# 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.