Nuclear Physics

							Nuclear and Particle Physics

           3 lectures:
          Nuclear Physics
         Particle Physics 1
         Particle Physics 2




                               1
             Nuclear Physics Topics

 Composition of Nucleus
 features of nuclei
 Nuclear Models
 nuclear energy
   Fission
   Fusion
 Summary



                                      2
                           About Units
 Energy - electron-volt
    1 electron-volt = kinetic energy of an electron when
     moving through potential difference of 1 Volt;
      o 1 eV = 1.6 × 10-19 Joules
      o 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV
      o 1 MeV = 106 eV, 1 GeV= 109 eV, 1 TeV = 1012 eV

 mass - eV/c2
      o   1 eV/c2 = 1.78 × 10-36 kg
      o   electron mass = 0.511 MeV/c2
      o   proton mass = 938 MeV/c2 = 0.938 GeV/ c2
      o   neutron mass = 939.6 MeV/c2

 momentum - eV/c:
      o 1 eV/c = 5.3 × 10-28 kg m/s
      o momentum of baseball at 80 mi/hr  5.29 kgm/s  9.9 × 1027
        eV/c
 Distance
      o 1 femtometer (“Fermi”) = 10-15 m
                                                                3
                             Radioactivity
 Discovery of Radioactivity
    Antoine Becquerel (1896): serendipitous discovery of radioactivity:
     penetrating radiation emitted by substances containing uranium
    A. Becquerel, Maria Curie, Pierre Curie(1896 – 1898):
       o also other heavy elements (thorium, radium) show radioactivity
       o three kinds of radiation, with different penetrating power
         (i.e. amount of material necessary to attenuate beam):
            “Alpha (a) rays” (least penetrating – stopped by paper)
            “Beta (b) rays” (need 2mm lead to absorb)
            “Gamma (g) rays” (need several cm of lead to be attenuated)
       o three kinds of rays have different electrical charge:
                        a: +, b: -, g: 0
 Identification of radiation:
   Ernest Rutherford (1899)
       o Beta (b) rays have same q/m ratio as electrons
       o Alpha (a) rays have same q/m ratio as He
       o Alpha (a) rays captured in container show He-like emission spectrum
                                                                           4
     Geiger, Marsden, Rutherford expt.
 (Geiger, Marsden, 1906 - 1911) (interpreted by Rutherford, 1911)
 get a particles from radioactive source
 make “beam” of particles using “collimators”
   (lead plates with holes in them, holes aligned in straight line)
 bombard foils of gold, silver, copper with beam
 measure scattering angles of particles with scintillating screen (ZnS)




                                                                      5
6
    Geiger Marsden experiment: result
 most particles only slightly deflected (i.e. by small
  angles), but some by large angles - even backward
 measured angular distribution of scattered particles did
  not agree with expectations from Thomson model (only
  small angles expected),
 but did agree with that expected from scattering on
  small, dense positively charged nucleus with diameter
  < 10-14 m, surrounded by electrons at 10-10 m
Ernest
Rutherford
1871-1937


                                                      7
                           Proton
 “Canal rays”
    1898: Wilhelm Wien:
     opposite of “cathode rays”
 Positive charge in
  nucleus (1900 – 1920)
    Atoms are neutral
      o positive charge needed to cancel electron’s negative charge
      o Rutherford atom: positive charge in nucleus
    periodic table  realized that the positive charge of
     any nucleus could be accounted for by an integer
     number of hydrogen nuclei -- protons




                                                                      8
                              Neutron
 Walther Bothe 1930:
    bombard light elements (e.g. 49Be) with alpha particles 
     neutral radiation emitted
 Irène and Frederic Joliot-Curie (1931)
    pass radiation released from Be target through paraffin wax 
     protons with energies up to 5.7 MeV released
    if neutral radiation = photons, their energy would have to be 50
     MeV -- puzzle
 puzzle solved by James Chadwick (1932):
    “assume that radiation is not quantum radiation, but a neutral
     particle with mass approximately equal to that of the proton”
    identified with the “neutron” suggested by Rutherford in 1920
    observed reaction was:
      a (24He++) + 49Be  613C*
                                13
                               6 C*     612C + n
                                                                  9
                Beta decay -- neutrino
 Beta decay puzzle :
      o decay changes a neutron into a proton
      o apparent “non-conservation” of energy
      o apparent non-conservation of angular momentum
 Wolfgang Pauli predicted a light, neutral, feebly
 interacting particle (called it neutron, later called
 neutrino by Fermi)




