Saddle-point Statistical Model Research Articles

Mass resolved angular distribution of fission products in 12C+232Th reaction at sub-barrier energy

This article reports the study of mass resolved angular distribution of the fission products and the angular anisotropy in 232Th(12C,f) reaction at sub-barrier energy to investigate the possible role of shell effects and non-compound nucleus fission. In literature, average anisotropy values reported earlier for this system at sub-barrier energy widely vary. The present study was carried out using the recoil catcher technique followed by off-line γ-ray spectrometry at 62.5 MeV beam energy. Angular anisotropies of fission products showed slight enhancement in the symmetric mass region. Significantly higher value of the experimental average anisotropy (1.46 ± 0.06) compared to that obtained by Statistical Saddle Point Model (SSPM) calculation indicated the possible role of shell effect and non-compound nucleus fission at the present beam energy. Consideration of shell effects resulted in an enhancement of the calculated anisotropy, though it was still slightly lower compared to the experimental value. The contribution from the non-compound nucleus fission was confirmed based of the deviation of the SSPM calculation in the symmetric mass region, where shell effects are not expected to be significant. In order to reproduce the error weighted average anisotropy (1.73 ± 0.18) for the symmetric mass region, the required value for the variance of K-distribution was much lower compared to the value obtained from the SSPM calculations. Presence of insignificant mass dependence of anisotropy suggests quasifission to be the dominant non-compound nucleus fission mechanism for the present system at the sub-barrier energy. This is consistent with the earlier studies [Mein et al., Phys. Rev. C55 (1997) R995; Williams et al. Phys. Rev. C 88 (2013) 034611] attributing anomaly in the overall fission fragment angular distribution to the contribution from quasifission.

Study of angular momentum effect on the fission process by angular anisotropy method in heavy-ion-induced reactions

The study of compound nucleus characteristics through fission fragment properties is a powerful tool to understand the fission mechanism of excited nuclei formed in heavy-ion-induced reactions. In this work, angular anisotropies of fission fragments from fissioning nuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] with normal behaviors in angular anisotropy have been analyzed. In this way, the quadrupole deformation parameter of the compound nucleus is calculated by comparison between the experimental data of angular anisotropy and those predicted by the standard saddle-point statistical model. Then the rotational energy, the fission barrier height, and the effective moment of inertia of the compound nucleus are obtained through the calculated quadrupole deformation parameters. It is observed that the quadrupole deformation parameter decreases with increasing the mean square angular momentum. The obtained results illustrate that the rotational energy and the effective moment of inertia increase almost linearly with increasing the mean square angular momentum, while the fission barrier height decreases as expected. However, the calculated values of fission barrier height overestimate the rotating finite-range model predictions. Also, the calculated values of effective moment of inertia represent a nearly linear trend despite those predicted by the rotating finite-range model. In order to discuss the physical ideas underlying the effect of angular momentum on the fission properties, the interaction potential energy during the capture process is studied for the lightest and heaviest reaction systems.

Mass distribution and mass-resolved angular distribution in the O16+U238 reaction at sub-barrier energy

Background: The angular distribution of fission fragments or products is a sensitive probe to investigate non-compound-nucleus (NCN) fission. However, the gross angular distribution cannot distinguish between different NCN fission processes. Both preequilibrium fission and quasifission contribute to NCN fission and would both result in deviations from the statistical saddle point model (SSPM). Mass-resolved angular distributions of the fission product offers the possibility to distinguish between the two mechanisms [Sodaye et al., Phys. Rev. C 95, 014612 (2017); Tripathi et al., Phys. Rev. C 88, 024603 (2013); Vorkapic and Ivanisevic, Phys. Rev. C 55, 2711 (1997)].Purpose: Mass and mass-resolved angular distributions of fission products have been measured in the $^{16}\mathrm{O}+^{238}\mathrm{U}$ reaction at ${E}_{\mathrm{lab}}=85.3\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ to investigate the dominant NCN fission mechanism at sub-barrier energy.Method: Mass and mass-resolved angular distributions were measured by recoil catcher technique followed by offline \ensuremath{\gamma}-ray spectrometry.Results: The mass distribution was observed to be predominantly asymmetric. The angular anisotropy of the fission products was observed to be independent of their mass.Conclusions: The mass independence of the angular anisotropy suggested quasifission to be the dominant NCN fission process. This was further confirmed from the underestimation of angular anisotropy by theoretical calculations even after including the contribution from preequilibrium fission.

