Basic Concepts in Nuclear Physics
|
|
- Christopher Pearson
- 7 years ago
- Views:
Transcription
1 Basic Concepts in Nuclear Physics Paolo Finelli Corso di Teoria delle Forze Nucleari 2011
2 Literature/Bibliography Some useful texts are available at the Library: Wong, Nuclear Physics Krane, Introductory Nuclear Physics Basdevant, Rich and Spiro, Fundamentals in Nuclear Physics Bertulani, Nuclear Physics in a Nutshell
3 Introduction Purpose of these introductory notes is recollecting few basic notions of Nuclear Physics. For more details, the reader is referred to the literature. Binding energy and Liquid Drop Model Nuclear dimensions Saturation of nuclear forces Fermi gas Shell model Isospin Several arguments will not be covered but, of course, are extremely important: pairing, deformations, single and collective excitations, α decay, β decay, γ decay, fusion process, fission process,...
4 The Nuclear Landscape The scope of nuclear physics is Improve the knowledge of all nuclei Understand the stellar nucleosynthesis Basdevant, Rich and Spiro
5 Stellar Nucleosynthesis The evolution of the nuclear abundances. Each square is a nucleus. The colors indicate the abundance of the nucleus: e 4 e 5 e 6 e 7 Dynamical r-process calculation assuming an expansion with an initial density of 0.029e4 g/cm3, an initial temperature of 1.5 GK and an expansion timescale of 0.83 s. The r-process is responsible for the origin of about half of the elements heavier than iron that are found in nature, including elements such as gold or uranium. Shown is the result of a model calculation for this process that might occur in a supernova explosion. Iron is bombarded with a huge flux of neutrons and a sequence of neutron captures and beta decays is then creating heavy elements. JINA
6 Binding energy Atomic Mass m N c 2 = m A c 2 Zm e c 2 + Electrons Mass (~Z) Z i=1 Electrons Binding Energies (negligible) B i m A c 2 Zm e c 2 Basdevant, Rich and Spiro B =(Zm p + Nm n ) c 2 m N c 2 [Zm p + Nm n (m A Zm e )] c 2 B = Zm( 1 H)+Nm n m( A X) c 2
7 Binding energy E/A (Binding Energy per nucleon) Nuclear Fusion Energy Fe The most bound isotopes Average mass of fission fragments is 118 A (Mass Number) Nuclear Fission Energy 235 U Gianluca Usai
8 Binding energy and Liquid Drop Model Volume term, proportional to R 3 (or A): saturation Surface term, proportional to R 2 (or A 2/3 ) Coulomb term, proportional to Z 2 /A 1/3 Asymmetry term, neutron-rich nuclei are favored Pairing term, nucleon pairs coupled to J Π =0 + are favored Basdevant, Rich and Spiro
9 Binding energy and Liquid Drop Model Comparison with empirical data Contributions to B/A as function of A Gianluca Usai
10 Nuclear Dimensions Excited States (~ev) Ground state Excited States (~ MeV) Ground state Excited States (~ GeV) Ground state Gianluca Usai
11 Nuclear Dimensions: energy scales
12 Nuclear Dimensions Fermi distribution ρ(0) ρ(r) = 1+e (r R)/s Basdevant, Rich and Spiro R : 1/2 density radius s : skin thickness
13 Nuclear forces saturation An old (but still good) definition: E. Fermi, Nuclear Physics
14 Mean potential method: Fermi gas model In this model, nuclei are considered to be composed of two fermion gases, a neutron gas and a proton gas. The particles do not interact, but they are confined in a sphere which has the dimension of the nucleus. The interaction appear implicitly through the assumption that the nucleons are confined in the sphere. If the liquid drop model is based on the saturation of nuclear forces, on the other hand the Fermi model is based on the quantum statistics effects. The Fermi model provides a way to calculate the basic constants in the Bethe-Weizsäcker formula
15 Fermi gas model (I) Hamiltonian Wavefunction factorization Boundary conditions Gasiorowicz, p.58 Separable equations
16 Fermi gas model (II) Solution Normalization
17 Fermi gas model (III) Density of states Number of particles Density of particles spin-isospin Fermi momentum
