Speaker
Description
In experimental papers [1, 2] the yields, angular and energy distributions of the pairs of light third and fourth particles formed with the highest probability, such as $\alpha$-particles pair $(\alpha_1,\alpha_2)$, were obtained for the spontaneous quaternary fission of the nucleus $^{252}$Cf. Using the theoretical concepts [3-5] of ternary and quaternary fission as virtual processes [6], we consider spontaneous quaternary fission from the ground states of even-even actinides [1,2] with the sequential emission of two $\alpha$-particles from the virtual states of nuclei $A$ and $(A-4)$ and the subsequent binary fission of the residual fissile nucleus $(A-8)$ into light and heavy fission fragments. These $\alpha$-particles, in contrast to the $\alpha$-particles that fly out in the sub-barrier $\alpha$-decay of the studied nuclei $A$ and $(A-4)$, when the energies $Q_{\alpha_1}^A$ and $Q_{\alpha_2}^{(A-4)}$ of this decays are close to 6 MeV, are long-range, since their asymptotic kinetic energies $T_{\alpha_1} \approx 16 $ MeV and $T_{\alpha_2} \approx 13 $ MeV, are markedly larger than energy values $Q_{\alpha_1}^A$ and $Q_{\alpha_2}^{(A-4)}$. Using the formula [4] for the width $ \Gamma_{\alpha_1\alpha_2 f}^A$ of the virtual quaternary fission of nucleus $A$, formulae for the widths $ \Gamma_{\alpha_1}^{A}(T_{\alpha_1})$ and $ \Gamma_{\alpha_2}^{(A-4)} (T_{\alpha_2})$ for $\alpha$-decays of nuclei $A$ and $(A-4)$ are constructed:
$
\Gamma_{\alpha_1}^{A}(T_{\alpha_1})=2\pi W_{\alpha_1}(T_{\alpha_1}) (Q_{\alpha_1}-T_{\alpha_1})^2;
\Gamma_{\alpha_2}^{(A-4)}(T_{\alpha_2})=2\pi W_{\alpha_2}(T_{\alpha_2}) (Q_{\alpha_2}-T_{\alpha_2})^2;
$
where $W_{\alpha_1}(T_{\alpha_1})$ and $W_{\alpha_2}(T_{\alpha_2})$ are the energy distributions of the first and second $\alpha$-particles, normalized by the ratio of the widths of these $\alpha$-particles emission to the width of the binary fission of the nuclei $A$ and $(A-4)$. The widths $\Gamma_ {\alpha_1}^{A}$ and $ \Gamma_{\alpha_2}^{A-4}$ take into account the fact that the emitting $\alpha$-particles are formed in such configurations of the fissile nuclei $A$ and $(A-4)$ that occur during their deformation motion from the ground states through the internal and external fission barriers and reach a pear-shaped forms corresponding to the appearance of two deformed fission prefragments connected by a neck. If we consider the ratio $ \Gamma_{\alpha_1}^{A}/\Gamma_{\alpha_2}^{(A-4)}=\sqrt{T_{\alpha_1}}P_1(T_{\alpha_1})/
\sqrt{T_{\alpha_2}}P_2(T_{\alpha_2})$ and take into account the fact that the probabilities of formation of the $\alpha_1$ and $\alpha_2$ particles are close to each other, and the radii of the neck of the nucleus $r_{A}$ before the emission of $\alpha_1$-particle does not differ much from the radius of the neck $r_{A-4}$ before the emission of the $\alpha_2$-particle, one can get the ratio of the Coulomb barrier penetrabilities $P_2(T_{\alpha_2})/P_1(T_{\alpha_1})$ for the first and second $\alpha$-particles. Using the experimental values of the kinetic energies $T_{\alpha_1}$ and $T_{\alpha_2}$ and maximum values of energy distributions $W_{\alpha_1} (T_{\alpha_1})$ and $W_{\alpha_2} (T_{\alpha_2} )$, the specified estimation of $P_2(T_{\alpha_2})/P_1(T_{\alpha_1})$ is 0.03 for spontaneous quaternary fission of $^{252}$Cf. This estimation $P_2(T_{\alpha_2})/P_1(T_{\alpha_1})$ demonstrates that the virtual decay of nucleus $(A-4)$ with $\alpha_2$ particle flight has subbarrier character in contrast to the virtual decay of nucleus $A$ with $\alpha_1$ particle flight.
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P. Jesinger et al., Eur. Phys. J. A. 2005. V. 24. P. 379.
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M. Mutterer et al., in Proceedings of "Dynamic. Aspects of Nuclear Fission", Slovakia, 2002, p. 191.
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S.G. Kadmensky, L.V. Titova / Physics of Atomic Nuclei. 2013. V. 76. P.16.
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S.G. Kadmensky, O.A. Bulychev / Bull. of RAS: Physics. 2016. V. 80. P. 921.
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S.G. Kadmensky, D.E. Lubashevsky, in Proceedings of Int. Conf. "Nucleus-2019", Dubna, Russia, 2019, p. 251.
