 \prod_{\alpha=c,s} {\hat{L}}^{\alpha\iota}_{-N_{ph}^{\alpha\iota}}(l)\right] \tilde{c}^{\dag }_{k_{F\sigma},\sigma }  \nonumber\\ & + & \sum_{\gamma '}\langle \gamma ';k=0|c^{\dag  }_{k_{F\sigma},\sigma }|0;i\rangle {\hat{A}}_{\gamma '} \tilde{c}^{\dag }_{