18 Fermi gas model (IV) ρ 0 =0.17 fm 3 k F =1.36 fm 1 T = 23 MeV The fermi level is the last level occupied F = 2 k 2 F 2M = MeV
19 Basdevant, Rich and Spiro Evidences of Shell Structure in Nuclei
20 Mean potential method: Shell model The shell model, in its most simple version, is composed of a mean field potential (maybe a harmonic oscillator) plus a spin-orbit potential in order to reproduce the empirical evidences of shell structure in nuclei E n =(n +3/2)ω H = V ls (r)l s/ 2 l s = 2 j(j+1) l(l+1) s(s+1) 2 = l/2 j = l +1/2 = (l + 1)/2 j = l 1/2 Basdevant, Rich and Spiro
21 Shell model (I)
22 Degeneracy Shell model (II)
23 Shell model (III)
24 Shell model (IV)
25 Shell model (V)
26 Shell model (V)
27 Isospin In 1932, Heisenberg suggested that the proton and the neutron could be seen as two charge states of a single particle MeV MeV EM 0 EM = 0 n p N Protons and neutrons have almost identical mass Low energy np scattering and pp scattering below E = 5 MeV, after correcting for Coulomb effects, is equal within a few percent Energy spectra of mirror nuclei, (N,Z) and (Z,N), are almost identical
28 Isospin (II) Isospin is an internal variable that determines the nucleon state ψp (r, σ, 1 ψ N (r, σ, τ) = 2 ) proton ψ n (r, σ, 1 2 ) neutron One could introduce a (2d) vector space that is mathematical copy of the usual spin space η 1 2, 1 2 = π = 1 0 proton state η 1 2, 1 2 = ν = 0 1 neutron state
29 Isospin eigenstates of the third component of isospin In general The isospin generators τ 3 π = π τ 3 ν = π a ψ N = a π + b ν = b [t i,t j ]=i ijk t k Pauli matrices τ 1, τ 2, τ 3 Fundamental representations t i = 1 2 τ i Projectors Raising and lowering operators P p = 1+τ 3 P n = 1 τ = ˆQ e neutron to proton t ± = t 1 ± it 2 t + ν = π t π = ν t + π =0 t ν =0 proton to neutron
30 Isospin for 2 nucleons T = t 1 + t 2 T =0, 1 T =0 η 0,0 = 1 2 (π 1 ν 2 ν 1 π 2 ) η 1,1 = π 1 π 2 T =1 η 1, 1 = ν 1 ν 2 η 1,0 = 1 2 (π 1 ν 2 + π 2 ν 1 ) Proton-proton state Neutron-neutron state Proton-neutron state T =1,T z =1 = pp T =1,T z = 1 = nn 1 [ T =1,T z =0 + T =0,T z =0] = pn 2
31 Isospin for 2 nucleons ψ(1, 2) = ψ pp (r 1, σ 1, r 2, σ 2 )η 1,1 + ψ nn (r 1, σ 1, r 2, σ 2 )η 1, 1 + ψ a np(r 1, σ 1, r 2, σ 2 )η 1,0 + ψ s np(r 1, σ 1, r 2, σ 2 )η 0,0 (1) Pν=1 T =1 1+τ 3 = 2 Pν= 1 T =1 = 1 τ (1) τ (2) τ (2) 3 Wavefunction η 1,1 P T =1 antisymmetric P T =0 = 1 τ (1) τ 2 ν=0 = 1 4 (1 + τ (1) τ (2) 2τ (1) 4 symmetric η 0,0 2 η 1, 1 η 1,0 3 τ (2) 3 )
32 Additional slides
33 ...many open questions
34 Mean potential method The concept of mean potential (or mean field) strongly relies on the basic assumption of independent particle motion, i.e. even if we know that the real nuclear potential is complicated and nucleons are strongly correlated, some basic properties can be adequately described assuming individual nucleons moving in an average potential (it means that all the nucleons experience the same field). V (r) = a rough approximation could be dr v(r r )ρ(r ) v(r r )= v 0 δ(r r ) where v0 can be phenomenologically estimated to be V (r) = dr v(r) 200 MeV fm 3 Then one can use a simple guess for V: harmonic oscillator, square well, Woods-Saxon shape... V 0 1+e (r R)/R
Basic Concepts in Nuclear Physics. Paolo Finelli
Basic Concepts in Nuclear Physics Paolo Finelli Literature/Bibliography Some useful texts are available at the Library: Wong, Nuclear Physics Krane, Introductory Nuclear Physics Basdevant, Rich and Spiro,
More informationNuclear Physics. Nuclear Physics comprises the study of:
Nuclear Physics Nuclear Physics comprises the study of: The general properties of nuclei The particles contained in the nucleus The interaction between these particles Radioactivity and nuclear reactions
More informationBasic Nuclear Concepts
Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section
More informationMasses in Atomic Units
Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents
More information2, 8, 20, 28, 50, 82, 126.
