- #1
erwinscat
- 7
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Hello all ! I was trying to solve the following problem : you have a particle with spin J=1 and unknown parity that decays into 2 indentical particles of spin = 1/2
We want to know how much the angular momentum of the final state is and also the final total spin.
Now, my reasonment was the following.
Stot_final = either 0 or 1 since it is the vector sum of the spin of both identical final particles.
Knowing that |L-S|<=J<= L+S we have to cases but I assumed that J=1 is conserved in the decay but it wasn't told so ...
we would have
for S=0 => L= 1
for S=1 => L= (0,1,2)
knowing that the final particles are indentical they must have a antisymmetric wave function due to Fermi Dirac...and so L must be odd . => L=1
but we still have to cases (S,L)= (0,1) or (1,1) if J=1 was to be conserved I'd say th only possible is (0,1) but the solutions say the only possibile solution knowing that J=1 is (1,1) ..
Conclusion, I don't know where I'm mistaking !
Any help would be appreciated ! Maybe I shouldn't assume that J was conserved...
Thanks in advance !
Erwin
We want to know how much the angular momentum of the final state is and also the final total spin.
Now, my reasonment was the following.
Stot_final = either 0 or 1 since it is the vector sum of the spin of both identical final particles.
Knowing that |L-S|<=J<= L+S we have to cases but I assumed that J=1 is conserved in the decay but it wasn't told so ...
we would have
for S=0 => L= 1
for S=1 => L= (0,1,2)
knowing that the final particles are indentical they must have a antisymmetric wave function due to Fermi Dirac...and so L must be odd . => L=1
but we still have to cases (S,L)= (0,1) or (1,1) if J=1 was to be conserved I'd say th only possible is (0,1) but the solutions say the only possibile solution knowing that J=1 is (1,1) ..
Conclusion, I don't know where I'm mistaking !
Any help would be appreciated ! Maybe I shouldn't assume that J was conserved...
Thanks in advance !
Erwin