Oct 14, 2020, 3:05 PM


Oral report Section 2. Experimental and theoretical studies of nuclear reactions. Section 2. Experimental and theoretical studies of nuclear reactions


Larisa Titova (Voronezh State University)


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.

  1. P. Jesinger et al., Eur. Phys. J. A. 2005. V. 24. P. 379.

  2. M. Mutterer et al., in Proceedings of "Dynamic. Aspects of Nuclear Fission", Slovakia, 2002, p. 191.

  3. S.G. Kadmensky, L.V. Titova / Physics of Atomic Nuclei. 2013. V. 76. P.16.

  4. S.G. Kadmensky, O.A. Bulychev / Bull. of RAS: Physics. 2016. V. 80. P. 921.

  5. S.G. Kadmensky, D.E. Lubashevsky, in Proceedings of Int. Conf. "Nucleus-2019", Dubna, Russia, 2019, p. 251.

Primary authors

Larisa Titova (Voronezh State University) Stanislav Kadmensky

Presentation materials