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Nuclear Magnetic Moments - Oxygen 15

  1. Oct 31, 2016 #1
    1. The problem statement, all variables and given/known data
    I am trying to calculate the nuclear magnetic moment for Oxygen 15 but my answer differs strongly from the value quoted in literature.

    2. Relevant equations


    3. The attempt at a solution

    ##\mu_J = g_J \mu_N J##

    This isotope of Oxygen has an unpaired Neutron with ##J = \frac{1}{2}##.

    Calculating the nuclear g-factor for ##J = l + \frac{1}{2}##

    ##g_J = g_l (1 - \frac{1}{2J}) + g_s(\frac{1}{2J})##

    For a neutron ##g_l = 0## and so in this case ##g_J = g_s = -3.82##

    I therefore find that ##\mu_J = -1.91 \mu_N## which is significantly different from the value I find in the NIST table of ##\pm 0.7189 \mu_N##

    http://nist.gov/data/PDFfiles/jpcrd85.pdf

    Is my treatment too simplistic to get a decent prediction, or am I making a fundamental error?

    Thanks for reading!
     
  2. jcsd
  3. Oct 31, 2016 #2
    I think I have found my mistake.

    My case is for J = L - S, with L = 1.

    My g-factor is therefore ##g_J = g_l (1 + \frac{1}{2l + 1}) - g_s (\frac{1}{2l + 1})##, with ##g_l = 0##

    I find that ##g_J = -0.63 \mu_N## which is much closer to my expected value.

    Sorry for posting prematurely.
     
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