- #1
hgandh
- 27
- 2
A pair of non-interacting particles can be described by the state vector:
\begin{equation}
\Psi_{p_1,\sigma_1,p_2,\sigma_1, t_1, T_1, t_2, T_2}
\end{equation}
Where T is the isospin and t is the 3rd-component. The parity of this state is the product of the intrinsic parities of the two particles. Now, we do a change of basis:
\begin{equation}
\Psi_{p_1,\sigma_1,p_2,\sigma_1, t_1, T_1, t_2, T_2} \Rightarrow \Psi_{E, p, j, \sigma, l, t, s, T}
\end{equation}
Where E is the total energy, p is the total momentum, j is the total angular momentum, l is the orbital angular momentum, sigma is the total angular momentum 3-component, s is the total spin, and t, T are the total isospin. My question is, how would we describe parity in this basis? Obviously the it must equal the product of the intrinsic parities of the two particles. Would the parity in this basis be
\begin{equation}
(-1)^{l}\eta_T
\end{equation}
Where [tex] \eta_T [/tex] is the intrinsic parity corresponding to isospin T? Or is this completely wrong?
\begin{equation}
\Psi_{p_1,\sigma_1,p_2,\sigma_1, t_1, T_1, t_2, T_2}
\end{equation}
Where T is the isospin and t is the 3rd-component. The parity of this state is the product of the intrinsic parities of the two particles. Now, we do a change of basis:
\begin{equation}
\Psi_{p_1,\sigma_1,p_2,\sigma_1, t_1, T_1, t_2, T_2} \Rightarrow \Psi_{E, p, j, \sigma, l, t, s, T}
\end{equation}
Where E is the total energy, p is the total momentum, j is the total angular momentum, l is the orbital angular momentum, sigma is the total angular momentum 3-component, s is the total spin, and t, T are the total isospin. My question is, how would we describe parity in this basis? Obviously the it must equal the product of the intrinsic parities of the two particles. Would the parity in this basis be
\begin{equation}
(-1)^{l}\eta_T
\end{equation}
Where [tex] \eta_T [/tex] is the intrinsic parity corresponding to isospin T? Or is this completely wrong?