Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Isospin question

  1. Jun 23, 2007 #1

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    This is from Krane, p 389:

    The neutron and the proton are treated as two different states of a single particle, the nucleon. The nucleon is assigned with a fictious spin vector, called isospin.

    Nucleon has isospin number t = ½, a proton has [itex] m_{t} = 1/2[/itex] and neutron has [itex] m_{t} = - 1/2 [/itex].

    The isospin obeys the same rules for angular momentum vecotrs.

    The third component of a nucleus isospin is:
    [tex] T_{3} = \frac{1}{2} (Z-N) [/tex]

    For any value on [itex] T_{3} [/itex], the total isospin [itex] T [/itex] can take any value at least as great as [itex] |T_{3} | [/tex].

    We consider as an example the two-nucleon system, wich can have T of 0 or 1. There are thus four possible 3-axis components: [itex] T_{3} = 1[/itex](two protons); [itex] T_{3} = - 1[/itex](two neutrons), and two combinations with [itex] T_{3} = 0 [/itex](one neutron and one proton). The first two states must have T = 1, while the latter two can have T = 0 and T =1.

    - - -

    Now this is really confusing me. I am think that the according to the statement: For any value on " [itex] T_{3} [/itex], the total isospin [itex] T [/itex] can take any value at least as great as [itex] |T_{3} | [/tex]." The two proton system can therefore have T = 0 or 1. And the same thing regarding the 2N system.

    And also how can there be two combinations of P-N that gives [itex] T_{3} = 0 [/itex]? And why isn't just T = 0 allowed?

    Should I try to think "backwards": Given a value on T, what values of [itex] T_{3} [/itex] can I have, and what combinations of N and P do they represent?

    Cheers:rolleyes:
     
  2. jcsd
  3. Jun 23, 2007 #2

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    "The two proton system can therefore have T = 0 or 1. And the same thing regarding the 2N system."

    The two p system has T_3=+1, so T cannot equal zero.
    The two n system has T_3=-1, so T cannot equal zero.
     
    Last edited: Jun 23, 2007
  4. Jun 23, 2007 #3

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    T_3=0 can come from the two different combinations
    (pn+np)/sqrt{2} for T=1, and
    (pn-np)/sqrt{2} for T=0.
     
  5. Jun 24, 2007 #4

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    okay, I think I got it now. Thanx a lot dude! =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Isospin question
  1. Photon Isospin (Replies: 3)

  2. Isospin question (Replies: 6)

  3. Isospin asymmetry (Replies: 1)

  4. Decomposed isospin (Replies: 9)

Loading...