Harmonic Oscillator with fermions

[milesAhead]

Hello...
We have 3 fermions (s=1/2) at the ground state of a harmonic oscillator moving over the x-axis with a the classic hamiltonian for a three particle oscillator :
H =(1/2m)*(P1)^2 +((1/2)*m(w^2)((x1)^2)) +(1/2m)*(P2)^2 +((1/2)*m(w^2)((x2)^2)) +(1/2m)*(P3)^2 +((1/2)*m(w^2)((x3)^2))

we have a pertubation between fermions that is:
W=g*m*((w^2)/h)*(S1z*x2*x3+S2z*x3*x1+S3z*x1*x2).

And it is asked the chande of the ground state's energy due to the pertubation.

 

[milesAhead]

With S1z,S2z,S3z the spin (z) of each fermion