
More informationPositron Emission Tomography (PET)
Positron Emission Tomography (PET) A radiological technique for functional imaging Please note that this exercise takes place at the Stockholm Centre for Physics, Astronomy and Biotechniques (Alba Nova).
More information