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Line 100: |
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| <math> | | <math> |
− | \langle \Omega_X 0 \lambda_{b_1} | U_X | J_X m_X \rangle | + | \langle \Omega_{b_1} 0 \lambda_{b_1} | U_X | J_X m_X \rangle |
| =\sum_{L_X} | | =\sum_{L_X} |
| \left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_X,0) \right] | | \left[ \sqrt{\frac{2J_X+1}{4\pi}} D_{m_X \lambda_{b_1}}^{J_X *}(\Omega_X,0) \right] |
Line 113: |
Line 113: |
| | | |
| <math> | | <math> |
− | \langle \Omega_{b_1} 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle | + | \langle \Omega_\omega 0 \lambda_\omega | U_{b_1} | 1 , m_{b_1}=\lambda_{b_1} \rangle |
| =\sum_{L_{b_1}} | | =\sum_{L_{b_1}} |
| \left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1}=\lambda_{b_1} \lambda_\omega}^{1 *}(\Omega_{b_1},0) \right] | | \left[ \sqrt{\frac{2J_{b_1}+1}{4\pi}} D_{m_{b_1}=\lambda_{b_1} \lambda_\omega}^{1 *}(\Omega_{b_1},0) \right] |
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Line 122: |
| \end{array}\right) | | \end{array}\right) |
| \right] | | \right] |
− | b_{L_{b_1}} | + | b_{L_{b_1}}^1 |
| </math> | | </math> |
| | | |
| <math> | | <math> |
− | \langle \Omega_\omega 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle | + | \langle \Omega_\rho 0 \lambda_\rho | U_\omega | 1 , m_\omega=\lambda_\omega \rangle |
| =\sum_{L_\omega J_\rho} | | =\sum_{L_\omega J_\rho} |
| \left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega=\lambda_\omega \lambda_\rho}^{1 *}(\Omega_\omega,0) \right] | | \left[ \sqrt{\frac{2J_\omega+1}{4\pi}} D_{m_\omega=\lambda_\omega \lambda_\rho}^{1 *}(\Omega_\omega,0) \right] |
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Line 135: |
| \end{array}\right) | | \end{array}\right) |
| \right] | | \right] |
− | c_{L_\omega J_\rho} | + | c_{L_\omega J_\rho}^1 |
| </math> | | </math> |
| | | |
| <math> | | <math> |
− | \langle \Omega_\rho 0 \lambda_\rho | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle | + | \langle \Omega_{\pi^+} 0 \lambda_\rho | U_\rho | J_\rho , m_\rho=\lambda_\rho \rangle |
| =\sum_{L_\rho} | | =\sum_{L_\rho} |
| \left[ \sqrt{\frac{2J_\rho+1}{4\pi}} D_{m_\rho 0}^{J_\rho *}(\Omega_\rho,0) \right] | | \left[ \sqrt{\frac{2J_\rho+1}{4\pi}} D_{m_\rho 0}^{J_\rho *}(\Omega_\rho,0) \right] |
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Line 149: |
| \right] | | \right] |
| d_{L_\rho} | | d_{L_\rho} |
− | =\sum_{L_\rho} | + | =Y_{m_\rho}^{J_\rho *}(\Omega_\rho) |
− | \sqrt{\frac{2L_\rho+1}{4\pi}}
| + | f_{J_\rho}^{J_\rho} |
− | Y_{m_\rho}^{J_\rho *}(\Omega_\rho) | |
− | d_{L_\rho}
| |
| </math> | | </math> |
| | | |
| + | * change subscripts on \Omega (e.g. X->b1) |
| + | * don't write m=lambda redundantly |
| + | * be consistent about indexing of known spins |
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