[1208] | 1 | \section{Fission probability calculation.} |
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| 2 | |
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| 3 | \hspace{1.0em}The fission decay channel (only for nuclei with $A > 65$) |
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| 4 | is taken into account as a competitor for fragment and photon evaporation |
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| 5 | channels. |
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| 6 | |
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| 7 | \subsection{The fission total probability.} |
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| 8 | |
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| 9 | \hspace{1.0em}The fission probability (per unit time) $W_{fis}$ |
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| 10 | in the Bohr |
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| 11 | and Wheeler theory of fission \cite{BW39} is proportional to the level |
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| 12 | density $\rho_{fis}(T)$ ( approximation Eq. ($\ref{evap:6}$) is used) at |
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| 13 | the saddle point, i.e. |
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| 14 | \begin{equation} |
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| 15 | \begin{array}{c} |
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| 16 | \label{FP1}W_{fis}=\frac{1}{2\pi \hbar \rho_{fis} |
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| 17 | (E^{*})}\int_{0}^{E^{*}-B_{fis}} |
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| 18 | \rho_{fis}(E^{*}-B_{fis}-T)dT =\\ |
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| 19 | =\frac{1 + (C_f - 1)\exp{(C_f)}}{4\pi a_{fis} \exp{(2\sqrt{aE^{*}})}}, |
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| 20 | \end{array} |
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| 21 | \end{equation} |
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| 22 | where |
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| 23 | $B_{fis}$ is the fission barrier height. |
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| 24 | The value of $C_f = 2\sqrt{a_{fis}(E^{*} - B_{fis})}$ and $a$, $a_{fis}$ are |
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| 25 | the level density parameters of the compound and of the fission saddle point |
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| 26 | nuclei, respectively. |
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| 27 | |
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| 28 | The value of the level density parameter is large at the saddle point, |
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| 29 | when excitation energy is given by initial excitation energy minus the |
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| 30 | fission barrier height, than in the ground state, i. e. $a_{fis} > a$. |
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| 31 | $a_{fis} = 1.08 a$ for $Z < 85$, $a_{fis} = 1.04 a$ for $Z \geq 89$ and |
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| 32 | $a_f=a[1.04+0.01(89.-Z)]$ for $85 \leq Z < 89$ is used. |
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| 33 | |
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| 34 | \subsection{The fission barrier.} |
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| 35 | |
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| 36 | \hspace{1.0em} |
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| 37 | The fission barrier is determined as difference |
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| 38 | between the saddle-point and |
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| 39 | ground state masses. |
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| 40 | |
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| 41 | We use simple semiphenomenological |
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| 42 | approach was suggested by Barashenkov and Gereghi \cite{Barash73}. In their |
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| 43 | approach fission barrier $B_{fis}(A,Z)$ is approximated by |
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| 44 | \begin{equation} |
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| 45 | \label{FP2} B_{fis} = B^{0}_{fis} + \Delta_g + \Delta_p. |
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| 46 | \end{equation} |
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| 47 | The fission barrier height $B^{0}_{fis}(x)$ |
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| 48 | varies with the fissility parameter $x = Z^2/A$. $B^{0}_{fis}(x)$ is |
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| 49 | given by |
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| 50 | \begin{equation} |
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| 51 | \label{FP3} B^{0}_{fis}(x) = 12.5 + 4.7 (33.5 -x )^{0.75} |
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| 52 | \end{equation} |
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| 53 | for $x \leq 33.5$ and |
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| 54 | \begin{equation} |
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| 55 | \label{FP4} B^{0}_{fis}(x) = 12.5 - 2.7 (x - 33.5)^{2/3} |
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| 56 | \end{equation} |
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| 57 | for $x > 33.5$. The $\Delta_g = \Delta M(N) + \Delta M(Z)$, where |
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| 58 | $\Delta M(N)$ and $\Delta M(Z)$ are shell corrections for Cameron's |
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| 59 | liquid drop mass formula \cite{CAM57} and the pairing energy |
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| 60 | corrections: $ \Delta_p = 1$ for odd-odd nuclei, $ \Delta_p = 0$ for |
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| 61 | odd-even nuclei, $ \Delta_p = 0.5$ for even-odd nuclei and $ \Delta_p = |
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| 62 | -0.5$ for even-even nuclei. |
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| 63 | |
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| 64 | |
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| 65 | %%% Local Variables: |
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| 66 | %%% mode: latex |
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| 67 | %%% TeX-master: t |
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| 68 | %%% End: |
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