===== 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<sub>2</sub> example is used, in which //S// = 1/2, //I//<sub>N</sub> = 1, and //I//<sub>H</sub> = 1/2 for both H nuclei and **N** + **S** = **J**; **J** + **I**<sub>N</sub> = **F**<sub>1</sub>; **I**<sub>H1</sub> + **I**<sub>H2</sub> = **I**<sub>tot</sub>; and **F**<sub>1</sub> + **I**<sub>tot</sub> = **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<sub>2</sub> as an example or one spin of 1, one spin of 1/2 and two equivalent spins of 1/2 with <sup>13</sup>CH<sub>2</sub> as an example.

<code>
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
</code>
**TSP** is the aggregate spin number, here 0. Subsequently, //N// and the other quanta (//J//, //F//<sub>1</sub>, and //I//<sub>tot</sub>) are given **relative to //F// = 0**.\\
If we take, for example, line number 12:

<code>
  3  3  1  0  0  6  4  1  3  0  0  7   11686.80
</code>
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//<sub>1</sub> = 4.5, and finally //I//<sub>tot</sub> = 1.0 is redundant.\\
Similarly for the upper state: //N// = 4, hence //F// = 6.5, //J// = 4.5, //F//<sub>1</sub> = 5.5, and finally //I//<sub>tot</sub> = 1.0 is again redundant.\\
For **TSP** = 1 we find:

<code>
    2    1    1    0    1  -1.5  -1.0   0.0   0.0
</code>
For example in line 21 there is **TSP** = 1 twice:

<code>
  5  2  3  0  1  7  6  1  6  0  1  8    8749.68
</code>
For the upper and lower state, respectively:\\
//N// = 5, //N// = 5.5, //F//<sub>1</sub> = 6.5, //I//<sub>tot</sub> = 0.0, and //F// = 6.5.\\
//N// = 6, //N// = 6.5, //F//<sub>1</sub> = 7.5, //I//<sub>tot</sub> = 0.0, and //F// = 7.5.

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