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Hyperfine splitting of deuterium

  1. Jan 24, 2008 #1
    [SOLVED] Hyperfine splitting of deuterium

    1. The problem statement, all variables and given/known data
    Calculate the wavelength of the photon emitted under a hyperfine transition in the ground state (n=1) of deuterium. Deuterium is a proton and a neutron in the nucleus, but still one electron. The spin of deuterium is 1.

    2. Relevant equations

    H prime=(magnetic moment)* B-field

    mag moment of electron = (g-factor*e) / m_e
    mag moment of deuterium = (g-factor*e) / (2m_d) g-factor for deut = 1.71

    3. The attempt at a solution

    I was able to solve up to the part where you get the expectation values...something like <S^2 - S(d)^2 - S(e)^2>. [the S(e) and S(d) are spin of electron and deuterium, sorry it's hard to read]

    I dont know how to add the spins for the total spin vector though. My attempt at the spin states was this.

    m = 1+1/2
    m = 1/2
    m = -1/2
    m = -3/2

    So S can be any of these values time hbar, and S^2 is hbar^2 *m(m+1)
    Last edited: Jan 24, 2008
  2. jcsd
  3. Jan 25, 2008 #2


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    Use clebsh gordan tables.
  4. Jan 25, 2008 #3
    Thank you i will try to make some sense of that thing!
  5. Jan 25, 2008 #4
    S= 3/2 and 1/2
    Last edited: Jan 25, 2008
  6. Jan 25, 2008 #5


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    You need s.S for s= spin 1/2 and S= spin 3/2.
    Since J=s+S, you get 2s.S=J^2-S^2-s^2=j(j+1)-2-3/2.
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