Chapter 5 Nuclear Shell Model 5.1 Magic Numbers The binding energies predicted by the Liquid Drop Model underestimate the actual binding energies of magic nuclei for which either the number of neutrons
More information............... [2] At the time of purchase of a Strontium-90 source, the activity is 3.7 10 6 Bq.
1 Strontium-90 decays with the emission of a β-particle to form Yttrium-90. The reaction is represented by the equation 90 38 The decay constant is 0.025 year 1. 90 39 0 1 Sr Y + e + 0.55 MeV. (a) Suggest,
More informationChapter NP-5. Nuclear Physics. Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 NUCLEAR REACTIONS 2.0 NEUTRON INTERACTIONS
Chapter NP-5 Nuclear Physics Nuclear Reactions TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 2.0 NEUTRON INTERACTIONS 2.1 ELASTIC SCATTERING 2.2 INELASTIC SCATTERING 2.3 RADIATIVE CAPTURE 2.4 PARTICLE
More informationPHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Test 3 November 22, 2004
PHY464 Introduction to Quantum Mechanics Fall 4 Practice Test 3 November, 4 These problems are similar but not identical to the actual test. One or two parts will actually show up.. Short answer. (a) Recall
More information(b) find the force of repulsion between a proton at the surface of a 12. 6 C nucleus and the remaining five protons.
Chapter 13 Nuclear Structure. Home Work s 13.1 Problem 13.10 (a) find the radius of the 12 6 C nucleus. (b) find the force of repulsion between a proton at the surface of a 12 6 C nucleus and the remaining
More informationBasics of Nuclear Physics and Fission
Basics of Nuclear Physics and Fission A basic background in nuclear physics for those who want to start at the beginning. Some of the terms used in this factsheet can be found in IEER s on-line glossary.
More informationKE A = PE MAX 1/2M v 2 = k q1 q2 /R
CHAPTER 13 NUCLEAR STRUCTURE NUCLEAR FORCE The nucleus is help firmly together by the nuclear or strong force, We can estimate the nuclear force by observing that protons residing about 1fm = 10-15m apart
More information22.02 INTRODUCTION to APPLIED NUCLEAR PHYSICS
Massachusetts Institute of Technology.0 INTRODUCTION to APPLIED NUCLEAR PHYSICS Spring 01 Prof. Paola Cappellaro Nuclear Science and Engineering Department [This page intentionally blank.] Contents 1 Introduction
More informationNuclear Physics and Radioactivity
Nuclear Physics and Radioactivity 1. The number of electrons in an atom of atomic number Z and mass number A is 1) A 2) Z 3) A+Z 4) A-Z 2. The repulsive force between the positively charged protons does
More informationPHYA5/1. General Certificate of Education Advanced Level Examination June 2011. Unit 5 Nuclear and Thermal Physics Section A
Centre Number Surname Candidate Number For Examinerʼs Use Other Names Candidate Signature Examinerʼs Initials General Certificate of Education Advanced Level Examination June 2011 Question 1 2 Mark Physics
More information0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3
Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There
More informationThe Universe Inside of You: Where do the atoms in your body come from?
