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 4
 Homework Statement
 Find the possible values of isospin, parity, charge conjugation, Gparity and totoal angular momentum J, up to J=2, for ##\rho^0 \rho^0## state
 Homework Equations

##(exchange) \psi_{space} = (parity) \psi_{space}##
##(exchange) \psi_{spin} = (1)^s for bosons##
##(exchange) \psi_{isospin} = (1)^s for bosons##
Hello everybody!
I have a problem with this exercise when I have to find the possible angular momentum.
Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange.
$$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} = (1)^l (1)^I (1)^s$$
Since I have still calculated that ##I = 0## or ##I = 2##:
$$(exchange)\psi_{\rho\rho} = (1)^{l+s}$$
To be symmetric ##\rightarrow## l+s must be even.
However, the solution of the exercise states that:
The two particles are identical bosons, hence l must be even (l=0, 2, 4, ...). The spin wave function must be symmetrical too, hence s=0, 2, 4, ...
This is different from my conclusion.
I'd like to ask you where is my mistake.
Thanks in advance!
I have a problem with this exercise when I have to find the possible angular momentum.
Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange.
$$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} = (1)^l (1)^I (1)^s$$
Since I have still calculated that ##I = 0## or ##I = 2##:
$$(exchange)\psi_{\rho\rho} = (1)^{l+s}$$
To be symmetric ##\rightarrow## l+s must be even.
However, the solution of the exercise states that:
The two particles are identical bosons, hence l must be even (l=0, 2, 4, ...). The spin wave function must be symmetrical too, hence s=0, 2, 4, ...
This is different from my conclusion.
I'd like to ask you where is my mistake.
Thanks in advance!