Total Kinetic Energy Distributions Research Articles

Measurement of mass-angle and mass-total kinetic energy distributions from the fission of 190Pt compound nucleus

We have measured the fission fragment mass-angle and mass-total kinetic energy (TKE) distributions for the neutron-deficient 190Pt compound nucleus (CN) populated via 12C + 178Hf reaction, at around and above barrier energies. No mass-angle correlation was observed in the fission of 190Pt signifying the absence of quasi-fission events in the studied reaction. The observed mass-TKE distributions have expected triangular shape and TKE distributions are well described with the single Gaussian fits, and mean TKE shows parabolic dependence on fragment mass as predicted based on liquid drop fission behaviour. The widths of measured TKE distributions agree well with the observed systematics for CN fission in this mass region. Though the CN is relatively neutron deficient, these observations suggest a clear picture of true CN fission behaviour for the chosen reaction in the studied energy domain.

Calculation of the fission products for neutron-induced fission of 235U

The fission model, G4ParaFissionModel, was enhanced in this study, mainly focusing on refining the energy dependence of the peak-to-valley ratio in the mass distribution and the energy dependence of the average total kinetic energy (TKE). The enhanced model was employed to investigate the characteristics of fission products from 235U(n, f) reaction. The calculated results, including fission yield, TKE distribution, prompt fission neutron and gamma spectra, were compared with both evaluated and experimental data. The comparison shows that these physical observables related nuclear data, which are of importance for developments of the nuclear power and physics, can be reasonably well reproduced.

Connection of four-dimensional Langevin model and Hauser-Feshbach theory to describe statistical decay of fission fragments

ABSTRACT We have developed a novel theoretical method to obtain independent fission product yields and prompt neutron observables by connecting mass and total kinetic energy (TKE) distributions calculated by a four-dimensional Langevin dynamical model to a Hauser-Feshbach statistical decay model. In the Langevin calculations, mass distributions corresponding to the standard I and II modes were obtained separately and superposed to reproduce the fission fragment yield of spontaneous fission of 238 , 240 , 242 Pu and thermal neutron-induced fission of 239 Pu . This was achieved by using different neck parameters for these two modes in the two-center shell model shape parametrization, and a systematics of the superposing ratio was obtained as a function of N − Z / A of the fissioning nuclei. The Hauser-Feshbach calculations were performed using a nuclear reaction code TALYS for 239 Pu n , f reaction in the incident energy range from thermal up to 5 MeV , and the calculated prompt fission observables were compared with experimental and evaluated data. Although further improvements are needed for the most important nuclides, it turned out that the present methodology has the capability to prepare fission-related nuclear data for nuclides for which measurements are difficult.

Fission fragment mass distribution of 187Ir

The fission fragment mass and total kinetic energy (TKE) distributions were studied for 187Ir populated using 12C + 175Lu reaction at excitation energies 24.8, 23.3, 20.8, and 16.7 MeV above the saddle point. Fission fragments (FF) were detected using position sensitive MWPC’s kept at a folding angle. The mass of the fragment was calculated using Time-of-Flight (TOF) difference method. The multi Gaussian fit to the extracted mass distributions shows the presence of narrower microscopic components corresponding to Z = 38 and 45 in addition to the liquid drop component at lower excitation energies. The GEF model predicts significant asymmetric components at all the measured energies. The TKE distribution investigations suggest the dominance of macroscopic liquid drop components at all energies.

A method to simulate Twin Frisch-grid ionization chamber response to fission fragments

In this study, the response of a Twin Frisch-grid ionization chamber (TFGIC) to fission fragments (FFs) was investigated using finite element and Monte Carlo methods. The entire process of the fission experiments, including FFs generation, gas ionization, electron drift and collection, and induced charge signal were well reproduced. Through data analysis, pulse height spectra from the anode and grid were transformed into energy and emission-angle information for the FFs. By means of double energy method, the pre-neutron emission fission fragment mass and total kinetic energy (TKE) can be finally determined. Experimental and calculated data of the mass and TKE distribution are shown in good agreement.

