On the Coding of the Aggregate Spin Number
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. 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.
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.