The Universe Inside of You: Where do the atoms in your body come from? Matthew Mumpower University of Notre Dame Thursday June 27th 2013 Nucleosynthesis nu cle o syn the sis The formation of new atomic
More informationLecture 09 Nuclear Physics Part 1
Lecture 09 Nuclear Physics Part 1 Structure and Size of the Nucleus Νuclear Masses Binding Energy The Strong Nuclear Force Structure of the Nucleus Discovered by Rutherford, Geiger and Marsden in 1909
More informationFree Electron Fermi Gas (Kittel Ch. 6)
Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)
More informationShell closure, magic and exotic nuclei
Shell closure, magic and exotic nuclei Olivier Sorlin Grand Accélérateur National d Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3 B.P. 55027, F-14076 Caen Cedex 5, France ABSTRACT : The advent of Radioactive
More information1. Degenerate Pressure
. Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively
More informationIntroduction to Nuclear Physics
Introduction to Nuclear Physics 1. Atomic Structure and the Periodic Table According to the Bohr-Rutherford model of the atom, also called the solar system model, the atom consists of a central nucleus
More informationAtomic Structure: Chapter Problems
Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand
More informationCORSO DI FISICA NUCLEARE - PAOLO FINELLI DIP. FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA
Fission 1 DIP FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA Nuclear Fission 2 DIP FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA 3 DIP FISICA ED ASTRONOMIA - UNIVERSITÀ DI BOLOGNA Fission timeline - I 4 DIP
More informationPHYA5/1. General Certificate of Education Advanced Level Examination June 2012. Unit 5 Nuclear and Thermal Physics Section A
Centre Number Surname Candidate Number For Examinerʼs Use Other Names Candidate Signature Examinerʼs Initials General Certificate of Education Advanced Level Examination June 2012 Question 1 2 Mark Physics
More informationLight as a Wave. The Nature of Light. EM Radiation Spectrum. EM Radiation Spectrum. Electromagnetic Radiation
The Nature of Light Light and other forms of radiation carry information to us from distance astronomical objects Visible light is a subset of a huge spectrum of electromagnetic radiation Maxwell pioneered
More informationThe rate of change of velocity with respect to time. The average rate of change of distance/displacement with respect to time.
H2 PHYSICS DEFINITIONS LIST Scalar Vector Term Displacement, s Speed Velocity, v Acceleration, a Average speed/velocity Instantaneous Velocity Newton s First Law Newton s Second Law Newton s Third Law
More informationEQUATION OF STATE. e (E µ)/kt ± 1 h 3 dp,
EQUATION OF STATE Consider elementary cell in a phase space with a volume x y z p x p y p z = h 3, (st.1) where h = 6.63 1 7 erg s is the Planck constant, x y z is volume in ordinary space measured in
More informationObjectives 404 CHAPTER 9 RADIATION
Objectives Explain the difference between isotopes of the same element. Describe the force that holds nucleons together. Explain the relationship between mass and energy according to Einstein s theory
More informationElectric Dipole moments as probes of physics beyond the Standard Model
Electric Dipole moments as probes of physics beyond the Standard Model K. V. P. Latha Non-Accelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Time-reversal
More informationCHAPTER 9 ATOMIC STRUCTURE AND THE PERIODIC LAW
CHAPTER 9 ATOMIC STRUCTURE AND THE PERIODIC LAW Quantum mechanics can account for the periodic structure of the elements, by any measure a major conceptual accomplishment for any theory. Although accurate
More informationParticle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims
Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2011 206 Introduction/Aims Symmetries play a central role in particle physics;
More informationthermal history of the universe and big bang nucleosynthesis
thermal history of the universe and big bang nucleosynthesis Kosmologie für Nichtphysiker Markus Pössel (vertreten durch Björn Malte Schäfer) Fakultät für Physik und Astronomie, Universität Heidelberg
More informationTopic 3. Evidence for the Big Bang
Topic 3 Primordial nucleosynthesis Evidence for the Big Bang! Back in the 1920s it was generally thought that the Universe was infinite! However a number of experimental observations started to question
More informationMain properties of atoms and nucleus
Main properties of atoms and nucleus. Atom Structure.... Structure of Nuclei... 3. Definition of Isotopes... 4. Energy Characteristics of Nuclei... 5. Laws of Radioactive Nuclei Transformation... 3. Atom
More informationCHEM 1411 Chapter 5 Homework Answers
1 CHEM 1411 Chapter 5 Homework Answers 1. Which statement regarding the gold foil experiment is false? (a) It was performed by Rutherford and his research group early in the 20 th century. (b) Most of
More informationStatistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics).
Fermi liquids The electric properties of most metals can be well understood from treating the electrons as non-interacting. This free electron model describes the electrons in the outermost shell of the
More informationHigh-K Isomers and the Role of
Bulg. J. Phys. 42 (2015) 382 386 High-K Isomers and the Role of β 6 Deformation β 6 P.M. Walker 1, H.L. Liu 2, F.R. Xu 3 1 Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
More informationWHERE DID ALL THE ELEMENTS COME FROM??