Microscopic study of neutron-induced fission process of 239Pu via zero- and finite-temperature density functional theory* *Supported by the National Natural Science Foundation of China (11790325, 12275081, 11790320, 11790321, 11961131010, 11605054, 12105369, 12147219, 12047568) and the Continuous Basic Scientific Research Project (WDJC-2019-09)

To study the neutron-induced fission of Pu, potential energy surface (PES) calculations were performed using zero and finite-temperature density functional theory (FT-DFT) with the Skyrme force. The energy of the incident neutron was simulated by the temperature of the FT-DFT. The variations of the least-energy fission path, fission barrier, total kinetic energy, scission line, and mass distribution of fission fragments with the incident neutron energy were analyzed. It was learned that an increase in the temperature lowers the barrier height, the isomeric-state energy, and the ridge between symmetric and asymmetric fission valleys. Additionally, the gaps of the single particle levels become smaller with an increase in the temperature. As the temperature increases, the pre-fission region shrinks, and the scission occurs at smaller deformation around the symmetric fission channel. At low temperatures, the pairing correlations in the collective space are similar to those in zero-temperature DFT, and when the temperature is 0.3 MeV, the pairing gaps decrease rapidly. Two different methods were used to calculate the fission yields of the neutron-induced fission Pu (n, f) with different incident neutron energies, in the framework of time-dependent generator coordinate method (TDGCM). One way to calculate the fission yield of Pu (n, f) is to solve the collective equation of the TDGCM by using the PES from the FT-DFT with the corresponding temperature. The other involves using the PES from the zero-temperature DFT and adjusting the initial collective energy of the wave packet in the TDGCM according to the incident neutron energy. For the cases of the lower incident neutron energies, these two methods gave similar results and reproduced the experimental peak and width of fission fragment distribution. However, for the highest incident neutron energy considered in this study, the results from the TDGCM using the PES from zero-temperature DFT deviated explicitly from the experimental data, whereas those obtained by using the PES from FT-DFT remained close to the experimental data. This indicated that, with the increase in the incident neutron energy, the shell structure of the compound nuclei changed explicitly; thus, it may not be effective to use the PES from zero-temperature to perform the fission dynamic calculation.

Time-dependent generator coordinate method study of fission. II. Total kinetic energy distribution

A model is developed to calculate the total kinetic energy (TKE) distribution of fission fragments in the framework of the time-dependent generator coordinate method (TDGCM), extended to include dissipation effects in the description of induced fission dynamics. Starting from an expression for the dissipative term in the GCM Hamiltonian that determines the time evolution of a statistical collective wave function, derived in the first part of this work, the integrated flux of the probability current through the scission hyper-surface can be computed at different temperatures. The kinetic energy at scission for a specific pair of fragments at a given temperature is determined by the energy balance formula. By folding the kinetic energies of the fragments with the flux of the probability current, the TKE distribution is calculated. The method is illustrated with a calculation of the TKE distribution for induced fission of $^{228}$Th, in the 3D space of collective coordinates: axially-symmetric quadrupole and octupole deformations, and nuclear temperature.

Influence of pre-scission neutron emission on high-energy U238 fission studied by the Langevin approach

Background: The information about the pre-scission emitted neutrons is crucial for the fission dynamics study such as fission time scale and dissipation mechanism. Purpose: The aim is to investigate the influence of the pre-scission neutron emission on the fragments mass, total kinetic energy, and the deformation distribution at the scission point in $^{238}\mathrm{U}(n,f)$ fissions at 110, 325, and 500 MeV. Method: A three-dimensional Langevin approach considering nucleus elongation, deformation, and mass asymmetry is applied to simulate fission dynamics. The Hauser-Feshbach statistical decay model is coupled to simulate the pre-scission neutron emission. Results: The properties of the pre-scission emitted neutron are first investigated. It is found that the multiplicity and the average kinetic energy increase with increasing excitation energy. The energy carried away by neutron emission is not negligible and it leads to the multichance fission, especially for the 110 MeV case. The fragments mass, total kinetic energy, and the deformation distribution at the scission point are then calculated with and without coupling the Hauser-Feshbach statistical decay model. It is found that the calculations partially reproduce the leftward shift of the experimental fragment mass distribution at high excitation energy. The pre-scission neutron emission also causes a reduction of the average total kinetic energy by about 2 MeV and a leftward shift of the distribution. The deformation distribution shows that about 75% of the fragments are produced in spherical and prolate ellipsoid shapes. No significant influence on deformation at the scission point was found. Conclusions: For high-energy fission, the energy reduction by pre-scission neutron emission should be considered, which will lead to the multichance fission. The pre-scission neutron emission is one of the reasons for the decrease of the average mass and the leftward shift of the fission fragments mass and total kinetic energy distribution.

