Gamma-Ray Emission Probabilities

The \(\gamma\)-ray transmission coefficients are obtained using the strength function formalism from the expression:

\[T^{Xl}(\epsilon_\gamma) = 2\pi f_{Xl}(\epsilon_\gamma)\epsilon_\gamma^{2l+1},\]

where \(\epsilon_\gamma\) is the energy of the emitted gamma ray, \(Xl\) is the multipolarity of the gamma ray, and \(f_{Xl}(\epsilon_\gamma)\) is the energy-dependent gamma-ray strength function.

For \(E1\) transitions, the Kopecky-Uhl generalized Lorentzian form for the strength function is used:

\[f_{E1}(\epsilon_\gamma,T) = K_{E1}\left[ \frac{\epsilon_\gamma \Gamma_{E1}(\epsilon_\gamma)}{\left( \epsilon_\gamma^2-E_{E1}^2\right)^2 + \epsilon^2_\gamma\Gamma_{E1}(\epsilon_\gamma)^2} +\frac{0.7\Gamma_{E1}4\pi^2T^2}{E_{E1}^5} \right] \sigma_{E1}\Gamma_{E1}\]

where \(\sigma_{E1}\), \(\Gamma_{E1}\), and \(E_{E1}\) are the standard giant dipole resonance (GDR) parameters. \(\Gamma_{E1}(\epsilon_\gamma)\) is an energy-dependent damping width given by

\[\Gamma_{E1}(\epsilon_\gamma) = \Gamma\frac{\epsilon_\gamma^2+4\pi^2T^2}{E_{E1}^2},\]

and \(T\) is the nuclear temperature given by

\[T=\sqrt{\frac{E^*-\epsilon_\gamma}{a(S_n)}}.\]

The quantity \(S_n\) is the neutron separation energy, \(E^*\) is the excitation energy of the nucleus, and \(a\) is the level density parameter. The quantity \(K_{E1}\) is obtained from normalization to experimental data on \(2\pi\langle \Gamma_{\gamma_0} \rangle / \langle D_0 \rangle\).

For \(E2\) and \(M1\) transitions, the Brink-Axel (Brink,1955) (Axel,1962) standard Lorentzian is used instead:

\[f_{Xl}(\epsilon_\gamma)=K_{Xl}\frac{\sigma_{Xl}\epsilon_\gamma\Gamma_{Xl}^2}{(\epsilon_\gamma^2-E_{Xl}^2)^2+\epsilon_\gamma^2\Gamma_{Xl}^2}.\]

In the current version of CGMF (ver. 0.1), only \(E1, E2\), and \(M1\) transitions are allowed, and higher multipolarity transitions are neglected.