Projectile-breakup-induced fission-fragment angular distributions in the Li6+Th232 reaction

Background: Experimental anisotropy in fission-fragment (FF) angular distribution in reactions involving weakly bound stable projectiles with actinide targets are enhanced compared to statistical saddle-point model (SSPM) predictions. Contributions from breakup- or transfer-induced fission to total fission are cited as possible reasons for such enhancement.Purpose: To identify the breakup- or transfer-induced fission channels in $^{6}\mathrm{Li}$+$^{232}\mathrm{Th}$ reaction and to investigate their effects on FF angular anisotropy.Methods: The FF angular distributions have been measured exclusively at three beam energies (28, 32, and 36 MeV) around the Coulomb barrier in coincidence with projectile breakup fragments like $\ensuremath{\alpha}, d$, and $p$ using Si strip detectors. The angular anisotropy obtained for different exclusive breakup- or transfer-induced fission channels are compared with that for total fission. SSPM and pre-equilibrium fission models have been employed to obtain theoretical FF angular anisotropy.Results: Angular anisotropy of the fission fragments produced by different transfer- or breakup-induced fission reactions have been obtained separately in the rest frame of respective recoiling nuclei. Some of these anisotropies were found to be stronger than those of the inclusive fission. Overall angular distributions of transfer or breakup fission, integrated over all possible recoil angles with weight factor proportional to differential cross section of the complementary breakup fragment emitted in coincidence in all possible directions, were obtained. It was observed that the overall FF angular anisotropy for each of these fission channels is less than or equal to the anisotropy of total fission at all the measured energies. Assuming isotropic out-of-plane correlations between the fission fragments and light-charged particles, the overall breakup- or transfer-induced fission fragment angular distributions do not explain the observed enhancement in FF anisotropy of total fission. Pre-equilibrium fission model provides a reasonable explanation of the enhanced experimental anisotropy of total fission.Conclusions: Angular anisotropies for different breakup or transfer fission channels involving emission of $\ensuremath{\alpha}, d$, and $p$ in the reaction plane have been measured for the $^{6}\mathrm{Li}+^{232}\mathrm{Th}$ reaction. The overall FF angular anisotropies of breakup- or transfer-induced fissions do not explain the enhanced anisotropy of total fission at near-barrier energies. A measurement of out-of-plane correlation is necessary to confirm the above observation and obtain a complete picture on the effect of transfer or breakup on total fission.

Fission fragment angular distributions in pre-actinide nuclei

Background: Complete fusion of two nuclei leading to formation of a heavy compound nucleus (CN) is known to be hindered by various fission-like processes, in which the composite system reseparates after capture of the target and the projectile inside the potential barrier. As a consequence of these non-CN fission (NCNF) processes, fusion probability $({P}_{\mathrm{CN}})$ starts deviating from unity. Despite substantial progress in understanding, the onset and the experimental signatures of NCNF and the degree of its influence on fusion have not yet been unambiguously identified.Purpose: This work aims to investigate the presence of NCNF, if any, in pre-actinide nuclei by systematic study of fission angular anisotropies and fission cross sections $({\ensuremath{\sigma}}_{\mathrm{fis}})$ in a number of nuclear reactions carried out at and above the Coulomb barrier $({V}_{\mathrm{B}})$.Method: Fission fragment angular distributions were measured for six $^{28}\mathrm{Si}\text{-induced}$ reactions involving isotopically enriched targets of $^{169}\mathrm{Tm},\phantom{\rule{0.16em}{0ex}}^{176}\mathrm{Yb},\phantom{\rule{0.16em}{0ex}}^{175}\mathrm{Lu},\phantom{\rule{0.16em}{0ex}}^{180}\mathrm{Hf},\phantom{\rule{0.16em}{0ex}}^{181}\mathrm{Ta}$, and $^{182}\mathrm{W}$ leading to probable formation of CN in the pre-actinide region, at a laboratory energy $({E}_{\mathrm{lab}})$ range of 129--146 MeV. Measurements were performed with large angular coverage $({\ensuremath{\theta}}_{\mathrm{lab}}={41}^{\ensuremath{\circ}}$--${170}^{\ensuremath{\circ}})$ in which fission fragments (FFs) were detected by nine hybrid telescope $(E\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}E)$ detectors. Extracted fission angular anisotropies and ${\ensuremath{\sigma}}_{\mathrm{fis}}$ were compared with statistical model (SM) predictions.Results: Barring two reactions involving targets with large non-zero ground state spin $(\mathcal{J})$, viz., $^{175}\mathrm{Lu}\left({\frac{7}{2}}^{+}\right)$ and $^{181}\mathrm{Ta}\phantom{\rule{4pt}{0ex}}\left({\frac{7}{2}}^{+}\right)$, experimental fission angular anisotropies were found to be higher in comparison with predictions of the statistical saddle point model (SSPM), at ${E}_{\mathrm{c}.\mathrm{m}.}$ near ${V}_{\mathrm{B}}$. Comparison of present results with those from neighboring systems revealed that experimental anisotropies increasingly deviated from SSPM predictions as one moved from pre-actinide to actinide nuclei. For reactions involving targets with large nonzero $\mathcal{J}$, this deviation was subdued. Comparison between measured ${\ensuremath{\sigma}}_{\mathrm{fis}}$ and predictions of SM indicated the presence of NCNF in at least four systems, when shell effects, both in the level density and the fission barrier, were included in the calculation.Conclusions: Systematic SM analysis of measured fission angular anisotropies and ${\ensuremath{\sigma}}_{\mathrm{fis}}$ confirmed the onset of NCNF in pre-actinide nuclei. Discrepancies between results about the degree of its influence on complete fusion, as deduced from various experimental probes, remain challenges to be solved. Complete measurement of all signatures of NCNF for many systems and preferably a dynamical description of the collisions between projectile and target nuclei are warranted for a deeper understanding.

