Scission-point Model Research Articles

Total kinetic, excitation energy and neutron multiplicity distribution of californium isotopes

The mean total kinetic energy as a function of fission fragments, <TKE>(A), is calculated for neutron-induced fission of 247,249,251,253,255Cf, as well as for spontaneous fission of 248,250,252,254Cf using the scission point model. A comparative analysis is performed between the calculated results and existing experimental data. Investigation into the behavior of <TKE>(A) is conducted, particularly focusing on intermediate and heavy actinides. While nuclear and Coulomb energy evaluations suffice for estimating <TKE> values in light actinides, this approximation proves inadequate for evaluating TKE values for intermediate and heavy actinides. Additionally, an evaluation is made of the total excitation energy as a function of fission fragments, <TXE>(A), concerning spontaneous fission in 247−254Cf. It is found that TXE values sharply increase near the symmetric region across all isotopes and exhibit a gradual increase in heavy fission fragments. Furthermore, an exploration of the total neutron multiplicity as a function of fission fragments, νT(A), is conducted for 252Cf fission using two methods. The νT(A) results obtained through these methods are compared with experimental data, and νT(A) is estimated for unmeasured californium isotopes. The average neutron emission per fission event, ν¯(Ai), is then calculated for spontaneous fission of 251Cf and 253Cf, yielding values of 3.46 and 3.59, respectively.

Correlated transitions in fission mode and shell correction energy at zero excitation in actinides fission

In this paper, the transitions between symmetric and asymmetric modes are investigated for the fission of actinides within the scission point model. All effective energies in fission are investigated in detail, separately. This indicates that the interaction energy and the liquid-drop energy do not change much in the symmetric region, so they cannot play a major role in the transition of actinide fission modes. Additionally, the sum of shell correction of complementary fragments at zero excitation energy is plotted over the fission fragment mass numbers. Also, the mass distributions of actinides fission are calculated within the scission point model. There is a good agreement between the calculated mass distribution and the total shell correction distribution. This indicates that the minimum total shell correction energy at the excitation energy corresponds to the maximum mass distribution for actinides fission, especially for the fermium 258 fission. Therefore, the main reason for the formation of fission mode in the actinides fission is the total shell correction energy of the complementary fission fragments at the zero excitation energy.

Evaluation of pre-neutron-emission mass distributions of neutron-induced typical actinide fission using scission point model * *Supported by the NSFC-Nuclear Technology Innovation Joint Fund (U1867213), the NSAF (U1830102), the National Natural Science Foundations of China (12075105, 11705071, 11875155) and the Fundamental Research Funds for the Central Universities (lzujbky-2021-kb09)

The scission point model is improved by considering the excitation-dependent liquid drop model to calculate mass distributions for neutron-induced actinide nuclei fission. Excitation energy effects influence the deformations of light and heavy fragments. The improved scission point model shows a significant advance with regard to accuracy for calculating pre-neutron-emission mass distributions of neutron-induced typical actinide fission with incident-neutron-energies up to 99.5 MeV. The theoretical frame assures that the improved scission point model is suitable for evaluating the fission fragment mass distributions, which will provide guidance for studying fission physics and designing nuclear fission engineering and nuclear transmutation systems.

Simultaneous description of charge, mass, total kinetic energy, and neutron multiplicity distributions in fission of Th and U isotopes

For fissioning isotopes of thorium and uranium, the simultaneous description of the charge, mass, total kinetic energy, and neutron multiplicity distributions of fission fragments is presented within the improved scission-point model. Correlations between all these observables are analyzed. The influence of the transition from symmetric to asymmetric fission mode on the shape of neutron multiplicity distribution is studied.

