1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Nuclear Shell Model - Spin-parity

  1. Feb 10, 2008 #1
    I am confused how to determine the spin / parity of excited states.

    In my textbook, one of the questions states:

    ------------------------------

    The ground state of the radioisotope 17-F-9 has spin-parity j_P = (5/2)+ and the first excited state has j_P=(1/2)-. Suggest two possible configurations for the latter state.

    -------------------------------

    Here is the answer in the back:

    The configuration of the ground state is:

    protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2(1d_\frac{5}{2})[/tex]
    neutrons:[tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2[/tex]

    To get j_P= (1/2)-, one could promote a p_1/2 proton to the d_5/2 shell giving

    protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^{-1}(1d_\frac{5}{2})^2[/tex]

    Then by the pairing hypothesis, the two d_5/2 protons could give j_P = 0+ so that the total spin-parity would be determined by the unpaired p_1/2 neutron (j_P=(1/2)-).

    Alternatively, one of the p_3/2 protons could be promoted to the d_5/2 shell, giving

    protons: protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^{-1}(1p_\frac{1}{2})^2(1d_\frac{5}{2})^2[/tex]

    and the two d_5/2 protons could combine to give j_P = 2+, so that when this combines with the single unpaired j_P = 3/2- proton, the overall spin is j_P = 1/2-

    -----------------------

    So here are two things I am confused about:

    Firstly, how can the two d_5/2 protons combine to have j_P = 0+ in the first case and j_P = 2+ in the second case?

    Secondly, how is it that in the second case, the spin-parity ends up being j_P = 1/2-. Is it that the parities of the two are multiplied (ie the parity of the two d_5/2 protons is 1+ and the parity of the unpaired p_3/2 proton is 1-, giving an overall parity of 1-, and then the spin is 2 - 3/2 = 1/2? I don't really get how that works).

    If I can understand this I may be able to even get started on the homework.
     
  2. jcsd
  3. Feb 11, 2008 #2

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    This has been posted twice, not ok!

    Yes parties are multiplied.

    And according to angular momenta addition , you can combine two J = 5/2 to a total J by anything from 0 to 5.
     
  4. Feb 11, 2008 #3
    Sorry about the 2x post. I posted here first, and then figured this might not be quite suitable in the homework forum.

    Thanks for the answer though.
     
  5. Feb 11, 2008 #4

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    there are people that moves threads etc. So next time, just dont do anything.
     
  6. Feb 11, 2008 #5
    One further question for this example:

    Since the resulting j_P = 2+ and j_P = 3/2- can result in (2-3/2)=(1/2)-, does that mean they can result in the range (5/2)- to (1/2)- ?
     
  7. Feb 11, 2008 #6

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    I dont understand you here. A single particle can not have an integer spin in the shell model.
     
  8. Feb 11, 2008 #7
    What I meant is, can it have either (5/2)-, (3/2)- or (1/2)- ?
     
  9. Feb 11, 2008 #8

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    Coupling angular momenta j1 = 2 with j2 = 3/2 can give you:

    7/2, 5/2, 3/2, 1/2

    Parity is negative, since +*- = -
     
  10. Feb 11, 2008 #9
    Alright, thanks again.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Nuclear Shell Model - Spin-parity
  1. Nuclear Shell Model (Replies: 10)

  2. Nuclear shell model (Replies: 10)

Loading...