Fission dynamics study inAm243andFm254

Fission fragment mass distributions in the reactions $^{11}\mathrm{B}+\phantom{\rule{0.16em}{0ex}}^{232}\mathrm{Th}$ and $^{11}\mathrm{B}+\phantom{\rule{0.16em}{0ex}}^{243}\mathrm{Am}$ were measured in an energy range around the barrier. No sudden change in the width of the mass distribution as a function of center-of-mass energy was observed at near-barrier energies, indicating no quasifission transition in the near-barrier energies. Interestingly, the previous measurements of fission fragment angular anisotropies for the same systems showed significant departure from the statistical saddle-point model predictions at near-barrier energies, indicating the presence of nonequilibrium fission processes.

Fission fragment angular distribution in heavy-ion-induced fission with anomalous behavior

Fission fragment angular distribution in heavy-ion-induced fission reactions is of particular importance. Transition state theory is provided to determine the angular distribution of fission fragments which includes standard saddle-point statistical and standard scission-point statistical models. The standard saddle-point statistical model was not able to reproduce the experimental fission fragment angular anisotropies for several heavy-ion-induced fission systems. In contrast to the standard saddle-point model, the standard scission-point statistical model was fairly successful in the prediction of angular anisotropy in heavy-ion-induced fission reaction systems with an anomalous behavior in angular anisotropy of fission fragments, but this model is not widely used as the standard saddle-point statistical model. In this research, a generalized model is introduced for the prediction of fission fragments angular anisotropy in the heavy-ion-induced fission reaction systems having an anomalous behavior. For this purpose, we study the $^{14}\mathrm{N},^{16}\mathrm{O},^{19}\mathrm{F}+^{232}\mathrm{Th};^{16}\mathrm{O},^{19}\mathrm{F}+^{238}\mathrm{U};^{24}\mathrm{Mg},^{28}\mathrm{Si},^{32}\mathrm{S}+^{208}\mathrm{Pb};^{32}\mathrm{S}+^{197}\mathrm{Au}$; and $^{16}\mathrm{O}+^{248}\mathrm{Cm}$ reaction systems. Finally, it is shown that the presented model is much more successful than previous models.

Fission fragment angular distributions inLi6,7+U235,238reactions

Fission fragment (FF) angular distributions for ${}^{6,7}\mathrm{Li}+^{235,238}\mathrm{U}$ reactions have been measured at energies near and above the Coulomb barrier. The angle integrated fission cross sections for $^{6}\mathrm{Li}$ induced reactions at sub-barrier energies are found to be higher than $^{7}\mathrm{Li}$ induced reactions possibly due to a larger contribution of breakup or transfer induced fission in cases of the former compared to the latter. The FF anisotropies for $^{6,7}\mathrm{Li}+^{235}\mathrm{U}$ are found to be slightly smaller than $^{6,7}\mathrm{Li}+^{238}\mathrm{U}$, manifesting the effect of target spin. The statistical saddle point model predictions underestimate the measured FF anisotropy for all four systems at measured energies. Anisotropy calculation by entrance channel dependent $K$-state distribution model and determination of $\ensuremath{\langle}{\ensuremath{\ell}}^{2}\ensuremath{\rangle}$ from continuum discretized coupled channels calculations suggest that the above enhancement in experimental anisotropy is due to a combined effect of entrance channel dependent pre-equilibrium fission and projectile breakup induced fission.