 Although accepted since it “fit” so well, not
 actually observed initiating interactions until 1956-
                                                   10
 1958 (Cowan and Reines)
                Puzzle with Beta Spectrum
 Three-types of radioactivity: a,
  b, g
 Both a, g discrete spectrum          F. A. Scott, Phys. Rev. 48, 391 (1935)
  because
       Ea, g = Ei – Ef
 But b spectrum continuous

 Energy conservation violated??
    Bohr:: “At the present stage
      of atomic theory, however,
      we may say that we have no
      argument, either empirical or
      theoretical, for upholding the
      energy principle in the case
      of β-ray disintegrations”
                                                                          11
Desperate Idea of Pauli




                          12
                          Positron
 Positron (anti-electron)
    Predicted by Dirac (1928) -- needed for relativistic
     quantum mechanics
    existence of antiparticles doubled the number of
     known particles!!!

      Positron track going
      upward through lead
      plate

 P.A.M. Dirac
    Nobel Prize (1933)
    member of FSU faculty
      (1972-1984)
    one of the greatest physicists of the 20th century     13
                 Structure of nucleus
 size (Rutherford 1910, Hofstadter 1950s):
   R = r0 A1/3, r0 = 1.2 x 10-15 m = 1.2 fm;
   i.e. ≈ 0.15 nucleons / fm3
 generally spherical shape, almost uniform density;
 made up of protons and neutrons
   protons and neutron -- “nucleons”;
      are fermions (spin ½), have magnetic moment
 nucleons confined to small region (“potential well”)
    occupy discrete energy levels
   two distinct (but similar) sets of energy levels,
      one for protons, one for neutrons
   proton energy levels slightly higher than those of
    neutrons (electrostatic repulsion)
 spin ½  Pauli principle                               14
       only two identical nucleons per eng. level
       Nuclear Sizes - examples
               1

 r  ro (A )   3
                             ro = 1.2 x 10-15 m


Find the ratio of the radii for the following nuclei:

             1H, 12C, 56Fe, 208Pb, 238U



              1     1    1        1       1
              3     3    3        3       3
             1 : 12 : 56 : 208 : 238

            1 : 2.89 : 3.83 : 5.92 : 6.20
                                                        15
                      A, N, Z

 for natural nuclei:
   Z range 1 (hydrogen) to
    92 (Uranium)
   A range from 1 ((hydrogen)
    to 238 (Uranium)
 N = neutron number = A-Z
 N – Z = “neutron excess”;
 increases with Z
 nomenclature:
   ZAXN or AXN or
      A
       X or X-A                  16
                Atomic mass unit

 “atomic number” Z
  Number of protons in nucleus

 Mass Number A
  Number of protons and neutrons in nucleus
  Atomic mass unit is defined in terms of the
   mass of 126C, with A = 12, Z = 6:
  1 amu = (mass of 126C atom)/12
  1 amu = 1.66 x 10-27kg
  1 amu = 931.494 MeV/c2
                                                 17
               Properties of Nucleons
 Proton
   Charge = 1 elementary charge e = 1.602 x 10-19 C
   Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u =
    1836 me
   spin ½, magnetic moment 2.79 eħ/2mp
 Neutron
   Charge = 0
   Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u =
    1839 me
   spin ½, magnetic moment -1.9 eħ/2mn



                                                      18
             Nuclear masses, isotopes

 Nuclear masses measured, e.g. by mass
 spectrography
 masses expressed in atomic mass units (amu),
 energy units MeV/c2
 all nuclei of certain element contain same number
 of protons, but may contain different number of
 neutrons
 examples:
   deuterium, heavy hydrogen 2D or 2H;
     heavy water = D2O (0.015% of natural water)
                                                        U),
   U- 235 (0.7% of natural U), U-238 (99.3% of natural 19
         Nuclear energy levels: example

Problem: Estimate the lowest possible energy of a neutron contained
     in a typical nucleus of radius 1.33×10-15 m.



