Fission Fragment Intrinsic Spins and Their Correlations

The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions, the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments’ intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their deexcitation mechanism. We outline here a framework for the theoretical extraction of the intrinsic spin distributions of the fragments and their correlations within the fully microscopic real-time density-functional theory formalism and illustrate it on the example of induced fission of ${}^{236}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$, using two nuclear energy density functionals. These fission fragment intrinsic spin distributions display new qualitative features previously not discussed in literature. Within this fully microscopic framework, we extract for the first time the intrinsic spin distributions of fission fragments of ${}^{236}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$ as well as the correlations of their intrinsic spins, which have been debated in literature for more than six decades with no definite conclusions so far.

Figure 1

Values of $|a_J^F{|}^2$ averaged over initial multipole moments $Q_{20}$, $Q_{30}$ from the even $J^F$ momenta are displayed with filled symbols, while the contributions arising from odd $J^F$ momenta are displayed with empty symbols. The “error bars” characterize the range of the variation due to the spread of initial multipole moments $Q_{20}$ and $Q_{30}$ and energies of the fissioning nucleus. The $|a_J^F{|}^2$ for the SeaLL1 [38] and ${\mathrm{SkM}}^{*}$ [37] (displaced by $\mathrm{\Delta }{J}^F=0.36$ for better visualization) NEDFs are displayed with filled and empty symbols for the even and odd values of $J$, respectively. The average (standard deviation) for ${}^{240}\mathrm{Pu}$ are $[A^L,Z^L]=[103.6(0.7),41.0(0.3)]$ and ${}^{236}\mathrm{U}$ [102.4(2.0), 40.4(0.7)] in case of SeaLL1 and [104.3(1.5), 41.4(0.5)] and [97.9(1.2), 38.9(0.4)] in case of ${\mathrm{SkM}}^{*}$, respectively. The evaluated FF intrinsic spins $S^{H,L}$ at different FF separations are shown in the inset for ${}^{236}\mathrm{U}$. Typical behavior of the overlaps $⟨\mathrm{\Phi }|{\widehat{R}}_x^F(\beta )|\mathrm{\Phi }⟩$ for one TDDFT trajectory is shown in the inset for ${}^{240}\mathrm{Pu}$. The overlaps’ widths narrow with increasing $\beta$ and the average $S^F$ increases.

Figure 2

The average intrinsic spins $S^{L,H}$ versus the initial FF equivalent incident neutron energy $E_n^{\prime }=E^{*}-S_n$ ($E^{*}$ and $S_n$ are the excitation energy and $S_n$ is the neutron separation energy) for the reaction ${}^{239}\mathrm{Pu}(n,f)$ with ${\mathrm{SkM}}^{*}$ NEDF. The solid lines are linear fits over the data, $S^L=0.0168E_n^{\prime }+9.197$ and $S^H=0.0732E_n^{\prime }+4.933$, respectively, as a function of equivalent neutron energy $E_n^{\prime }$ along with their linear fits. Inset: the FF excitation energies and their linear fits $E_{\mathrm{int}}^L=0.4505E_n^{\prime }+13.25$ and $E_{\mathrm{int}}^H=0.5676E_n^{\prime }+13.40$. Using $E_{\mathrm{int}}^F\approx A^F(T^F{)}^2/10$ [43, 51], it follows that, on average, $T^L>T^H$.