Understanding the isoscaling relationship in the fissioning system with evaluated data * *Supported by the National Natural Science Foundation of China (11790325, 11875323, 11875125, 11947410, 11705163, 11790320, 11790323, 11961141003), the National Key R&D Program of China (2018 YFA0404404), the Continuous Basic Scientific Research Project (WDJC-2019-09, WDJC-2019-13, BJ20002501) of the funding of China Institute of Atomic Energy, and Chinese-Polish Joint project

The isoscaling parameters in the fissioning systems, i.e., those extracted from the Evaluated Nuclear Data Library (ENDF/B-VIII.0) and the Joint Evaluated Fission and Fusion File (JEFF-3.3), show an obvious difference from simple statistic model prediction where only the symmetry energy plays the dominant role. To explain the as a function of the charge number of the fission fragment, a statistic scission point model is adopted. Our analysis shows that the effects of the shell correction, nuclear shape deformation, and intrinsic temperature of fission fragments are indispensable as well as the symmetry energy. Furthermore, an alternative method for extracting the intrinsic temperatures of fission fragments is proposed based on the isoscaling relationship in fission fragments. The intrinsic temperatures of the light fragments are higher than those of the heavy fragments.

Deformation parameter changes in fission mass yields within the systematic statistical scission-point model

The fission fragment mass-yields are evaluated for pre-actinide and actinide isotopes using a systematic statistical scission point model. The total potential energy of the fissioning systems at the scission point is presented in approximate relations as functions of mass numbers, deformation parameters and the temperature of complementary fission fragments. The collective temperature, T coll, and the temperature of fission fragments, T i , are separated and the effect of collective temperature on mass yields results is investigated. The fragment temperature has been calculated with the generalized superfluid model. The sum of deformation parameters of complementary fission fragments has been obtained by fitting the calculated results with the experimental data. To investigate the transitions between symmetric and asymmetric modes mass yields for pre-actinide and heavy actinides are calculated with this model. The transition from asymmetric to symmetric fission is well reproduced using this systematic statistical scission point model. The calculated results are in good agreement with the experimental data with T coll = 2 MeV at intermediate excitation energy and with T coll = 1 MeV for spontaneous fission. Despite the Langevin model, in the scission point model, a constraint on the deformation parameters of fission fragments has little effect on the results of the mass yield.

Cold and spontaneous fission fragments mass yield of [formula omitted]Cf using the statistical scission point model with the pairing energy and temperature dependent shell energy corrections

The cold and spontaneous fission fragments mass yield of 252Cf is calculated using the statistical scission point model. The results are compared with the available experimental data and the calculated results of the WKB model. This comparison indicates that the fission fragments mass distribution obtained by the statistical method are well agreed with the experimental data than the WKB model. The finite-range liquid-drop (FRLDM) as a macroscopic model with shell effects and pairing energy was used as the microscopic energy. On the other hand, for the microscopic energy, the deformation energy is substituted by the temperature dependence of the nuclear excited energy. The shell correction energy as a function of mass and atomic numbers of fission fragments is formulated in our systematic approach. The deformation parameters and the fragment temperature are obtained by fitting the calculated results with the experimental data. Analysis of calculated results of fragments mass yields clear that the pairing energy has relatively weak effect on cold fission fragments yields against spontaneous fission, although the deformation parameters are effective on cold fission fragments yield than the spontaneous fission.

Deformation Parameters and Collective Temperature Changes in Photofission Mass Yields of Actinides Within the Systematic Statistical Scission Point Model

The photofission fragment mass yields of actinides are evaluated using a systematic statistical scission point model. In this model, all energies at the scission point are presented as a linear function of the mass numbers of fission fragments. The mass yields are calculated with a new approximated relative probability for each complementary fragment. The agreement with the experimental data is quite good, especially with a collective temperature Tcol of 2 MeV at intermediate excitation energy and Tcol = 1 MeV for spontaneous fission. This indicates that the collective temperature is greater than the value obtained by the initial excitation energy. The generalized superfluid model is applied for calculating the fragment temperature. The deformation parameters of fission fragments have been obtained by fitting the calculated results with the experimental values. This indicates that the deformation parameters decrease with increasing excitation energy. Also, these parameters decrease for fissioning systems with odd mass numbers.

Fission fragment distributions and their impact on the r -process nucleosynthesis in neutron star mergers

Neutron star merger ejecta are currently the most viable astrophysical site for $r$-process nucleosynthesis. Fission plays a fundamental role. The manuscript presents an updated scission-point model for fission fragment distributions, which improves agreement with experimental fission yields. Two astrophysical scenarios, based on alternative weak-interaction hypotheses, are employed to reanalyze the role of fission. Regions of the nuclear chart where fission is important are identified, and the impact of fission yields on the final $r$-process abundance distribution is elaborated.