E = p2/2m = (cp)2/2mc2


x p = h/2                    x (cp) = hc/2
(cp) = hc/(2 x) = hc/(2 r)
(cp) = 6.63x10-34 Js * 3x108 m/s / (2 * 1.33x10-15 m)
(cp) = 2.38x10-11 J = 148.6 MeV

E = p2/2m = (cp)2/2mc2 = (148.6 MeV)2/(2*940 MeV) = 11.7 MeV
                                                                 20
   Nuclear Masses, binding energy
 Mass of Nucleus  Z(mp) + N(mn)
 “mass defect” m = difference
 between mass of nucleus and mass of
 constituents
 energy defect = binding energy EB
    EB = m c2
 binding energy = amount of energy that
 must be invested to break up nucleus
 into its constituents
 binding energy per nucleon = EB /A
                                      21
         Nuclear Binding Energy
                                 The difference between
                                  the energy (or mass) of
                                  the nucleus and the
1 amu =           931.5 MeV       energy (or mass) of its
                                  constituent neutrons and
m(proton)             1.00782     protons.
m(neutron)            1.00867    = the energy needed to
                                  break the nucleus apart.
             A=            56    Average binding energy
             Z=            26     per nucleon = total
                                  binding energy divided by
             N=            30     the number of nucleons
Mass (amu)           55.92066     (A).
                                 Example: Fe-56
Ebinding (MeV)     -505.58094
EB/A(MeV)            -9.02823
                                                        22
                 Problem – set 4
 Compute binding energy per nucleon for
   42He          4.00153 amu
   168O          15.991 amu
   5626Fe        55.922 amu
   23592U        234.995 amu
 Is there a trend?
 If there is, what might be its significance?
 note:
   1 amu =       931.5 MeV/c2
   m(proton) = 1.00782 amu
   m(neutron)= 1.00867 amu
                                                 23
    Binding energy per nucleon






                                 24
            Nuclear Radioactivity


 Alpha Decay
   AZ  A-4(Z-2) + 4He
     o Number of protons is conserved.
     o Number of neutrons is conserved.
 Gamma Decay
   AZ*  AZ + g
     o An excited nucleus loses energy by emitting
       a photon.

                                                     25
                       Beta Decay


 Beta Decay
   AZ  A(Z+1) + e- + an anti-neutrino
      o A neutron has converted into a proton, electron and
        an anti-neutrino.
 Positron Decay
   AZ  A(Z-1) + e+ + a neutrino
      o A proton has converted into a neutron, positron and a
        neutrino.
 Electron Capture
   AZ + e-  A(Z-1) + a neutrino
      o A proton and an electron have converted into a
        neutron and a neutrino.
                                                                26
                                Radioactivity
                                                Electron capture:
 Several decay processes:
a decay: A    A- 4
                                                          A
                                                              X + e - Z -AY +
            Z   X  Z -2Y + 2 He
                    4                                     Z               1


            e.g.,210Po206Pb+ 2 He
                  84    82
                              4
                                                        e.g.,12N + e - 12C +
                                                              7          6

                                                g decay:
b- decay:
                                    ~             A
                                                      X * ZAX + g
      A
      Z   X  Z +1Y + e - + 
                 A                                Z


                                                  e.g.,99Tc* 99Tc + g (140keV )
                                            ~
      e.g ., Tc  Rb + e + 
                99
                43
                         99
                         44
                                        -
                                                       43     43

b+ decay:
            A
            Z   X Z -AY + e + +
                      1


            e.g.,12N 12C + e + +
                  7    6                                                          27
           Law of radioactive decay
 Activity A = number            dN
                              A    .
  of                             dt
  decays per unit time
 decay constant  =
  probability of decay       dN
                                 -N .
  per unit time              dt
 Rate of decay 
                                                   - t
  number N of nuclei       N (t )  N 0 e .
 Solution of diff.
  equation (N0 = nb. of             

  nuclei at t=0)                     t e -t dt
                            t dN               
                                                       1
 Mean life  = 1/ 
                                    0

