Nuclear models
Download
1 / 33

Nuclear Models - PowerPoint PPT Presentation


  • 140 Views
  • Updated On :

Nuclear Models. Nuclear force is not yet fully understood. No absolutely satisfying model, but models. Specific experimental data  specific model. Model  success in a certain range. Some are: Individual particle model. (No interaction, E. states, static properties, …).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Nuclear Models' - kimn


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Nuclear models l.jpg
Nuclear Models

  • Nuclear force is not yet fully understood.

  • No absolutely satisfying model, but models.

  • Specific experimental data  specific model.

  • Model  success in a certain range.

  • Some are:

    • Individual particle model.(No interaction, E. states, static properties, …).

    • Liquid drop model.(Strong force, B.E., Fission, …).

    • Collective model.

    • -particle model.

    • Optical model.

    • Fermi Gas model.

    • others …..

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


Shell model l.jpg
Shell model

  • Electron configuration….

    • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 ….

  • AtomicElectron magic numbers: 2, 10, 18, 36, 54,…

    • Common center of “external” attraction.

    • Well understood Coulomb force.

    • One kind of particles.

    • Clear meaning for electron orbits.

  • Nuclearmagic numbers: 2, 8, 20, 28, 50, 82,126, …

  • (for Z or N).

  • Chemistry!

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model3 l.jpg
    Shell model

    • Evidence:

    • End of radioactive series:

      • thorium series 208Pburanium series 206Pbactinium series 207Pbneptunium series 209Bi

  • At Z and N mn’s there are relatively large numbers of isotopes and isotones.

  • Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model4 l.jpg
    Shell model

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model5 l.jpg
    Shell model

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model6 l.jpg
    Shell model

    • Natural abundances.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model7 l.jpg
    Shell model

    • Neutron capture cross section.

    NEUTRON CAPTURE

    CROSS SECTION

    NEUTRON NUMBER

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model8 l.jpg
    Shell model

    • Binding energy of the last neutron

    • (Separation Energy).

    • (The measured values are plotted relative to the calculations without ).

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model9 l.jpg
    Shell model

    • Excited states.

    Pb (even-A) isotopes.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model10 l.jpg
    Shell model

    All are even-even.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model11 l.jpg
    Shell model

    • Quadrupole moments ….. ?

    HW 22

    Work out more examples for the above evidences. For example, take part of a plot and work on a group of relevant nuclides.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model12 l.jpg
    Shell model

    • Nucleons are in definite states of energy and angular momentum.

    • Nucleon orbit ?? Continuous scattering expected ..!!

    • No vacancy for scattering at low energy levels.

    • Potential of all other nucleons.

    • Infinite square well:

    • Harmonic oscillator:

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model13 l.jpg
    Shell model

    ?

    ?

    2(2l + 1)

    accounts correctly for the number of nucleons in each level.

    But what about magic numbers?

    ?

    Infinite spherical well

    (R=8F)

    Harmonic oscillator

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model14 l.jpg
    Shell model

    • More realistic! (Can it solve the problem?)

    • Finite square well potential:

    • Rounded well potential:

    • Correction for asymmetry and Coulomb repulsion.

    Adjusted by the separation energies.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model15 l.jpg
    Shell model

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model16 l.jpg
    Shell model

    HW 23

    Coulomb repulsion? Vc(r) = ??

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model17 l.jpg
    Shell model

    • Separation of variables:

    • For a given spherically symmetric potential V(r), the bound-state energy levels can be calculated from radial wave equation for a particular orbital angular momentum l.

    • Notice the important centrifugal potential.

    HW 24

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model18 l.jpg
    Shell model

    centrifugal potential

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Slide19 l.jpg

    ml

    ms

    • 2, 8, 20 ok.

    • What about other magic numbers?

    • Situation does not improve with other potentials.

    • Something very fundamental about the single-particle interaction picture is missing in the description…..!!!!!

    • Spin-orbit coupling.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model20 l.jpg
    Shell model

    • So far, 2(2l + 1) accounts correctly for the number of nucleons in each level, since we already considered both orbital angular momentum, and spin, but still not for closed shells.

    Separate.

    Spherical Harmonics, Eigenfunctions of L2 and Lz.

    But this representation does not solve the problem.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model21 l.jpg
    Shell model

    • Spin-Orbit Coupling

      • M. G. Mayer and independently Haxel, Jensen, and Suess.

      • Spin-Orbit term added to the Hamiltonian:

    Orientation

    No longer

    Spherically symmetric

    Central, attractive

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model22 l.jpg
    Shell model

    L

    S

    LL

    antiparallel

    UL

    parallel

    J

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model23 l.jpg
    Shell model

    2j+1

    2(2x3 + 1) = 14

    l = 3

    1f7/2

    j

    First time

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model24 l.jpg
    Shell model

    HW 25

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model25 l.jpg
    Shell model

    Notes:

    1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei.

    2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate.

    3. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l.

    4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core.

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model26 l.jpg
    Shell model

    Fermi Gas

    EF n2/3

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model27 l.jpg
    Shell model

    Nuclear reactions?

    Transition probability?

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model28 l.jpg
    Shell model

    Ground state:(near closed shells)

    1. Angular momentum of odd-A nuclei is determined by the angular momentum of the last nucleon that is odd.

    2. Even-even nuclei have zero ground-state spin, because the net angular momentum associated with even N and even Z is zero, and even parity.

    3. In odd-odd nuclei the last neutron couples to the last proton with their intrinsic spins in parallel orientation.

    Provided that the ordering is known….!!

    A < 150

    190 < A < 220

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model29 l.jpg
    Shell model

    Harmonic oscillator

    Near drip line

    No spin-orbit coupling

    Near valley of  stability

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).



    Shell model31 l.jpg
    Shell model 2007-2008 (Saed Dababneh).

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model32 l.jpg
    Shell model 2007-2008 (Saed Dababneh).

    • 17 p, 21 n.

    • p in 1d3/2l  s   = +

    • n in 1f7/2l  s   = -

    • Rule 3 sp  sn   lp  ln 

    • ½ + ½ + 3 – 2 = 2

     total  = -

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).


    Shell model33 l.jpg
    Shell model 2007-2008 (Saed Dababneh).

    Excited states:

    Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).