Mass-resolved angular distribution of fission products in the20Ne+232Th reaction

Mass-resolved angular distributions of fission product were measured in the ${}^{20}$Ne + ${}^{232}$Th reaction at ${E}_{\mathrm{lab}}$ $=$ 125.6 and 142.5 MeV using the recoil catcher technique followed by offline \ensuremath{\gamma}-ray spectrometry. Angular anisotropy was found to decrease with increasing asymmetry of mass division. Angular anisotropies of the fission products in the symmetric region were significantly higher compared to those calculated using the statistical saddle-point model. Experimental anisotropies could be explained after considering the contribution from pre-equilibrium fission. Use of barrier energies corresponding to different mass asymmetry values in the calculations could reasonably reproduce the mass dependence of angular anisotropies. The role of barrier energies in governing the angular anisotropy indicates that the mass dependence of anisotropy may possibly be a distinguishing feature of pre-equilibrium fission from quasifission, in which the composite system escapes into the exit channel without being captured inside the saddle point.

Pre-saddle neutron multiplicity for fission reactions induced by heavy ions and light particles

Pre-saddle neutron multiplicity has been calculated for several fission reactions induced by heavy ions and light particles. Experimentally, it is impossible to determine the contribution of neutrons being emitted before the saddle point and those emitted between the saddle and the scission points. Determination of the pre-saddle neutron multiplicity in our research is based on the comparison between the experimental anisotropies and those predicted by the standard saddle-point statistical model. Analysis of the results shows that the pre-saddle neutron multiplicity depends on the fission barrier height and stability of the compound nucleus. In heavy-ion-induced fission, the number of pre-saddle neutrons decreases with increasing excitation energy of the compound nucleus. A main cause of this behavior is due to a reduction in the ground-state--to--saddle-point transition time with increasing excitation energy of the compound nucleus. However, in induced fission by light particles, the number of pre-saddle neutrons increases with increasing excitation energy of the compound nucleus.

Fission fragment angular distribution measurements for 16O +194Pt reaction at energies near the Coulomb barrier

Abstract Fission fragment angular distributions have been measured for 16O + 194Pt reaction forming the compound system 210Rn, in the laboratory energy range from 79 to 90 MeV. The measured fission fragment anisotropies as a function of E c . m . / V B are compared with the predictions of standard saddle point statistical model ( sspm ). Anisotropies calculated using the average excitation energy and angular momentum values could not reasonably fit the experimental data. Statistical model calculations were performed using the pace with modified fission barrier and level density parameters. Fission probability, evaporation residue cross section and neutron multiplicity were simultaneously used to fix the statistical parameters. Model calculations incorporating the chance nature of fission decay and scaled values of the rotating finite range model (RFRM) moment of inertia could reasonably fit the fragment angular anisotropies.

Non-compound-nucleus fission events and standard saddle-point statistical model

The large body of experimental data on the fission fragments anisotropies are analyzed in several heavy-ion induced fission reaction systems. The entrance channel mass asymmetry parameters of these systems put on the both sides of the Businaro-Gallone mass asymmetry parameters. The role of the mass numbers of the projectile and the target in the prediction of a normal or an anomalous behavior in angular anisotropy, as well as the validity of standard saddle-point statistical model are considered. The average contribution of non compound nucleus fission for the systems with an anomalous behavior in anisotropy are also determined. PACS numbers: 25.70.Jj *Corresponding author: s.soheyli@basu.ac.ir

Effective moment of inertia for several fission reaction systems induced by nucleons, light particles, and heavy ions

The effective moment of inertia of the compound nucleus is calculated for several fission reaction systems induced by nucleons, light particles, and heavy ions. The determination of this quantity for these systems is based upon the comparison between the experimental data of the fission fragment angular distributions as well as the prediction of the standard saddle-point statistical model. For the systems, the two cases, namely with and without neutron emission corrections, were considered. Afterward, our theoretical results are compared with the data obtained from the rotational liquid drop model as well as the Sierk model and satisfactory agreements were found. We also calculated the quadrupole deformation and mass asymmetry parameters of the fissioning nuclei at the saddle point by two methods, the first method is based on an ellipsoid shape assumption for the fissioning nucleus, and the other is based on dinuclear system model, since in heavy ion induced fission reactions, the compound nuclei which undergo fission can be considered as states of two touching clusters (dinuclear system). Afterward, the results of these two methods were compared and satisfactory agreements were found between them.

Fission fragment angular distributions in theBe9+Th232reaction

Fission fragment angular distributions have been measured for a $^{9}\mathrm{Be}$ $+$ $^{232}\mathrm{Th}$ system at four different beam energies around the Coulomb barrier. The experimental results on fission fragment anisotropies have been compared with predictions of the standard statistical saddle-point model (SSPM) and the preequilibrium fission (PEQ) model including projectile ground-state spin. It is observed that both SSPM and the PEQ model fail to reproduce the experimental results, indicating that projectile breakup may affect the fission fragment anisotropies.

