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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