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Description
It was proved [1] that P-even T-odd asymmetry in differential cross sections of nuclear ternary fission reactions by cold polarized neutrons with the flight of $\alpha$-particles can be represented in common case through the sum of triple ${{\sigma }_{3}}\left( \Omega \right)={{A}_{3}}\left( \theta \right)\left( {{\mathbf{\sigma }}_{n}}\left[ {{\mathbf{p}}_{LF}},{{\mathbf{p}}_{\alpha }} \right] \right)$ and quinary ${{\sigma }_{5}}\left( \Omega \right)={{A}_{5}}\left( \theta \right)\left( {{\mathbf{\sigma }}_{n}}\left[ {{\mathbf{p}}_{LF}},{{\mathbf{p}}_{\alpha }} \right] \right)\left( {{\mathbf{p}}_{LF}},{{\mathbf{p}}_{\alpha }} \right)$ scalar correlators, depending from spin ${{\mathbf{\sigma}}_{n}}$ of polarized neutron, oriented along the axis Y, momentum of light fission fragment ${{\mathbf{p}}_{LF}}$, oriented along the axis Z, and momentum of $\alpha $–particle ${{\mathbf{p}}_{\alpha }}$ emitted in solid angle $ \Omega \left( \theta ,\varphi \right))$. Coefficients ${{A}_{3}}$ and ${{A}_{5}}$ are connected with sums of quantities ${{\left( {{\mathbf{p}}_{LF}},{{\mathbf{p}}_{\alpha }} \right)}^{n}}={{\cos }^{n}}\left( \theta \right)$ with even values $\textit{n}$. For the case of $\alpha$-particle emission in plane (Z,X) when $\varphi =0$, this correlators are presented as ${{\sigma }_{3}}\left( \theta \right)\sim \sin \theta $ and ${{\sigma }_{5}}\left( \theta \right)\sim \sin \theta \cos \theta\ $ and satisfy the symmetry condition: ${{\sigma }_{3}}\left( \theta \right)={{\sigma }_{3}}\left( \pi -\theta \right)$, ${{\sigma }_{5}}\left( \theta \right)=-{{\sigma }_{5}}\left( \pi -\theta \right)$. Then investigated correlators can be expressed through the coefficient of researched above asymmetry [2]: $D\left( \theta \right)={\left[ {{\sigma }_{3}}\left( \theta \right)+{{\sigma }_{5}}\left( \theta \right) \right]}/{{{\sigma }_{0}}\left( \theta \right)}\;$, where ${{\sigma }_{0}}\left( \theta \right)$ is the differential cross section of analogous reaction with cold polarized neutrons, as $\sigma _{3,5}^{{}}\left( \theta \right)={1}/{2}\;\left[ D\left( \theta \right){{\sigma }_{0}}\left( \theta \right)\pm D\left( \pi -\theta \right){{\sigma }_{0}}\left( \pi -\theta \right) \right]$ (1). Using experimental values ${{D}^{exp}}\left( \theta \right)$ and $\sigma _{0}^{exp}\left( \theta \right)$ for target nuclei ${}^{233}$U, ${}^{235}$U, ${}^{239}$Pu and ${}^{241}$Pu [2], the values of triple $\sigma _{3}^{exp}\left( \theta \right)$ and quinary $\sigma _{5}^{exp}\left( \theta \right)$ correlations were calculated. Taking into account the mechanism of the T-odd asymmetries formation, due to the influence of quantum rotation of the compound fissile system around an axis perpendicular to its symmetry axis on the angular distribution of fission fragments and $\alpha $–particles, these correlators can be represented as $\sigma _{3}^{th}\left( \theta \right)={{\Delta }_{3}}\left( {d\sigma _{odd}^{0}(\theta )}/{d\theta }\; \right)$, $\sigma _{5}^{th}\left( \theta \right)={{\Delta }_{5}}\left( {d\sigma _{ev}^{0}(\theta )}/{d\theta }\; \right)$(2), where $\sigma _{ev}^{0}$ and $\sigma _{odd}^{0}$ are the components [1] of the differential cross section ${{\sigma }_{0}}\left( \theta \right)$, connected accordingly with even and odd orbital moments of $\alpha $-particles, and ${{\Delta }_{3}}$, ${{\Delta }_{5}}$ are the effective rotation angles of ${{\mathbf{p}}_{\alpha }}$ relative to ${{\mathbf{p}}_{LF}}$. A comparison of the correlations from formulae (1), (2) allows to find the values of the angles ${{\Delta }_{3}}$, ${{\Delta }_{5}}$ by the ${{\chi }^{2}}$-method, and using them to calculate the correlators $\sigma _{3}^{th}$ and $\sigma _{5}^{th}$. The calculated angles ${{\Delta }_{3}}$ are comparable with the angles obtained in the classical approach [2] and have a positive sign for all nuclei. At the same time, it is possible to achieve acceptable agreement between the correlators for ${}^{235}$U, ${}^{239}$Pu and ${}^{241}$Pu, however, these correlators are very different from each other for ${}^{233}$U. A reasonable agreement of $\sigma _{5}^{th}\left( \theta \right)$ and $\sigma _{5}^{}\left( \theta \right)$ is observed for all nuclei, but the sign of ${{\Delta }_{5}}$ is positive and coincides with $\Delta $ that is calculated in the framework of the classical approach [2], but when switching from ${}^{235}$U, ${}^{239}$Pu and ${}^{241}$Pu to ${}^{233}$U, the sign changes.The differences obtained above for the classical and quantum approaches of the studied T-odd asymmetries can be used in the analysis of the reliability of these approaches.
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S.G. Kadmensky, V.E. Bunakov, D.E. Lubashevsky // Bull. Russ. Acad. Sci.: Phys., 2019, vol. 83, p. 1236.
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A. Gagarsky et al., Phys. Rev. C. 2016. V. 93. P 054619.
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S.G. Kadmensky, L.V. Titova, V.E. Bunakov//Phys. Atom. Nucl. 82, 239 (2019).
