Chapter 5. Par+cle Physics

Transcription

1 Chapter 5 Par+cle Physics

2 Types of Forces Force Range (m) Relative Strength Force Carrier Gravitational! Graviton Weak W ±, Z 0 Electromagnetic! =1/137 Photon Strong Gluon

3 What does this mean? Force Electromagne+ c Exchange Par.cle Mass Range photon 0 infinite Gravity graviton 0 infinite Weak W boson 90 GeV/c fm Strong gluon > 140 MeV/c 2 < 1.4 fm

4 Exchange Particles and Force Carriers Forces occur through the notion of the virtual exchange of bosons that are force carriers!t =!!E

5 Range of Forces Range! c"t!! 2mc

6 Defini+ons Fermions vs bosons Leptons vs hadrons (strong interac+on)

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8 Back to Fundamental Particles Classification of Particles Using Spin For Classification Fermions(e,p,n) ½ integer spin No two particles may occupy the same quantum state. Bosons(photon) Integer spin Do not obey Pauli exclusion principle (Anima+on)

9 Types of Fermions Fermionic Hadrons interact via the strong interaction p,n Leptons Do not interact via the strong interaction--e

10 Examples of Fermions

11 Lepton conservation The number of leptons is conserved in nuclear processes L=1 for each particle, L=-1 for each antiparticle n! p + + e " +! e 0=0+1-1! e + p +! e + + n =- 1+0

12 The neutron and the proton Mn~Mp~1 amu Mn-Mp=1.29 MeV/c 2 The free neutron can decay into a proton T 1/2 ~ 10 min (881.5 s) Because Mn~Mp, we refer to them as nucleons Mnucleon ~ 938 MeV/c 2

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15 Types of Hadrons Baryons (Fermionic Hadrons) Composed of three quarks like the proton or neutron They are fermions Strongly interacting Mesons (Bosonic Hadrons) Composed of quark/anti-quark pairs. They are bosons Strongly interacting

16 Properties of the quarks

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18 Conserva+on of Baryon Number Each of the baryons is assigned a baryon number B=1. This can be considered to be equivalent to assigning each quark a baryon number of 1/3. This implies that the mesons, with one quark and one antiquark, have a baryon number B=0. No known decay process or interaction in nature changes the net baryon number. Conserva+on of baryon number prohibits a decay of the type But allows p + n! p + µ + + µ " B = 1+1 # p + n! p + n + p + p B = 1+1 = 1+1+1"1

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20 Some familiar par+cles Proton

21 Some familiar par+cles Neutron

22 Pi meson

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24 Examples of Bosons

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27 !

28 The Strong Force and The Nuclear Force What is the difference? What is the range of each force? What is the force carrier? What are the characteris+cs of each force?

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30 The nuclear force general proper+es Short range Saturates A]rac+ve Repulsive core

31 The Deuteron Neutron- proton bound together Q= b - > two component force, symmetric central force and asymmetric tensor force Only 1 bound state (triplet) weakly bound (2.2 MeV) J,π=1+ Singlet state is unbound Spin dependence of nuclear force Μ=0.857 nm % 3 D state

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33 The nuclear force

34 Realis+c forms of the nuclear force

35 Other potentials of note

36 Other potentials of note

37 Charge independence of nuclear nn=pp=np forces

38 Isospin Isospin quantum number T Projec+on of T on the 3- axis in isospace =T z or T 3 T z = +1/2 (proton); T z =- 1/2 (neutron) (PP has opposite sign conven+on) For a system (nucleus) T z =(Z- N)/2 For a system of isospin T, there are 2T+1 members of the isospin mul+plet

39 Example A=14 system ( 14 C, 14 N, 14 O) T z =+1( 14 C);T z =- 1( 14 O) These must be 2 members of the T=1 isospin mul+plet In 14 N there must be a state with T=1. But the ground state is T z =0. So this must be an excited state.

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41 Who dat?

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43 Nuclear Physics Problems 2.3. Mirror nuclei are pairs of nuclei in which the proton number in one equals the neutron number in the other and vice versa. The simplest examples are provided by odd- A nuclei with one odd nucleon. In one of the mirror nuclei the charge isz = (A + 1)/2 and the neutron number is N = (A 1)/2; whilst in the other thecharge is Z = (A 1)/2 and the neutron number N = (A + 1)/2. Examples are 13N and 13C or 31S and 31P. The nuclei in these pairs differ from each other only in that a proton in one is exchanged for the neutron in the other. There is strong reason to believe that the force between nucleons does not differen+ate between neutrons and protons; consequently, the nuclear part of the binding energy of two mirror nuclei must be the same. Hence, the mass difference of two mirror nuclei can be due only to the difference between the proton mass and the neutron mass, and the different Coulomb energies of the two. This can be used to find the radius of the two nuclei (assumed to be the same), thus: 1. Show that the electrosta+c poten+al energy (Coulomb energy) of a uniformly charged sphere of radius R and charge Ze is 3Z 2 e 2 / (20πε 0 R). 2. The nucleus 21 Na is more massive than its mirror partner 21 Ne by 4.02 MeV/c 2.What is the difference between their Coulomb energies? Use this to es+mate a value for R. (The neutron- proton mass difference is 1.29 MeV/c 2.)