Solving 3-Body System w/ Angular Momentum J=5/2

[stefano]

I have a problem to solve:
Suppose I have an orbital with angular momentum of single-particle J=5/2 (then M=+-5/2, +-3/2, +-1/2), and I have to write the ground-state of system with three particles.
To do this I have to couple the three angular momentum like J=j_1+j_2+j_3, in order to write eigenstates of J. I tried to do this but I didn't able to obtaine anti-symmetric wave-function (there would be some states, like J=5/2 all projections composed by two or three Slater's determinants).
Someone can help me by calculating this for me? Or someone know an utility or computer program to perform this calculations?

Thank's

 

[LightHero]

in advance!The ground state of a three-particle system with angular momentum J=5/2 can be written as a combination of Slater determinants with the following spin configurations:(5/2, -1/2, -1/2) (3/2, -3/2, 1/2) (1/2, -5/2, 3/2) The resulting wavefunction would be an antisymmetric combination of the three Slater determinants, which can be written as: Ψ = (1/√6) (|5/2, -1/2, -1/2> - |3/2, -3/2, 1/2> + |1/2, -5/2, 3/2>) If you wish to find a computer program to perform this calculation, there are several available options depending on your needs. Some examples include MOLPRO, GAMESS, and ORCA.