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Register a new userDynamics of the tri-nuclear system at spontaneous fission of $^{252}$Cf
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R.B. Tashkhodjaev
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To describe of dynamics of ternary fission of $^{252}$Cf an equation of motion of the tri-nuclear system is calculated. The fission of the $^{70}$Ni+$^{50}$Ca+$^{132}$Sn channel was chosen as one of the more probable channels of true ternary fission of $^{252}$Cf. The collinearity of ternary fission has been checked by analyzing results of the equation of motion. The results show that if initially all nuclei are placed collinearly (potential energy of this position is the smallest) and the component of the middle fragments initial velocity which is perpendicular to this line, is zero then ternary fission is collinear, otherwise the non collinear ternary fission takes place.
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The time-dependent generator coordinate method with the gaussian overlap approximation (TDGCM+GOA) formalism is applied to describe the fission of $^{252}$Cf. We perform analysis of fission from the initial states laying in the energetic range from the ground state to the state located 4 MeV above the fission barrier. The fission fragment mass distributions, obtained for different parity, energy of levels and types of mixed states, are calculated and compared with experimental data. The impact of the total time of wave packet propagation on the final results is studied as well. The weak dependence of obtained mass yields on the initial conditions is shown.
The yields of light elements ($Z=1,2$) obtained from spontaneous ternary fission of $^{252}$Cf are treated within a nonequilibrium approach, and the contribution of unstable nuclei and excited bound states is taken into account. These light cluster yields may be used to probe dense matter, and to infer in-medium corrections. Continuum correlations are calculated from scattering phase shifts using the Beth-Uhlenbeck formula, and the effect of medium modification is estimated. The relevant distribution is reconstructed from the measured yields of isotopes. This describes the state of the nucleon system at scission and cluster formation, using only three Lagrange parameters which are the nonequilibrium counterparts of the temperature and chemical potentials, as defined in thermodynamic equilibrium. We concluded that a simple nuclear statistical equilibrium model neglecting continuum correlations and medium effects is not able to describe the measured distribution of H and He isotopes. Moreover, the freeze-out concept may serve as an important ingredient to the nonequilibrium approach using the relevant statistical operator concept.
The microscopic studies on nuclear fission require the evaluation of the potential energy surface as a function of the collective coordinates. A reasonable choice of constraints on multipole moments should be made to describe the topography of the surface completely within a reasonable amount of computing time. We present a detailed analysis of fission barriers in the self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing different spontaneous fission modes - $^{252}$Cf (asymmetric) and $^{258}$No (bimodal) - have been chosen for the analysis. We have shown the existence of complicated structures on the energy surface that can not be fully described in two-dimensional calculations. We analyze apparent problems that can be encountered in this type of calculations: multiple solutions for given constraints and transitions between various potential energy surfaces. We present possible solutions on how to deal with these issues.
We reinvestigated the neutron multiplicity yields of Ba-Mo, Ce-Zr, Te-Pd, and Nd-Sr from the spontaneous fission of $^{252}$Cf; by (i) using both $gamma$-$gamma$-$gamma$-$gamma$ and $gamma$-$gamma$-$gamma$ coincidence data, (ii) using up to date level scheme structures, and (iii) cross-checking analogous energy transitions in multiple isotopes, we have achieved higher precision than previous analyses. Particular attention was given to the Ba-Mo pairs where our results clearly confirm that the Ba-Mo yield data have a second hot fission mode where 8, 9, 10, and now 11 neutron evaporation channels are observed. These are the first observations of the 11 neutron channel. These 8-11 neutron channels are observed for the first time in the Ce-Zr pairs, but are not observed in other fission pairs. The measured intensities of the second mode in Ba-Mo and Ce-Zr pairs are $sim$1.5(4)$%$ and $sim$1.0(3)$%$, respectively. These high neutron number evaporation modes can be an indication of hyperdeformation and/or octupole deformation in $^{143-145}$Ba and in $^{146,148}$Ce at scission to give rise to such high neutron multiplicities.
Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent framework. We employ the superfluid nuclear density functional theory with the Skyrme energy density functional SkM$^*$ and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates. Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of $^{264}$Fm, where the effect of triaxiality on the fission barrier is large, the geometry of fission pathway in the space of shape degrees of freedom is weakly impacted by pairing. This is not the case for $^{240}$Pu where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory. The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.
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