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Description
The $\beta$-transition probability is proportional to the product of the lepton part described by the Fermi function $f( \textit{Q}_{\beta} - E)$ and the nucleon part described by the $\beta$-decay strength function $S_{\beta}(\textit{E})$, where $E$ is the excitation energy in daughter nuclei and $ \textit{Q}_{\beta}$ is the total energy of $\beta$-decay.
The previously dominant statistical model assumed that there were no resonances in $S_{\beta}(\textit{E})$ in $\textit{Q}_{\beta}$-window and the relations $S_{\beta}(\textit{E})=Const$ or $S_{\beta}(\textit{E})\sim\rho(E)$, where $\rho(E)$ is the level density of the daughter nucleus, were considered to be a good approximations for medium and heavy nuclei for excitation energies $E > 2\div3 MeV$. The effect of the non-statistical resonance structure of the $S_{\beta}(\textit{E})$ on the probability of delayed fission was first investigated in [1]. Then the method developed in [1] for the description of delayed processes by considering the $S_{\beta}(\textit{E})$ structure was used to analyze delayed fission of a wide range of nuclei [2–6]. Ideas about the non-statistical structure of the strength functions $S_{\beta}(\textit{E})$ have turned out to be important for widely differing areas of nuclear physics [4].
When studying delayed fission, (i.e., fission of nuclei after the $\beta$-decay) one can obtain information on fission barriers for nuclei rather far from the stability line [1-3]. The delayed fission probability substantially depends on the resonance structure of the $S_{\beta}(\textit{E})$ both for $\beta^{-}$ and $\beta^{+}/EC$-decays [1-6]. It can therefore be concluded from this analysis of the experimental data on delayed fission [1-6] that delayed fission can be correctly described only by using the non-statistical β-transition strength function reflecting nuclear-structure effects.
In $\beta$-decay the simple (non-statistical) configurations are populated and as a consequence the non-statistical effects may be observed in $\gamma$-decay of such configurations. In delayed fission analysis the γ-decay widths $\Gamma_{\gamma}$ calculated using the statistical model, which, in general, can only be an approximation. Non-statistical effects in $(p,\gamma)$ nuclear reactions in the excitation and decay of the non-analog resonances, for which simple configurations play an important role, were analyzed in [5]. The strong non-statistical effects were observed for $M1$ and $E2$ $\gamma$-transitions. Because the information about $\gamma$-decay is very important for delayed fission analysis, it is necessary to consider the influence of non-statistical effects on delayed fission probability not only for $\beta$-decay, but also for $\gamma$-decay.
In this report some features of $\beta $-delayed fission probability analysis are considered. It is shown that only after proper consideration of non-statistical effects both for $\beta$-decay and $\gamma$-decay it is possible to make a quantitative conclusion about fission barriers.
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https://www.researchgate.net/publication/322539669 - H.V. Klapdor, C.O. Wene, I.N. Isosimow, Yu.V. Naumow, Phys. Lett., $\textbf{78B}$, 20 (1978).
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- I.N. Izosimov, et al, Phys. Part. Nucl., $\textbf{14}$, 963 (2011). DOI: 10.1134/S1063779611060049
