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gammaEmission.rst

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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 :program:`CGMF` (ver. |version|), only E1, E2, and M1 transitions are allowed, and higher multipolarity transitions are neglected.