WHERE DID ALL THE ELEMENTS COME FROM?? In the very beginning, both space and time were created in the Big Bang. It happened 13.7 billion years ago. Afterwards, the universe was a very hot, expanding soup
More informationBrief remarks. m 2hyp,i + p2π,i + 2π + p 2π,i = m 2 hyp,i + p2 π,i + E π,i (2) m K + m A =
1 Brief remarks In FINUDA the strangeness-exchange reaction is used to produce Λ- hypernuclei with stopped K s: K stop + Z A Z Λ A + π (1) Thanks to the energy conservation, we can write for each bound
More informationFor convenience, we may consider an atom in two parts: the nucleus and the electrons.
Atomic structure A. Introduction: In 1808, an English scientist called John Dalton proposed an atomic theory based on experimental findings. (1) Elements are made of extremely small particles called atoms.
More informationThe properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >> 1,
Chapter 3 Ideal Fermi gas The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >>, which defines the degenerate Fermi gas. In
More informationGamma Ray Detection at RIA
Gamma Ray Detection at RIA Summary Report: Physics & Functional Requirements Cyrus Baktash Physics goals Experimental tools: Techniques & Reactions Functional Requirements Physics Questions (Discussed
More informationChapter 18: The Structure of the Atom
Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.
More informationInstructors Guide: Atoms and Their Isotopes
Instructors Guide: Atoms and Their Isotopes Standards Connections Connections to NSTA Standards for Science Teacher Preparation C.3.a.1 Fundamental structures of atoms and molecules. C.3.b.27 Applications
More informationThe Physics of Energy sources Nuclear Reactor Practicalities
The Physics of Energy sources Nuclear Reactor Practicalities B. Maffei Bruno.maffei@manchester.ac.uk www.jb.man.ac.uk/~bm Nuclear Reactor 1 Commonalities between reactors All reactors will have the same
More informationMASS DEFECT AND BINDING ENERGY
MASS DEFECT AND BINDING ENERGY The separate laws of Conservation of Mass and Conservation of Energy are not applied strictly on the nuclear level. It is possible to convert between mass and energy. Instead
More informationPhysics 1104 Midterm 2 Review: Solutions
Physics 114 Midterm 2 Review: Solutions These review sheets cover only selected topics from the chemical and nuclear energy chapters and are not meant to be a comprehensive review. Topics covered in these
More informationStructure and Properties of Atoms
PS-2.1 Compare the subatomic particles (protons, neutrons, electrons) of an atom with regard to mass, location, and charge, and explain how these particles affect the properties of an atom (including identity,
More informationNOTES ON The Structure of the Atom
NOTES ON The Structure of the Atom Chemistry is the study of matter and its properties. Those properties can be explained by examining the atoms that compose the matter. An atom is the smallest particle
More informationChemistry 1000 Lecture 2: Nuclear reactions and radiation. Marc R. Roussel
Chemistry 1000 Lecture 2: Nuclear reactions and radiation Marc R. Roussel Nuclear reactions Ordinary chemical reactions do not involve the nuclei, so we can balance these reactions by making sure that
More informationThe Sun and Solar Energy
I The Sun and Solar Energy One of the most important forces behind global change on Earth is over 90 million miles distant from the planet. The Sun is the ultimate, original source of the energy that drives
More informationNuclear ZPE Tapping. Horace Heffner May 2007
ENERGY FROM UNCERTAINTY The uncertainty of momentum for a particle constrained by distance Δx is given, according to Heisenberg, by: Δmv = h/(2 π Δx) but since KE = (1/2) m v 2 = (1/(2 m) ) (Δmv) 2 ΔKE
More informationMATHEMATICAL MODELS Vol. II - Mathematical Models of Nuclear Energy - Yu. A. Svistunov MATHEMATICAL MODELS OF NUCLEAR ENERGY
MATHEMATICAL MODELS OF NUCLEAR ENERGY Yu. A. Svistunov Department of Applied Mathematics and Control Processes, State University of St- Petersburg, Russia Keywords: Nucleus, neutron, nuclear reactor, transfer
More informationObjectives. PAM1014 Introduction to Radiation Physics. Constituents of Atoms. Atoms. Atoms. Atoms. Basic Atomic Theory
PAM1014 Introduction to Radiation Physics Basic Atomic Theory Objectives Introduce and Molecules The periodic Table Electronic Energy Levels Atomic excitation & de-excitation Ionisation Molecules Constituents
More informationModern Physics 9p ECTS
Modern physics 1 Modern Physics 9p ECTS Contents 1. Introduction 2. The special relativity 3. The original quantum theory 4. The photon 5. Statistical physics 6. The Schrödinger equation 7. Atoms 8. Molecules
More informationThe content is based on the National Science Teachers Association (NSTA) standards and is aligned with state standards.