Hg178 and asymmetric fission of neutron-deficient pre-actinides

Fission at low excitation energy is an ideal playground to probe the impact of nuclear structure on nuclear dynamics. While the importance of structural effects in the nascent fragments is well-established in the (trans-)actinide region, the observation of asymmetric fission in several neutron-deficient pre-actinides can be explained by various mechanisms. To deepen our insight into that puzzle, an innovative approach based on inverse kinematics and an enhanced version of the VAMOS++ heavy-ion spectrometer was implemented at the GANIL facility, Caen. Fission of $^{178}$Hg was induced by fusion of $^{124}$Xe and $^{54}$Fe. The two fragments were detected in coincidence using VAMOS++ supplemented with a new SEcond Detection arm. For the first time in the pre-actinide region, access to the pre-neutron mass and total kinetic energy distributions, and the simultaneous isotopic identification of one the fission fragment, was achieved. The present work describes the experimental approach, and discusses the pre-neutron observables in the context of an extended asymmetric-fission island located south-west of $^{208}Pb. A comparison with different models is performed, demonstrating the importance of this "new" asymmetric-fission island for elaborating on driving effects in fission.

Influence of the neck parameter on the fission dynamics within the two-center shell model parametrization* *Supported by the National Natural Science Foundation of China (12105369, 11790324, 11790325, 11790323, 11790320) and the Continuous Basic Scientific Research Project (WDJC-2019-09)

The influence of the neck parameter on the fission dynamics at low excitation energy is studied based on the three-dimensional Langevin approach, in which the nuclear shape is described with the two-center shell model (TCSM) parametrization, and the elongation, mass asymmetry, and fragment deformation are set to be the generalized coordinates of the Langevin equation. We first study the influence of the neck parameter on the scission configuration. We find that there is almost no obvious correlation between the neck parameter and mass asymmetry η at the scission point, indicating that has no evident impact on the fragment mass distribution. The elongation and its correlation with the mass asymmetry η at the scission point are clearly influenced by the neck parameter , which has a strong effect on the total kinetic energy (TKE) distribution of the fragments. The pre-neutron emission fragment mass distributions for 14 MeV n+ U and Pu are calculated, and then, based on these results, the post-neutron emission fragment mass distributions are obtained by using the experimental data of prompt neutron emission. The calculated post-neutron emission fragment mass distributions can reproduce the experimental data well. The TKE distributions for 14 MeV n+ U fission are calculated for =0.25, 0.35, and 0.45, and the results show that the TKE distribution cannot be described very well for the three cases. However, the trend of the calculated TKE distribution with is just as expected from the scission configuration calculations. The results with =0.35 present a better agreement with the experiment data compared with the other two cases.

Microscopic study on asymmetric fission dynamics of Hg180 within covariant density functional theory

The asymmetric fission dynamics of $^{180}\mathrm{Hg}$ has been analyzed in the framework of the time-dependent generator coordinate method (TDGCM) based on covariant density functional theory (CDFT) with the relativistic PC-PK1 functional. Three-dimensional $({\ensuremath{\beta}}_{2},{\ensuremath{\beta}}_{3},{q}_{N})$ constrained CDFT calculations have been performed to determine the scission configurations. Remarkably, an asymmetric fission valley is observed in the potential energy surface in the ${\ensuremath{\beta}}_{2}\text{\ensuremath{-}}{\ensuremath{\beta}}_{3}$ plane and the heavy/light fragments at scission are $^{101}\mathrm{Rh}/^{79}\mathrm{Br}$, in good agreement with the data. Furthermore, we find that the heavy fragments of lowest-energy scission configurations, compared to those of other scission points, have rather small quadrupole deformations (${\ensuremath{\beta}}_{2}\ensuremath{\sim}0.4$) and certain octupole deformations (${\ensuremath{\beta}}_{3}\ensuremath{\sim}0.3--0.4$), which are driven by the extended neutron octupole shell gap with $N=56$. Based on the scission configurations, the estimated total kinetic energy distribution is consistent with the trend of experimental data. Finally, the dynamical TDGCM calculation reproduces the asymmetric yield distribution of the low-energy fission of $^{180}\mathrm{Hg}$, especially for the peak positions.