Multi-parameter global calculations of fission fragments using a simplified two-dimensional scission-point model * *Supported by National Natural Science Foundation of China (11875301, U1832167)

Exploiting the concept of the dinuclear system, the interaction potential energy of two fragments that are quite close to each other is analyzed. A semi-classical method is used to calculate fission fragment yields using a simplified two-dimensional scission-point model. By considering the tip-to-tip orientation at the scission point of the fission process, we investigate the mass, charge, and kinetic-energy distributions of the fission fragments, for excitation energies in the 0-20 MeV range. Our results show that the fission fragment distributions are reproduced quite well, including the recent experimental results for the isotone chain [D Ramos et al. Phys. Rev. C 97, 054612 (2018)]. Thus, the simplified model is useful for multi-parameter global measurements of fission products.

Systematic Approach to Calculate the Total Kinetic Energy Distribution of Actinides for the Photofission Phenomenon

The total kinetic energy as a function of fragment mass (TKE/A) was calculated for photofission of $${}^{232}$$ Th, $${}^{234}$$ U, $${}^{238}$$ U, $${}^{240}$$ Pu, and $${}^{242}$$ Pu using a systematic statistical scission point model. In the proposed systematic method, all the energies involved in fission need to be expressed as a function of mass and atomic numbers of fission fragments. Therefore, the shell correction energy of fission fragments was approximated in terms of fission fragment mass numbers based on Ruben’s idea. The deformability parameter ( $$\alpha$$ ) of fission fragments was also formulated as a function of mass and atomic numbers of fission fragments by fitting the calculations and experimental data according to Terrell’s formulas. The calculated results are in good agreement with the experimental data, except for fragments with magic numbers, which their shell correction energy and deformability parameters change rapidly.

Kinetic energy distribution for neutron-induced fission of neptunium isotopes

The mean total kinetic energy as a function of fission fragments, the <TKE> distribution, is presented for neutron-induced fission of Np using the scission point model. The calculated results of <TKE> for neutron-induced fission of Np are compared with the available experimental data to obtain the deformation parameters in the scission point model. The deformation parameters of fission fragments are discussed at the scission point. The calculated results are also compared with the results from other methods and with experimental data. The behavior of the <TKE> distribution is then studied for the neutron-induced fission of actinides. This indicates that the <TKE> values for neutron-induced fission of actinides with odd mass numbers are greater than for those with even mass numbers.

Kinetic Energy Distribution for Neutron-Induced Fission of Thorium Isotopes

The fission fragment total kinetic energy TKE(A) was calculated for neutron-induced fission of 229,232Th using the scission point model. The calculated results were compared with the available experimental data to obtain the parameters of the scission point model. With these parameters, the total kinetic energy distribution was evaluated for neutron-induced fission of Thorium isotopes. The deformation parameters of the Thorium isotopes were discussed at the scission point.

Kinetic energy distribution for photofission of light actinides

The scission point model has been used to calculate the total kinetic energy (TKE) as a function of fission fragments for photofission reactions. By comparing the calculated TKE values with the available experimental data, the deformation parameters of the fission fragments are obtained in the scission point model. The results show that the deformation parameters of the fission fragments have a large change near the symmetrical region. TKE distribution has been investigated for neutron-induced fission, spontaneous fission, and photofission to predict actinide TKE distribution. This indicates that the TKE distribution depends on the mass and atomic number of compound nuclei and, of course, the excitation energy. The odd-even effect plays an important role in predicting TKE distribution behavior. Also, TKE distribution has a similar trend for all isotopes and the TKE distribution of spontaneous fission is significantly different from the TKE distribution of photofission. At last, the total kinetic energy distributions for the photofission fragments of light actinides are evaluated in the scission point model.