Literacy Advantage Physical Science Physical Science Literacy Advantage offers a tightly focused curriculum designed to address fundamental concepts such as the nature and structure of matter, the characteristics
More information2 ATOMIC SYSTEMATICS AND NUCLEAR STRUCTURE
2 ATOMIC SYSTEMATICS AND NUCLEAR STRUCTURE In this chapter the principles and systematics of atomic and nuclear physics are summarised briefly, in order to introduce the existence and characteristics of
More informationThe Physics of Neutron Stars
The Physics of Neutron Stars Alfred Whitehead Physics 518, Fall 009 The Problem Describe how a white dwarf evolves into a neutron star. Compute the neutron degeneracy pressure and balance the gravitational
More informationSolar Energy Production
Solar Energy Production We re now ready to address the very important question: What makes the Sun shine? Why is this such an important topic in astronomy? As humans, we see in the visible part of the
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Elliptic Flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy
More informationNuclear Mass and Stability
CHAPTER 3 Nuclear Mass and Stability Contents 3.1. Patterns of nuclear stability 41 3.2. Neutron to proton ratio 43 3.3. Mass defect 45 3.4. Binding energy 47 3.5. Nuclear radius 48 3.6. Semiempirical
More informationChem 1A Exam 2 Review Problems
Chem 1A Exam 2 Review Problems 1. At 0.967 atm, the height of mercury in a barometer is 0.735 m. If the mercury were replaced with water, what height of water (in meters) would be supported at this pressure?
More information13- What is the maximum number of electrons that can occupy the subshell 3d? a) 1 b) 3 c) 5 d) 2
Assignment 06 A 1- What is the energy in joules of an electron undergoing a transition from n = 3 to n = 5 in a Bohr hydrogen atom? a) -3.48 x 10-17 J b) 2.18 x 10-19 J c) 1.55 x 10-19 J d) -2.56 x 10-19
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance NMR is probably the most useful and powerful technique for identifying and characterizing organic compounds. Felix Bloch and Edward Mills Purcell were awarded the 1952 Nobel
More informationChapter 9 Unitary Groups and SU(N)
Chapter 9 Unitary Groups and SU(N) The irreducible representations of SO(3) are appropriate for describing the degeneracies of states of quantum mechanical systems which have rotational symmetry in three
More informationLecture 5 Motion of a charged particle in a magnetic field
Lecture 5 Motion of a charged particle in a magnetic field Charged particle in a magnetic field: Outline 1 Canonical quantization: lessons from classical dynamics 2 Quantum mechanics of a particle in a
More information( + and - ) ( - and - ) ( + and + ) Atoms are mostly empty space. = the # of protons in the nucleus. = the # of protons in the nucleus
Atoms are mostly empty space Atomic Structure Two regions of every atom: Nucleus - is made of protons and neutrons - is small and dense Electron cloud -is a region where you might find an electron -is
More informationLecture 3: Optical Properties of Bulk and Nano. 5 nm
Lecture 3: Optical Properties of Bulk and Nano 5 nm The Previous Lecture Origin frequency dependence of χ in real materials Lorentz model (harmonic oscillator model) 0 e - n( ) n' n '' n ' = 1 + Nucleus
More informationENERGY LOSS OF ALPHA PARTICLES IN GASES
Vilnius University Faculty of Physics Department of Solid State Electronics Laboratory of Applied Nuclear Physics Experiment No. ENERGY LOSS OF ALPHA PARTICLES IN GASES by Andrius Poškus (e-mail: andrius.poskus@ff.vu.lt)
More informationCondensates in Neutron Star Interiors
Condensates in Neutron Star Interiors Vatsal Dwivedi submitted as a term essay for Phys 569 : Emergent States of Matter Dec 19, 2012 Abstract The pulsars, now identified as neutron stars, are one of the
More information= N 2 = 3π2 n = k 3 F. The kinetic energy of the uniform system is given by: 4πk 2 dk h2 k 2 2m. (2π) 3 0
Chapter 1 Thomas-Fermi Theory The Thomas-Fermi theory provides a functional form for the kinetic energy of a non-interacting electron gas in some known external potential V (r) (usually due to impurities)
More informationAtoms and Elements. Atoms: Learning Goals. Chapter 3. Atoms and Elements; Isotopes and Ions; Minerals and Rocks. Clicker 1. Chemistry Background?
