Mach 6 Science
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Calculating degeneracy

Calculating degeneracy

@(QCT)

nuclear degneracy:

  • atom: 2I+1 data for I nuclear spin number
  • molecule:
    • totoal degeneracy: (2I_1+1)(2I_2+1)
    • for homonuclear molecule: I(2I+1) antisymmetric, (I+1)(2I+1) symmetric

examples:
+ N: I=1,\, g_N=2I+1=3
+ N_2: 3 antisymmetric, 6 symmetric
+ NO: I_1=1, I_2=0, 3\times1=3

electronic degeneracy:

  • atom: \Sigma_J(2J+1),\, J=|L-S|...L+S
  • molecule: ^{2S+1}\Lambda_\Omega, \phi=1 for \Omega=0=\Sigma \phi= 2 for \Omega=1,2,..=\Pi,\Delta,.... Total degeneracy = (2S+1)\phi=\Sigma_{\Omega}(2S+1)

examples:
+ N: \, ^4S \quad S=3/2,\, L =0,\, J=3/2 \quad g_{elec}=4
+ O: \, ^3P \quad S=1,\, L =1, \, J=0,1,2 correspond to ^3P_0(227cm^{-1})\; ^3P_1(158.3cm^{-1})\; ^3P_2(0cm^{-1})\quad g_{elec}=5(base)+3+1, temperature difference|^3P_2-^3P_1|=227.76K, |^3P_2-^3P_0|=326.6K then we can get the degeneracy function g_{elec}=5+3exp(-227.76/T)+exp(-326.6/T)
+ O_2:\, X^3\Sigma\, S=1,\,J=2,\, g_{elec}=3
+ N_2:\, X^1\Sigma\, S=0, \, J=1,\, g_{elec}=1
+ NO :\,X^2\Pi\,: S=1/2\,\Lambda=1,\,\Omega=1/2,3/2 similarly, ^2\Pi_{1/2}=0K,\, ^2\Pi_{3/2}=174.237K g_{elec}=2+2exp(-174.237/T)

rotational degeneracy 2J+1:

  • homonuclear molecule: should consider bosons or ferminus for symmetry or asymmetric
  • heteronuclear molecule: just sum all

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