Preequilibrium emission of photonucleons and the method of quantum Green's functions

It is shown that for $E_{\gamma}\le 50$ MeV, the $T_{\gamma N}$ matrix of the reaction $(\gamma,N)$ can be expressed in terms of the vector vertex $\tau [n+1]$: $\tau_{\gamma}[n+1]=V_{\gamma}GG\Gamma_{2,n+1}$ where $V_{\gamma}$ is the vertex of noninteracting nucleons with respect to the field of the gamma quantum, and $\Gamma_{2,n+1}$ is the full vertex part (total interaction amplitude). We obtain the renormalized equations for $\Gamma_{2,n+1}$, which contain the products of polar single-particle Green's functions G and the effective interactions amplitudes $\Gamma_{2,n+1}$. The T matrix of the reaction $(\gamma,N)$ can be decomposed into two parts. One part describes a direct multistep nuclear photoeffect (without formation of the compound nucleus), and the other part describes a resonant multistep nuclear photoeffect (via intermediate states of the compound nucleus). After statistical averaging, we obtain expressions for $|T_N|^2$ which describe a $(\gamma,N)$ reaction for the energies of the gamma quanta $E \le 50$ MeV.