Chapter 3 Atoms Atoms and Elements; Isotopes and Ions; Minerals and Rocks A Review of Chemistry: What geochemistry tells us Clicker 1 Chemistry Background? A. No HS or College Chemistry B. High School
More informationMagnetism and Magnetic Materials K. Inomata
Magnetism and Magnetic Materials K. Inomata 1. Origin of magnetism 1.1 Magnetism of free atoms and ions 1.2 Magnetism for localized electrons 1.3 Itinerant electron magnetism 2. Magnetic properties of
More informationSection 5 Molecular Electronic Spectroscopy (lecture 9 ish)
Section 5 Molecular Electronic Spectroscopy (lecture 9 ish) Previously: Quantum theory of atoms / molecules Quantum Mechanics Vl Valence Molecular Electronic Spectroscopy Classification of electronic states
More informationB2.IV Nuclear and Particle Physics. A.J. Barr
B2.IV Nuclear and Particle Physics A.J. Barr February 13, 2014 ii Contents 1 Introduction 1 2 Nuclear 3 2.1 Structure of matter and energy scales................ 3 2.2 Binding Energy............................
More informationChapter NP-1. Nuclear Physics. Atomic Nature of Matter TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 PROPERTIES OF SUBSTANCES
Chapter NP-1 Nuclear Physics Atomic Nature of Matter TABLE OF CONTENTS INTRODUCTION OBJECTIVES 1.0 PROPERTIES OF SUBSTANCES 1.1 CHEMICAL AND PHYSICAL PROPERTIES 2.0 COMPOSITION OF ATOMS 2.1 ATOMIC STRUCTURE
More informationMulti-electron atoms
Multi-electron atoms Today: Using hydrogen as a model. The Periodic Table HWK 13 available online. Please fill out the online participation survey. Worth 10points on HWK 13. Final Exam is Monday, Dec.
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables τ
More informationNMR - Basic principles
NMR - Basic principles Subatomic particles like electrons, protons and neutrons are associated with spin - a fundamental property like charge or mass. In the case of nuclei with even number of protons
More informationQuark Model. Quark Model
Quark odel Outline Hadrons Isosin Strangeness Quark odel Flavours u d s esons Pseudoscalar and vector mesons Baryons Deculet octet Hadron asses Sin-sin couling Heavy Quarks Charm bottom Heavy quark esons
More informationCross section, Flux, Luminosity, Scattering Rates
Cross section, Flux, Luminosity, Scattering Rates Table of Contents Paul Avery (Andrey Korytov) Sep. 9, 013 1 Introduction... 1 Cross section, flux and scattering... 1 3 Scattering length λ and λ ρ...
More informationBig Bang Nucleosynthesis
Big Bang Nucleosynthesis The emergence of elements in the universe Benjamin Topper Abstract. In this paper, I will first give a brief overview of what general relativity has to say about cosmology, getting
More informationEXPERIMENT 4 The Periodic Table - Atoms and Elements
EXPERIMENT 4 The Periodic Table - Atoms and Elements INTRODUCTION Primary substances, called elements, build all the materials around you. There are more than 109 different elements known today. The elements
More informationRadioactivity III: Measurement of Half Life.
PHY 192 Half Life 1 Radioactivity III: Measurement of Half Life. Introduction This experiment will once again use the apparatus of the first experiment, this time to measure radiation intensity as a function
More informationChemistry. The student will be able to identify and apply basic safety procedures and identify basic equipment.
