source: trunk/documents/UserDoc/DocBookUsersGuides/PhysicsReferenceManual/latex/hadronic/theory_driven/Evaporation/FissionProbability.tex @ 1345

\section{Fission probability calculation.}

\hspace{1.0em}The fission decay channel (only for nuclei with $A > 65$)
is taken into account as a competitor for fragment and photon evaporation
channels.

\subsection{The fission total probability.}

\hspace{1.0em}The fission probability (per unit time) $W_{fis}$ 
in the Bohr
and Wheeler theory of fission \cite{BW39} is proportional to the level
density $\rho_{fis}(T)$ ( approximation Eq. ($\ref{evap:6}$) is used) at
the saddle point, i.e.
\begin{equation}
\begin{array}{c}
\label{FP1}W_{fis}=\frac{1}{2\pi \hbar \rho_{fis}
(E^{*})}\int_{0}^{E^{*}-B_{fis}}
\rho_{fis}(E^{*}-B_{fis}-T)dT =\\
=\frac{1 + (C_f - 1)\exp{(C_f)}}{4\pi a_{fis} \exp{(2\sqrt{aE^{*}})}},
\end{array}
\end{equation}
where 
 $B_{fis}$ is the fission barrier height.
The value of $C_f = 2\sqrt{a_{fis}(E^{*} - B_{fis})}$ and $a$, $a_{fis}$ are 
the level density parameters of the compound and of the fission saddle point
nuclei, respectively.

The value of the level density parameter is large at the saddle point,
when excitation energy is given by initial excitation energy minus the
fission barrier height, than in the ground state, i. e. $a_{fis} > a$.
$a_{fis} = 1.08 a$ for $Z < 85$, $a_{fis} = 1.04 a$ for $Z \geq 89$ and
$a_f=a[1.04+0.01(89.-Z)]$ for $85 \leq Z < 89$ is used.
 
\subsection{The fission barrier.}

\hspace{1.0em}
The fission barrier is determined as difference 
between the saddle-point and
 ground state masses. 

We use simple semiphenomenological 
approach was suggested by Barashenkov and Gereghi \cite{Barash73}. In their 
approach fission barrier $B_{fis}(A,Z)$ is approximated by 
\begin{equation}
\label{FP2} B_{fis} = B^{0}_{fis} + \Delta_g  + \Delta_p.
\end{equation}
The fission barrier height $B^{0}_{fis}(x)$
varies with the fissility parameter $x = Z^2/A$. $B^{0}_{fis}(x)$ is
given by
\begin{equation}
\label{FP3} B^{0}_{fis}(x) = 12.5 + 4.7 (33.5 -x )^{0.75}
\end{equation}
for $x \leq 33.5$ and
\begin{equation}
\label{FP4} B^{0}_{fis}(x) = 12.5 - 2.7 (x - 33.5)^{2/3}
\end{equation}
for $x > 33.5$.  The $\Delta_g = \Delta M(N) + \Delta M(Z)$, where
$\Delta M(N)$ and $\Delta M(Z)$ are shell corrections for Cameron's
liquid drop mass formula \cite{CAM57} and the pairing energy
corrections: $ \Delta_p = 1$ for odd-odd nuclei, $ \Delta_p = 0$ for
odd-even nuclei, $ \Delta_p = 0.5$ for even-odd nuclei and $ \Delta_p =
-0.5$ for even-even nuclei.


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