Mass yield of spontaneous fission of 238U within the systematic statistical scission-point model

The spontaneous fission fragments mass yield of 238U is calculated with two models: WKB approximation model and statistical scission-point model. The results are compared with experimental data. This shows that the statistical scission-point model results are closer to the experimental data of the spontaneous fission fragments mass distributions than the WKB model. Also, experimental values are obtained by changing the deformation parameter for light fragments. The influence of temperature, deformation parameters, and pairing energy on the spontaneous fission fragments mass yield has been investigated within the statistical scission-point model. Adding the pairing correction energy to the total energy of the fission system adds some oscillations in theoretical results of fission fragments mass yields, also the inclusion of fission fragments temperature regardless of the pairing energy causes some theoretical results to be overestimated compared to the experimental data. It is seen that adding the pairing correction energy with the fragments temperature together leads to acceptable results compared to the experimental values. Therefore, the theoretical results of the systematic modified statistical scission-point model are in good agreement with the experimental values. This shows that although the statistical model is commonly used for the even–even isotopes, all isotopes can be investigated using the modified statistical model.

Scission point model applied to $$^{181} \hbox {Re}^{*}$$ formed in $$^{12}{} \mathbf{C}+^{169}$$Tm reaction

Scission point model applied to $$^{181} \hbox {Re}^{*}$$ formed in $$^{12}{} \mathbf{C}+^{169}$$Tm reaction

Yields distribution of induced fission with improved scission point model

The charge distributions from induced fission of nuclei 230–234U, 206–212Fr, 214–226Ac and 220–229Th are determined by an improved scission point model. The calculated results can reasonably reproduce the experimental trends, and the asymmetric and symmetric fission modes are anticipated. The order of magnitude of the yield’s distribution is reproduced especially well for the U isotope. The semi-empirical parameters in the scission point model associated with the nuclear structure that can be changed to improve the model. We studied the influences of damping constant ED on the shell correction and the level density parameter a on the calculation results.

Change of the shape of mass and charge distributions in fission of Cf isotopes with excitation energy

Using the improved scission-point model, the mass and charge distributions of fragments resulting from the fission of californium isotopes are calculated and compared with the available experimental data. The change of the shape of mass and charge distributions with increasing excitation energy is predicted for future experiments.

Scission point model for the mass distribution of ternary fission

A modified scission point model is adopted to study the mass distribution of thermal neutron induced binary and ternary fission of 235U. The scission configuration and the most favourable fragment deformation is identified through an energy balance criterion where the macroscopic part due to liquid drop and the microscopic part due to shell correction together with the deformation dependent interaction potential are used. The available energy for each channel together with fragment deformation is used to evaluate nuclear level densities in the Fermi gas model. Since the model is found to give the expected double humped mass distribution for binary fission of 236U, this is then applied for the ternary fission of the same nuclei with fixed third fragment. Two different third fragments with two cases of collinear arrangement were studied with the model. The obtained ternary mass distribution was then compared with the calculated binary mass distribution. In all the cases, the influence of shell effects is found to be prominent with one of the fragments associated with the Sn nucleus. The closed shell nuclei possess maximum yield in both binary and ternary mass distribution.

Fully microscopic scission-point model to predict fission fragment observables

We present an upgraded version of the SPY model, called SPY2 for version 2 of the scission point yield, to estimate mainly the yields and the kinetic energy distributions of fission fragments: The theoretical framework is similar to our previous version, i.e., a statistical scission point model, but this version is based on fully microscopic nuclear ingredients describing the fragments properties at the scission point. These include the static properties of some 7000 nuclei at 120 axial quadrupole deformations, such as binding energies, proton densities, single-particle level schemes, and states densities, coherently calculated within the constrained Hartree-Fock-Bogoliubov model on the basis of the Skyrme BSk27 interaction. The use of microscopic ingredients has been extended to the proton density distribution and the nuclear states densities. Considering realistic proton densities of fragments allows us to improve the definition of the scission point as well as the prediction of the kinetic energy distribution and to link the kinetic energy to the diffuseness of the fragments' proton density. New microscopic nuclear states densities improve the general coherence of the model, in particular regarding the inclusion of the odd-even pairing effect. In this updated SPY2 version, the calculation of the fission yields and kinetic energy distributions is significantly improved and found to be in relatively good agreement with experiments, at least qualitatively. A detailed study is performed for three well known fissioning systems, namely, thermal neutron induced fission of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$ and spontaneous fission of $^{252}\mathrm{Cf}$. A systematic analysis of the fission mode as well as mean fragments deformation and total kinetic energies has been performed for some 2000 fissioning nuclei with $78\ensuremath{\le}Z\ensuremath{\le}110$ lying between the proton and neutron drip lines.