                               dN  e  dt
                                     
                                         - t           
                                     0                     28
                                        Nuclear decay rates
                                  Nuclear Decay

                   1000.0
Nuclei Remaining




                    800.0
                                                                             - t
                    600.0                                         N (t )  N 0e .
                    400.0
                                                                  At t = 1/,
                    200.0
                                                                  N is 1/e (0.368)
                      0.0                                         of the original
                            0.0   1.0     2.0   3.0   4.0   5.0   amount
                                           Time(s)



                                                                             29
           Nuclear (“strong”) force
 atomic nuclei small -- about 1 to 8fm
 at small distance, electrostatic repulsive forces
             are of macroscopic size (10 – 100 N)
 there must be short-range attractive force
      between nucleons -- the “strong force”
 strong force essentially charge-independent
   “mirror nuclei” have almost identical binding
    energies
   mirror nuclei = nuclei for which n  p or p  n
      (e.g. 3He and 3H, 7Be and 7Li, 35Cl and 35Ar);
      slight differences due to electrostatic
    repulsion
 strong force must have very short range – <<
 atomic size, otherwise isotopes would not have
 same chemical properties
                                                       30
               Strong force -- 2
 range: fades away at distance ≈ 3fm
   force between 2 nucleons at 2fm distance ≈
    2000N
   nucleons on one side of U nucleus hardly
    affected by nucleons on other side
 experimental evidence for nuclear force from
 scattering experiments;
   low energy p or a scattering: scattered
    particles unaffected by nuclear force
   high energy p or a scattering:
     particles can overcome electrostatic
    repulsion and can penetrate deep enough to
    enter range of nuclear force                 31
           N-Z and binding energy vs A
 small nuclei (A<10):
   All nucleons are within range of strong force
               exerted by all other nucleons;
   add another nucleon  enhance overall cohesive force
                EB rises sharply with increase in A
 medium size nuclei (10 < A < 60)
   nucleons on one side are at edge of nucl. force range from
    nucleons on other side  each add’l nucleon gives diminishing
    return in terms of binding energy  slow rise of EB /A
 heavy nuclei (A>60)
   adding more nucleons does not increase overall cohesion due
    to nuclear attraction
   Repulsive electrostatic forces (infinite range!) begin to have
    stronger effect
   N-Z must be bigger for heavy nuclei (neutrons provide
    attraction without electrostatic repulsion
   heaviest stable nucleus: 209Bi
               – all nuclei heavier than 209Bi are unstable
               (radioactive)
                                                                 32
EB/A vs A




            33
    Nuclear Models – liquid drop model
 liquid drop model (Bohr, Bethe, Weizsäcker):
   nucleus = drop of incompressible nuclear fluid.
   fluid made of nucleons, nucleons interact
     strongly (by nuclear force) with each other,
             just like molecules in a drop of liquid.
   introduced to explain binding energy
      and mass of nuclei
   predicts generally spherical shape of nuclei
   good qualitative description of fission
      of large nuclei
   provides good empirical description
      of binding energy vs A
                                                        34
  Bethe – Weizsäcker formula for binding energy
 Bethe - Weizsäcker formula:
   an empirically refined form of the liquid drop model for the
    binding energy of a nucleus of mass number A with Z protons
    and N neutrons
    binding energy has five terms describing different aspects
    of the binding of all the nucleons:
       o   volume energy
       o   surface energy
       o    Coulomb energy (electrostatic repulsion of the protons,)
       o    an asymmetry term (N vs Z)
       o    an exchange (pairing) term (even-even vs odd-even vs odd-odd
           number of nucleons)


B(A, Z)  a V A - a S A   2/3         Z 2
                                - a C 1/3 - a Sy m
                                                   Z - N  - λ a A -3/4
                                                            2

