[Test] permutation factor

[mmikhasenko]

The claim is

h_ls^{k1,k2} = (-1)^{l+s-j1-j2} h_ls^{k2,k1}

it can be checked numerically

[mmikhasenko]

The difference only appears in interference, therefore the test should be checking the interference of the reference chain with that test chain that is being permuted.

I = |A1(ref) + A3|ˆ2

1. check that interference is not zero, e.g, #64 setup
2. Computed the intensity with the permuted chain3

I' = |A1(ref) + c * permute(A3)|ˆ2

where c is the symmetry factor from the header. Is I equal to I'?

3. modify spin, quantum numbers, make sure that both c positive and negative are covered. See if the identity always true.

[mmikhasenko]

There is a chance that it works :-)

I've looked at the same exercise with DPD. It's a but tricky to figure out either pi, or -pi appears for the aligned confuguration if one starts messing up with the order.

for the records, what I get is

(-1)^{j-l-s} * # from Clebsch
 (-1)^{j-lambda}*(-1)^{lambda} * # from D(theta_12)
 (-1)^{j1-lambda1}*(-1)^{lambda1} * # from WignerD: I did not get exactly this, because of +- pi complications
 (-1)^{j2-lambda2}*(-1)^{lambda2} * # from WignerD: I guess this 

If I guess right, the product gives exactly (-1)^{l+s-j1-j2}

[KaiHabermann]

Im working on it, but cant quite show the desired result yet. The interference does not properly match yet