Measurement of mass and total kinetic energy distributions for the C12+Lu175 system

Fission fragment mass and total kinetic energy (TKE) distributions were measured for $^{12}\mathrm{C}+^{175}\mathrm{Lu}$ system at excitation energies down to 16.7 MeV above the saddle point. The overall mass and TKE distributions could be fitted with single Gaussian functions. The observed width of the mass and TKE distributions agree well with the systematics based on liquid drop (LD) behavior. The average TKE also shows parabolic dependence on fragment mass, as expected from LD behavior. Small contributions due to microscopic corrections from $Z\ensuremath{\approx}38$ and 45 shells can be extracted, if the widths of the LD component are fixed from systematics. Contrary to the theoretical predictions of substantial contributions from microscopic corrections, dominance of liquid drop behavior was observed.

Search for possible fission modes at high excitation energies inFm254

Background: Shell effects have been found to influence both the compound nuclear fission (CNF) and quasifission processes. Besides quasifission processes, which fission modes remain active at excitation energy (${E}^{*}$) as high as 56 MeV should be investigated.Purpose: We investigate the signatures of fission modes in $^{254}\mathrm{Fm}$ populated by $^{16}\mathrm{O}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U}$ through the mass distribution (MD) and total kinetic energy distribution (TKED).Method: The mass--total kinetic energy distributions (M-TKED) of fission fragments of the reaction $^{16}\mathrm{O}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U}$ have been measured at two laboratory energies ${E}_{\text{lab}}=89$ and 101 MeV. The spontaneous fission (SF) of $^{254}\mathrm{Fm}$, one-dimensional (1D) fragment MD, and two-dimensional (2D) M-TKEDs of $^{16}\mathrm{O}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}^{238}\mathrm{U}$ have been described by the multimodal random neck rupture (MM-RNR) model.Results: Channel probabilities and the characteristics of different fission modes are obtained and discussed in detail. The enhancement observed in the mass yield ($\ensuremath{\approx}{10}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}%$) in the region 60--70 u for the light fragments at ${E}^{*}\ensuremath{\approx}45$ MeV goes away at the higher ${E}^{*}\ensuremath{\approx}56$ MeV. The heavy fragments of S1 and S2 modes are found to be associated with $Z\ensuremath{\approx}53$ and $Z\ensuremath{\approx}56$ shells, respectively. The slope of asymmetric to symmetric fission yields (when plotted against ${E}^{*}$) of $^{16}\mathrm{O}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U}$ is found to be similar to that of previously reported $^{18}\mathrm{O}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{208}\mathrm{Pb}$.Conclusions: Analysis of 2D M-TKED data by the MM-RNR model reveals the possible presence of fission modes in $^{16}\mathrm{O}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}^{238}\mathrm{U}$. The liquid-drop-like broad symmetric SL mode is found to peak at a lower energy than predicted by the Viola systematic, which matches mostly with that of Standard 2 mode. No signature of asymmetric quasifission is observed. The MD widths show a linear dependence with the measured energies.

Impact of nuclear dissipation on the fission dynamics within the Langevin approach

The impact of nuclear dissipation on the dynamics of nuclear fission at low excitation energy is studied with a three-dimensional Langevin approach in which the two-center shell model is adopted to describe the nuclear shape and the single-particle potential. With three types of formulas for the friction tensor, such as the wall formula, the wall-and-window formula with and without the term related to the mass asymmetry change, the fragment mass and the total kinetic energy (TKE) distributions in low-energy fission are calculated. The calculated fragment mass distributions are almost identical for both with the wall formula and with the wall-and-window model without the term related to the mass asymmetry change, and both the results are consistent with the evaluated mass yields and the calculated results with the GEF model. Our study found that the term related to the mass asymmetry change in the window formula leads to an unreasonable shift of the peak position of the mass distribution. The TKE values calculated with the wall model are slightly larger than those with the wall-and-window model due to the more compact configuration obtained with the pure wall model. Moreover, the influences of the strength of friction tensor on the fragment distribution, the scission configuration, and the fission time distribution are investigated. With the present model the fission fragment mass distributions of U, Np, Pu, and Am isotopes are well reproduced and the systematic dependence of the averaged TKE on the Coulomb parameter is also well reproduced.