                                                                 P
                                     A                A
                                                                           35
“liquid drop” terms in B-W formula




                                     36
         Independent Particle Models
 assume nucleons move inside nucleus without interacting
              with each other
 Fermi- gas model:
   Protons and neutrons move freely within nuclear volume,
              considered a rectangular box
   Protons and neutrons are distinguishable and so move
              in separate potential wells
 Shell Model
   formulated (independently)
                      by Hans Jensen and Maria Goeppert-Mayer
   Each nucleon (proton or neutron) moves in the average
    potential of remaining nucleons, assumed to be spherically
    symmetric.
   Also takes account of the interaction between a nucleon’s
              spin and its angular momentum (“spin-orbit
    coupling”)
   derive “magic numbers” (of protons and/or neutrons) for
    which nuclei are particularly stable: 2, 8, 20, 28, 50, 82, 126, ..37
         Fermi-Gas Model of Nucleus
 Ground State
                                     Potential well
    In each potential well,
     the lowest energy states
     are occupied.

    Because of the Coulomb
     repulsion the proton well
     is shallower than that of
     the neutron.
                                  Therefore, as Z increases
    But the nuclear energy        we would expect nuclei to
     is minimized when the         contain progressively
     maximum energy level is       more neutrons than
     about the same for            protons.
     protons and neutrons
                                  U has A = 238, Z = 92
                                                           38
                 Collective model
 collective model is “eclectic”, combining aspects
 of other models
   consider nucleus as composed of “stable core”
    of closed shells, plus additional nucleons outside
    of core
   additional nucleons move in potential well due to
    interaction with the core
   interaction of external nucleons with the core
     agitate core – set up rotational and
    vibrational motions in core, similar to those that
    occur in droplets
   gives best quantitative description of nuclei
                                                     39
                         Nuclear energy
   very heavy nuclei:
    energy released if break up into two medium sized nuclei
    “fission”
 light nuclei:
    energy released if two light nuclei combine -- “fuse” into a
     heavier nucleus – “fusion”




                                                                    40
Nuclear Energy - Fission




        + about 200 MeV energy   41
Fission




          42
Nuclear Fusion




                 43
            Sun’s Power Output

Unit of Power
  1 Watt = 1 Joule/second
  100 Watt light bulb = 100 Joules/second

 Sun’s power output
   3.826 x 1026 Watts
   exercise: calculate sun’s power output
   using Stefan-Boltzmann law (assume sun
   is a black body)

                                             44
The Proton-Proton Cycle            1H + 1H → 2H + e+ + 
                                                  e+ + e- → g + g
                                   2H + 1H → 3He + g
1 pp collision in 1022 → fusion!
                                   3He   + 3He → 4He + 1H + 1H



                                                           4H → 4He




Deuterium creation 3He creation           4He   creation

                                                               45
Super Kamiokande: Solar Neutrinos


                   Solar neutrino




            Electron

                                    46
A Nearby Super-Giant




                       47
      Life of a 20 Solar Mass Super-Giant
 Hydrogen fusion
    ~ 10 million years
 Helium fusion
    ~ 1 million years
 Carbon fusion
    ~ 300 years
 Oxygen fusion
    ~ 9 months
 Silicon fusion
    ~ 2 days

                                                                     48
                 http://cassfos02.ucsd.edu/public/tutorial/SN.html
Supernova 1987A   Before




    After



                       49
                             Stardust

                                        Sir Fred Hoyle
                                        1915-2001




7.65 MeV above 12C ground state




                                                 50
           Stardust – II




                7.19 MeV
7.12 MeV


                           51
                      Summary
 nuclei made of protons and neutrons,
 held together by short-range strong nuclear force
 models describe most observed features,
     still being tweaked and modified
     to incorporate newest observations
 no full-fledged theory of nucleons yet
 development of nuclear theory based on
     QCD has begun
 nuclear fusion is the process of energy
     production of Sun and other stars
 we (solar system with all that’s in it)
     are made of debris from dying stars        52