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Spectroscopy Cheat Sheet. Atomic Spectroscopy. • Energy of hydrogen atom ... Vibrational Spectroscopy. • Anharmonic (Morse) Oscillator energies.
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En =
Z^2 ħ^2 2 μ a^2 μ
n^2
a μ =
4 π≤ 0 ħ^2 μ e^2
me μ
a 0 (2)
n^2
〈r〉 = a μ n^2 (1 + (1 − l(l + 1)/n^2 )/2) (4)
1/r^3
and the nuclear charge Z, so overall you would expect SO coupling to be proportional to Z^4. In fact 〈 1 r^3
a^3 μ n^3 l(l + 1)(2l + 1)
gJ = 1 +
En = ħ ω e(n + 1/2) − ħ ω e xe(n + 1/2)^2 (15)
xe =
ħ ω e 4 De