Chemistry UNIT I: Introduction to Chemistry The student will be able to describe what chemistry is and its scope. a. Define chemistry. b. Explain that chemistry overlaps many other areas of science. The
More information1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our
1 1 Introduction Cosmology is the study of the universe as a whole, its structure, its origin, and its evolution. Cosmology is soundly based on observations, mostly astronomical, and laws of physics. These
More informationThe shell model MARIA GOEPPERT MAYER. Nobel Lecture, December 12, 1963
MARIA GOEPPERT MAYER The shell model Nobel Lecture, December 12, 1963 1. Models There are essentially two ways in which physicists at present seek to obtain a consistent picture of atomic nucleus. The
More informationDO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS
DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.
More informationPHYS 1624 University Physics I. PHYS 2644 University Physics II
PHYS 1624 Physics I An introduction to mechanics, heat, and wave motion. This is a calculus- based course for Scientists and Engineers. 4 hours (3 lecture/3 lab) Prerequisites: Credit for MATH 2413 (Calculus
More information22.1 Nuclear Reactions
In the Middle Ages, individuals called alchemists spent a lot of time trying to make gold. Often, they fooled people into believing that they had made gold. Although alchemists never succeeded in making
More informationSEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel)
SEMICONDUCTOR I: Doping, semiconductor statistics (REF: Sze, McKelvey, and Kittel) Introduction Based on known band structures of Si, Ge, and GaAs, we will begin to focus on specific properties of semiconductors,
More informationNUCLEI. Chapter Thirteen. Physics 13.1 INTRODUCTION 13.2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS
Chapter Thirteen NUCLEI 13.1 INTRODUCTION In the previous chapter, we have learnt that in every atom, the positive charge and mass are densely concentrated at the centre of the atom forming its nucleus.
More informationPerfect Fluids: From Nano to Tera
Perfect Fluids: From Nano to Tera Thomas Schaefer North Carolina State University 1 2 Perfect Fluids sqgp (T=180 MeV) Neutron Matter (T=1 MeV) Trapped Atoms (T=0.1 nev) 3 Hydrodynamics Long-wavelength,
More informationAtomic and Nuclear Physics Laboratory (Physics 4780)
Gamma Ray Spectroscopy Week of September 27, 2010 Atomic and Nuclear Physics Laboratory (Physics 4780) The University of Toledo Instructor: Randy Ellingson Gamma Ray Production: Co 60 60 60 27Co28Ni *
More informationThe Physics of Energy sources Nuclear Fusion
The Physics of Energy sources Nuclear Fusion B. Maffei Bruno.maffei@manchester.ac.uk www.jb.man.ac.uk/~bm Nuclear Fusion 1 What is nuclear fusion? We have seen that fission is the fragmentation of a heavy
More informationExcitation transfer and energy exchange processes for modeling the Fleischmann-Pons excess heat effect
Hagelstein, P.L. and I. Chaudhary. Excitation transfer and energy exchange processes for modeling the Fleischmann-Pons excess heat effect. in ICCF-14 International Conference on Condensed Matter Nuclear
More informationSUPERCONDUCTIVITY. PH 318- Introduction to superconductors 1
SUPERCONDUCTIVITY property of complete disappearance of electrical resistance in solids when they are cooled below a characteristic temperature. This temperature is called transition temperature or critical
More information3. Derive the partition function for the ideal monoatomic gas. Use Boltzmann statistics, and a quantum mechanical model for the gas.
Tentamen i Statistisk Fysik I den tjugosjunde februari 2009, under tiden 9.00-15.00. Lärare: Ingemar Bengtsson. Hjälpmedel: Penna, suddgummi och linjal. Bedömning: 3 poäng/uppgift. Betyg: 0-3 = F, 4-6
More informationChapter 5. Second Edition ( 2001 McGraw-Hill) 5.6 Doped GaAs. Solution
Chapter 5 5.6 Doped GaAs Consider the GaAs crystal at 300 K. a. Calculate the intrinsic conductivity and resistivity. Second Edition ( 2001 McGraw-Hill) b. In a sample containing only 10 15 cm -3 ionized
More informationElliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies
Elliptical Galaxies Houjun Mo April 19, 2004 Basic properties of elliptical galaxies Formation of elliptical galaxies Photometric Properties Isophotes of elliptical galaxies are usually fitted by ellipses:
More information