Particle Octet: Explaining No Spin 1/2 Particles

[lark]

Would anyone like to tell me if I did this right? see attached .gif. It's an exercise in a book I'm reading, about explaining why there aren't any spin 1/2 particles with uuu, ddd, or sss quarks, 1 each of uud, uus, etc., and 2 of uds quarks: the particle octet.
Laura

 

[pam]

I can't make out the thumbnail or make sense of it.
You can't have three u quarks in a spin 1/2 state, because the spin 1/2 state has mixed symmetry, and only purely symmetric states are allowed for three identical quarks in a completely symmetric spatial state.

 

[nrqed]

Would anyone like to tell me if I did this right? see attached .gif. It's an exercise in a book I'm reading, about explaining why there aren't any spin 1/2 particles with uuu, ddd, or sss quarks, 1 each of uud, uus, etc., and 2 of uds quarks: the particle octet.
Laura

The first statement makes no sense. You say that quarks follow Bose statistics even though they are fermions!

Of course they follow Fermi-Dirac statistics!
But it's a bit complicated because the total wavefunction has a spin dependence, a spatial dependence but a colour dependence as well. All this must be taken into account.

 

[lark]

The first statement makes no sense. You say that quarks follow Bose statistics even though they are fermions

That exercise is before the book talks about color, it just says the quarks (appear to) follow boson statistics.

Other than that, which is kind of a minor point, does anyone have any comments? Are the wavefunctions for the particles with uds quarks right? That was mostly what I was asking about, because I just came up with a couple of wavefunctions that are linearly independent and look nice and symmetrical.

Laura