Calculation of spin distribution for several fission reaction systems induced by nucleons and heavy ions

Compound nucleus spin distribution has been calculated for several fission reaction systems induced by nucleons and heavy ions. Determination of the spin distribution for these systems is based upon the comparison between the experimental data of the fission fragment angular distributions as well as the prediction of the standard saddle-point statistical model (SSPSM). For the systems, the two cases, namely with and without neutron emission corrections were considered. This method is used for the first time to determine compound nucleus spin distribution. Afterwards, our theoretical results have been compared with the data obtained from the coupled-channel technique as well as the Wong model, and satisfactory agreements were found. Furthermore, we have introduced a semiclassical approximation relation for the compound nucleus spin distribution of these systems.

Absence of entrance channel effects in fission fragment anisotropies of theFr215compound nucleus

Fission fragment angular distributions have been measured for the reactions {sup 11}B+{sup 204}Pb and {sup 18}O+{sup 197}Au, both leading to the same compound nucleus {sup 215}Fr at near barrier energies. The measured fission fragment anisotropies as a function of E{sub c.m.}/V{sub B} are found to be consistent with the predictions of the standard saddle point statistical model (SSPM) for both the systems, suggesting the absence of entrance channel effects on fission fragment anisotropies even though the entrance channel mass asymmetries for both these systems fall on either side of the Bussinaro-Gallone critical mass asymmetry. The consistency of the present results with SSPM predictions can be understood within the framework of the pre-equilibrium fission model where fission before K equilibration is severely inhibited by the high values of ratios of fission barrier height to nuclear temperature.

Fission fragment anisotropies for theC13+U235system at near-Coulomb barrier energies

The fission fragment angular distribution measurements for the {sup 13}C+{sup 235}U system have been carried out to study the entrance channel dependence and spin dependent effects in the fission fragment anisotropies. This particular combination of target and projectile leads to {sup 248}Cf compound nucleus that has been studied earlier using three other entrance channels viz. {sup 11}B+{sup 237}Np, {sup 12}C+{sup 236}U, and {sup 16}O+{sup 232}Th. A comparison of the measured anisotropy data for all the four systems, with the statistical saddle-point model and pre-equilibrium fission (PEF) model, brings out a clear signature of entrance channel dependence in fission anisotropy values, characteristic of the PEF model.

CALCULATION OF FISSION FRAGMENT ANGULAR ANISOTROPY IN HEAVY-ION INDUCED FISSION

Fission fragment angular anisotropies from 16 O + 232 Th , 12 C + 236 U , 11 B + 237 Np , 14 N + 232 Th , 11 B + 235 U and 12 C + 232 Th systems were calculated by means of the standard saddle point statistical model (SSPSM). The results were obtained with and without neutron emission correction in the reactions, and comparisons were made with the corresponding experimental data. The normal and anomalous behaviors of fission fragment anisotropies are extensively discussed.

MEASUREMENT OF FISSION FRAGMENT ANISOTROPIES FOR PROTON-INDUCED FISSION OF TWO PRE-ACTINIDE NUCLEI AT SEVERAL ENERGIES

The angular distribution of fission fragments has been measured for proton-induced fission of197Au and209Bi nuclei at several energies between 25 and 30 MeV using surface-barrier detectors. The measured anisotropies are found to be in agreement with the predictions of the standard saddle-point statistical model. The measured anisotropies for neither of the nuclei show any anomalous behavior as a function of both energy and entrance channel mass asymmetry. The fission cross sections of197Au and209Bi nuclei were also measured and compared with that of the previous works.

Influence of multichance fission on fragment angular anisotropy in the 232Th( [formula omitted]) and 238U( [formula omitted]) reactions at intermediate energies

Fission fragment angular distributions have been measured for the 232Th( n , f ) and 238U( n , f ) reactions in the neutron energy range 20–100 MeV. The fragment angular anisotropy for 232Th was found to be systematically larger than that for 238U. The obtained results have been analyzed in the framework of the statistical saddle-point model combined with pre-equilibrium and Hauser–Feshbach calculations of partial fission cross sections. The calculations have revealed that fission following multiple neutron emission takes place in both reactions, resulting in a considerable contribution of high chances to the total fission fragment angular anisotropy. This gives grounds to expect that the observed difference is mainly due to nuclei fissioning at the end of the neutron evaporation chain.