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Universität zu Köln
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Mathematisch-Naturwissenschaftliche Fakultät
Fachgruppe Physik

I. Physikalisches Institut

On the Coding of the Aggregate Spin Number

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The aggregate spin number is used in the SPFIT and SPCAT programs whenver more than six quantum numbers are needed to descibe a state – even if some of the quantum numbers are redundant. It can be decoded using information provided in the .fit file or the .out file after the list of parameters in both cases. The NH2 example is used, in which S = 1/2, IN = 1, and IH = 1/2 for both H nuclei and N + S = J; J + IN = F1; IH1 + IH2 = Itot; and F1 + Itot = F.

Please note: The coding will be the same for equivalent spin combinations, meaning one spin of 1/2, one spin of 1, and two equivalent spins of 1/2. The coding will be different for other spin combinations, e. g. two spins of 1/2 and two equivalent spins of 1/2 with PH2 as an example or one spin of 1, one spin of 1/2 and two equivalent spins of 1/2 with 13CH2 as an example.

BLOCK - WT - SYM - V - TSP - N  -  other quanta  (rel. to F=0 )
    1    1    0    0    0  -2.5  -2.0  -1.0   1.0

TSP is the aggregate spin number, here 0. Subsequently, N and the other quanta (J, F1, and Itot) are given relative to F = 0.
If we take, for example, line number 12:

  3  3  1  0  0  6  4  1  3  0  0  7   11686.80

we see that for the upper state we have N = 3, hence F = 3 + 2.5 = 6 – 0.5 = 5.5, J = 3.5, F1 = 4.5, and finally Itot = 1.0 is redundant.
Similarly for the upper state: N = 4, hence F = 6.5, J = 4.5, F1 = 5.5, and finally Itot = 1.0 is again redundant.
For TSP = 1 we find:

    2    1    1    0    1  -1.5  -1.0   0.0   0.0

For example in line 21 there is TSP = 1 twice:

  5  2  3  0  1  7  6  1  6  0  1  8    8749.68

For the upper and lower state, respectively:
N = 5, N = 5.5, F1 = 6.5, Itot = 0.0, and F = 6.5.
N = 6, N = 6.5, F1 = 7.5, Itot = 0.0, and F = 7.5.