Characterize the grid inefficiency correction of Frisch grid ionization chamber with Garfield and SRIM

Grid inefficiency (GI) correction is critically important to accurately determine the energy and emission angle of charged particles in Frisch grid ionization chambers (FGIC). Presently, three correction methods have been proposed in the literature. All these three methods rely strongly on the accurate and stable calibration between two different electrical chain gains in experiments. To avoid these challenges, they are firstly investigated with Monte Carlo method by using Garfield and SRIM toolkit. Two types of grid wire (diameter 90 and 180 μm) were simulated to investigate the impacts of GI correction on energy correction, and ten different emission angles were adopted to estimate the effects of these correction methods on the angle reconstruction. The simulation results clearly distinguished the differences among these correction methods in energy determination. The correlation analysis (R = 0.99) among these different correction methods indicated that the impact of either correction approach is small on the determination of emission angle. The present work firstly investigates the effects of GI correction on emission angle with Monte Carlo methods, which is the basis of future work to measure the total kinetic energy and mass distribution of Fission Fragment (FF).

Quasifission in Kr84,86 -induced reactions populating superheavy elements

Background: Quasifission plays a detrimental role in the synthesis of superheavy elements. Understanding the dynamics of quasifission helps in selecting the optimum target projectile combinations for the synthesis of new superheavy elements.Purpose: The influence of various entrance channel parameters on the quasifission dynamics was explored. Three reactions, $^{84}\mathrm{Kr}+^{198}\mathrm{Pt}$, $^{86}\mathrm{Kr}+^{198}\mathrm{Pt}$, and $^{86}\mathrm{Kr}+^{197}\mathrm{Au}$, expected to be dominated by quasifission, were studied near the Coulomb barrier energies.Methods: The binary fission fragments from the three reactions were detected using the double arm time-of-flight spectrometer CORSET. The mass and total kinetic energy distributions, which are sensitive to the quasifission dynamics, were measured and analyzed for the three reactions.Results: The mass and total kinetic energy distributions of all the three reactions have the characteristics that show the dominance of quasifission. For the reaction $^{84}\mathrm{Kr}+^{198}\mathrm{Pt}$, symmetric quasifission has been found to be relatively more dominant compared to $^{86}\mathrm{Kr}+^{198}\mathrm{Pt}$ reaction. The results have been compared with $^{48}\mathrm{Ca}$- and $^{52}\mathrm{Cr}$-induced reactions, populating nearby nuclei, to understand the evolution of quasifission. An analysis of the timescales in these reactions using a dynamical calculation shows that $^{84}\mathrm{Kr}+^{198}\mathrm{Pt}$ takes a longer time to reach a particular dinuclear shape compared to the other two reactions. The driving potential at the barrier radius also shows a shallower pocket for $^{84}\mathrm{Kr}+^{198}\mathrm{Pt}$ compared to $^{86}\mathrm{Kr}+^{198}\mathrm{Pt}$ and $^{86}\mathrm{Kr}+^{197}\mathrm{Au}$ reactions.Conclusion: The entrance channel isospin difference is found to influence the quasifission dynamics. A higher entrance channel isospin difference may have a larger evolution time, thus driving the systems toward a more symmetric mass split.

