## 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 NH_{2} example is used, in which *S* = 1/2, *I*_{N} = 1, and *I*_{H} = 1/2 for both H nuclei and **N** + **S** = **J**; **J** + **I**_{N} = **F**_{1}; **I**_{H1} + **I**_{H2} = **I**_{tot}; and **F**_{1} + **I**_{tot} = **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 PH_{2} as an example or one spin of 1, one spin of 1/2 and two equivalent spins of 1/2 with ^{13}CH_{2} 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*, *F*_{1}, and *I*_{tot}) 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, *F*_{1} = 4.5, and finally *I*_{tot} = 1.0 is redundant.

Similarly for the upper state: *N* = 4, hence *F* = 6.5, *J* = 4.5, *F*_{1} = 5.5, and finally *I*_{tot} = 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, *F*_{1} = 6.5, *I*_{tot} = 0.0, and *F* = 6.5.

*N* = 6, *N* = 6.5, *F*_{1} = 7.5, *I*_{tot} = 0.0, and *F* = 7.5.

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