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Jun 29, 2020 at 18:11 comment added ZeroTheHero Yeah I don' have Jutsis with me but it's an extremely good reference, and I would not be surprised if you could express your overlap as a sum of 6j's.
Jun 29, 2020 at 18:00 comment added 081N I'm asking if 1. and 2. (each one separately) can be expressed in terms of 9-j symbols. Looking to Yutsis' graphs I think 1. and 2. can be expressed as 6-j symbols as they can be seen as recoupling of three angular momentum (I'll post a more detailed description). As you said you have some contrains in building the 9-j coefficient and at first glance it seems not possible with the coupling chosen.
Jun 29, 2020 at 17:40 answer added ZeroTheHero timeline score: 2
Jun 29, 2020 at 16:38 comment added ZeroTheHero what do you mean by "relate the scheme"? Are you asking if 1. and 2. can be expressed in terms of standard 9-j symbols or are you asking if one can define this overlap, compute from the get-go, and figure out if the resulting symbols as 9-j-like properties?
Jun 29, 2020 at 13:39 comment added 081N I think that since this can be seen as a recoupling of three of the four angular momentum (where two terms are of the type $j$ and one of the type $J_{i,k}$), the wigner's coefficient between these two coupling schemes reduces to Wigner's 6-j symbol.
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