Observation of a fission mode with very short elongation for the neutron-rich Md257 nucleus at high excitation energy

Mass and total kinetic-energy (TKE) distributions of fission fragments from $^{257}\mathrm{Md}$ nucleus populated by complete fusion of $^{19}\mathrm{F}$ with $^{238}\mathrm{U}$ have been measured in the range of excitation energy ${E}^{*}\ensuremath{\approx}37\text{\ensuremath{-}}48\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. Due to the skewness of the measured TKE distributions, two Gaussian distributions were required to explain the data. The events with high TKE must originate from the supershort mode of fission, the presence of which has been confirmed by measuring two additional reactions: $^{19}\mathrm{F}+^{232}\mathrm{Th}$ and $^{18}\mathrm{O}+^{238}\mathrm{U}$ involving first a different target and then a different projectile leading to compound nuclei $^{251}\mathrm{Es}$ and $^{256}\mathrm{Fm}$, respectively, at similar excitation energies and comparing their mass-TKE correlation plots. The existence of considerable supershort mode of fission for the $^{257}\mathrm{Md}$ nucleus up to ${E}^{*}\ensuremath{\approx}48$ MeV, observed for the first time, reveals that such rare fission modes for neutron-rich exotic nuclei are far off from the liquid drop model predictions, even at high excitation energies.

Singlet O2 Produced by Ultraviolet Dissociation of the β-ionone-O2 Complex.

We formed the gas-phase β-ionone-O2 complex in a supersonic expansion and then photodissociated the complex with light near 312 nm. Photodissociation resulted in the production of O2 in the a 1Δg state, which was ionized at 312 nm using (2 + 1) resonance-enhanced multiphoton ionization (REMPI). We recorded the 1O2 REMPI action spectrum and O2+ velocity map ion image following photodissociation of the complex. From the velocity map image, we determined the total recoil kinetic energy distribution from dissociation of the complex. Fitting the REMPI spectrum showed that the 1O2 product has an effective rotational temperature of about 50 K, while the recoil kinetic energy distribution was well fit with a statistical Boltzmann distribution having an effective translational temperature of 289 K. Using the average translational energy from the Boltzmann fit along with the complex dissociation energy from ab initio calculations, we determined that β-ionone was formed with an average of 2.87 eV of internal energy, which was 0.49 eV higher than previous measurements for the β-ionone triplet-state energy. Our own CCSD/cc-pVDZ//(U)MP2/cc-pVDZ calculations gave a minimum triplet-state energy of 2.04 eV. However, a large structural change occurs between the minimum singlet-ground-state geometry and the minimum triplet-excited-state geometry, and as a result, the calculated vertical energy for the triplet-state β-ionone was determined to be 3.30 eV. Comparing the ab initio and experimental results indicated that following excitation, β-ionone was formed in the triplet state but with significant internal vibrational energy. As such, complex dissociation likely proceeds following internal vibrational energy redistribution, which explains the statistical recoil kinetic energy distribution.

Mesoscopic Lattice Boltzmann Modeling of the Liquid-Vapor Phase Transition.

We develop a mesoscopic lattice Boltzmann model for liquid-vapor phase transition by handling the microscopic molecular interaction. The short-range molecular interaction is incorporated by recovering an equation of state for dense gases, and the long-range molecular interaction is mimicked by introducing a pairwise interaction force. Double distribution functions are employed, with the density distribution function for the mass and momentum conservation laws and an innovative total kinetic energy distribution function for the energy conservation law. The recovered mesomacroscopic governing equations are fully consistent with kinetic theory, and thermodynamic consistency is naturally satisfied.

Analysis of nuclear fission properties with the Langevin approach in Fourier shape parametrization

The Langevin approach is extendedly applied to study the dynamical process of nuclear fission within the Fourier shape parametrization, where the potential energy is calculated with the macroscopic-microscopic model based on the Lublin-Strasbourg drop model and the Yukawa-folded potential. The fragment mass distribution and the total kinetic energy as a function of heavy fragment mass in 14 MeV $n+^{235}\mathrm{U}$ fission are calculated and compared with the evaluated data from ENDF/B-VIII.0 and the experimental data. It is found that the Wall model for the friction tensor is available to describe both of the mass distribution and the total kinetic energy (TKE) distribution in the nuclear fission within the present model. In addition, the mass distributions and the TKE distributions in 14 MeV $n+^{233,236,238}\mathrm{U}$ and $^{239}\mathrm{Pu}$ fission are well described. Furthermore, the behavior of the correlation of the distance between the centers of mass of two fragments with the heavy fragment mass at the scission point is found to be consistent with that of the TKE distribution where the shortest ${R}_{12}$ locates around ${A}_{h}=135$ which is due to the influence of the shell effects.