- #1

Aleolomorfo

- 73

- 4

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

- Relevant 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:

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!